Visionary Calculations Inventing the Mathematical Economy in Nineteenth-Century America By Rachel Knecht B.A., Tufts University, 2011 M.A., Brown University, 2014 Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of History at Brown University. Providence, Rhode Island May 2018 © Copyright 2018 by Rachel Knecht This dissertation of Rachel Knecht is accepted in its present form by the Department of History as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date __________________ ______________________________________ Seth Rockman, Advisor Recommended to the Graduate Council Date __________________ ______________________________________ Joan Richards, Reader Date __________________ ______________________________________ Lukas Rieppel, Reader Approved by the Graduate Council Date __________________ ______________________________________ Andrew Campbell, Dean of the Graduate School iii Vitae Rachel Knecht received her B.A. in History from Tufts University, magna cum laude, in 2011 and her M.A. in History from Brown University in 2014. Her research has been supported by the Program in Early American Economy and Society at the Library Company of Philadelphia, the American Philosophical Society, the American Antiquarian Society, and the member institutions of the New England Regional Consortium, as well as the Department of History and Graduate School at Brown University. In 2017, she received a Deans’ Faculty Fellowship from Brown and joined the History Department as a Visiting Professor in 2018. iv Acknowledgements This dissertation is the product of many years of help, support, criticism, and inspiration. I am deeply indebted not only to the following people, but also to many others who have encouraged me to see this project to its completion. Thank you all, for everything. My dissertation committee members have been uniformly helpful and supportive along the way, even though I managed to drag each into a project beyond his or her immediate familiarity. I am particularly grateful to Seth Rockman, for taking a chance on me and on this project, despite neither of us knowing much at all about the history of mathematics at the start, and for six years of guidance in what it means to be a historian. An enormous thank-you as well to Joan Richards, for those hours spent patiently recovering my high school mathematics education and then teaching me to turn that into historical thinking, and for many good conversations along the way. Finally, a heartfelt thank-you as well to Lukas Rieppel, for letting me turn him into my personal STS tutor, and for somehow always being able to ask the right question at the right time. The History Department at Brown University is one of the best communities I have ever had the privilege to join. Thank you to Michael Vorenberg and Kerry Smith, for their comments on the earliest stages of this project; Robert Self, for everything from teaching me all of modern American history to fixing the radiator in my office; Lin Fisher, for organizing the Early American Studies workshop; Tara Nummedal and Rebecca Nedostup, for giving so much time to improving the graduate program; and to Mary Beth Bryson, Julissa Bautista, and Cherrie Guerzon, without whom I would have been lost to financial ruin or starvation long ago. In addition, I want to thank Dan Hirschman, for helping me think through the final chapter; Tamara Plakins Thornton, for her generous comments on various aspects of this project; Sharon Murphy, for seemingly always being v ready to advise and chat; and to all my conference co-panelists, commenters, and questioners along the way. I also owe an immense debt to Benjamin Carp, especially for not talking me out of this. I also want to thank Richard Kollen of Lexington High School, for introducing me to doing original historical research, and to the joy of rifling through forgotten boxes. This project would not have been feasible without the generous financial support of various institutions. At Brown, the Peter Green Doctoral Scholarship allowed me to research widely at the beginning of the project, and the Deans’ Faculty Fellowship got me to the finish line. I also thank the Program in Early American Economy and Society at the Library Company of Philadelphia, the American Philosophical Society, the American Antiquarian Society, and the members of the New England Regional Fellowship Consortium, particularly the Boston Public Library, Baker Library, the Schlesinger Library, the Rhode Island Historical Society, and Rauner Library, for helping me access their incredible collections. It would be impossible to name every person who made these archival visits as productive and encouraging as they were, but I would particularly like to thank Kathrine Fox at Baker Library and Nan Wolverton at American Antiquarian. I am also grateful for travel grants from the Hagley Library and the McNeil Center for Early American Studies, and to my fellow researchers, especially those in residence at LCP and AAS. I have learned the most from my fellow graduate students, and it would be impossible to capture in a few words every conversation, debate, comment, dinner, and drink that got me here. I especially want to thank Alicia Maggard, Daniel Platt, Lindsay Schakenbach, Jonathan Lande, Frances Tanzer, and Ann Daly, who have been invaluable as scholars and as friends. A huge thank you also to the rest of my cohort, all of whom helped me think through this project in its earliest days: Anne Gray-Fischer, Amy Kerner, Judith Smith, Andre Pagliarini, Abhilash Medhi, and Ayse vi Topaloglu. Thank you as well to the members of the Market Societies Mellon Workshop, Brooke Lamperd, Sam Franklin, Paul Guitierrez, Zach Dorner, and Kathrinne Duffy, for creating such an unreasonably intelligent group of scholars. Lastly, my thanks to the members of the Brown Early American Graduate Student Workshop and the Brown Dissertation Writing Group, for providing feedback, emotional support, and for simply getting me to produce pages. As much help as my fellow graduate students have been, I never would have made it this far without also having the friendship and support of civilians. Therefore, thank you to my running (and theater, and wine) buddy Robin Wetherill; the incredible ladies of the Fun Girls Book Club, Grace Cleary and Kate Bayer; my beloved “cousins” Lily Fesler, Sarah Baughman, and Katherine Mechling; and my real reason for making regular trips to Philadelphia, Emily Spooner. It would be impossible to properly thank you all for everything you’ve done for me over the last five, ten, or twenty-nine years, but this will have to be enough for now. My biggest thanks go to my family, for so many years of their unwavering love and support. Thank you to my sister Abby, for explaining science to me, joining me on therapeutic outlet mall trips, and sending Parks & Rec gifs at just the right time; to my dad, Bob, for explaining economics to me, lifting my spirits when they fell, and helping move my stuff even though I definitely misled him about the number of stairs; and to my mom, Sheera, for everything, but especially for driving down to Providence to ride the East Bay Bike Path and talk about math. Lastly, I want to thank Henk Isom, for being there for me since the beginning of this project. You are the best person I know, and I could not have done this without you. Providence, RI December 2017 vii Table of Contents Vitae ............................................................................................................................................... iv Acknowledgements ......................................................................................................................... v Table of Contents ......................................................................................................................... viii Table of Figures ............................................................................................................................. ix Introduction ..................................................................................................................................... 1 Chapter 1: The Useful Knowledge Economy ............................................................................... 28 Chapter 2: Commercial Arithmetic ............................................................................................... 76 Chapter 3: Men of Science .......................................................................................................... 124 Chapter 4: Corporate Calculators................................................................................................ 177 Chapter 5: The Mathematical Economy ..................................................................................... 232 Epilogue ...................................................................................................................................... 282 Bibliography ............................................................................................................................... 290 viii Table of Figures Figure 1. Example of Rule of Three from Benjamin Workman, The American Accountant or, Schoolmasters’ New Assistant (Philadelphia: William Young, 1793) ................................. 92 Figure 2. Image from Charles Ellet, Jr., An Essay on the Laws of Trade, in Reference to the Works of Internal Improvement in the United States (New York: Augustus M. Kelley, 1966) ............................................................................................................................................. 169 Figure 3. Potential losses from worker strike, from J. B. Clark, “A Theory of Collective Bargaining” American Economic Association Quarterly, 3rd Series, Vol. 10, No. 1, (Apr., 1909), pp. 24-39. ................................................................................................................. 250 Figure 4. Image from “Recipe for Disaster” Wired Magazine (2009) ........................................ 282 ix Introduction In June 1805, Nathaniel Bowditch sighed to a friend that “any writing except mercantile business or mathematical subjects is a task to me.”1 At the time, Bowditch had recently joined the Essex Fire and Marine Insurance Company in Salem, Massachusetts. He had no previous insurance experience, but he had authored The American Practical Navigator, a book of updated calculations used by American sailors. This text had already made him a regional household name as a talented amateur mathematician, and the firm had hired Bowditch to make calculations for their policies on its basis. Between the Practical Navigator and his later translation of Simon LaPlace’s Celestial Mechanics, Bowditch would eventually become nationally recognized as the “father of American mathematics.” But his real pride was in combining his twin passion for “mercantile business” and mathematics to create a busy and comfortable life for himself and his family.2 The overlap of commerce and mathematics is a given in the modern world, but it was not an obvious combination for Bowditch’s peers. In the intervening centuries, most Americans have become accustomed to the idea of a mathematical economy. Today, we understand “the economy” to be a distinct sphere of experience that can be measured, modeled, and predicted by professional experts. It is mathematical in various senses—in the importance of certain quantitative models to various industries, in the statistics that government agencies develop and disseminate, and, perhaps 1 Nathaniel Bowditch to Caroline Plummer, Jun 30, 1805. Bowditch Family Papers, 1726-1942: Series I, Box 1, Folder 1. Phillips Library, Peabody Essex Museum (Salem, MA). 2 On Bowditch, see Tamara Plakins Thornton, Nathaniel Bowditch and the Power of Numbers: How a Nineteenth- Century Man of Business, Science, and the Sea Changed American Life (Chapel Hill: University of North Carolina Press, 2016). 1 most centrally, in the assumption that every person is a “rational” actor whose economic life can be modeled because he (the explicitly gendered “economic man”) is making constant calculations. Finding the links between this world and Nathaniel Bowditch’s has been the goal of a wide variety of scholarship; historians, sociologists, science studies scholars, and even some economists have sought the processes by which “the economy” came into being, and primarily focus on the crucial decades around the 1930s and 1940s.3 This dissertation aims to disrupt this conversation by turning our attention to the longer history of mathematical commerce. Rather than ask what mathematics did to modern economics, it asks why anyone, at the outset of the twentieth century, would have considered mathematics useful for understanding economic life at all. When one studies the history of mathematics in the nineteenth-century United States—the debates over what it was, how it could be made useful, how it should be taught, and who should do it—one quickly realizes that the economy did not follow a clear linear trajectory to its modern mathematical form. The proliferation of numbers did not magically make the world mathematical, when “mathematical” has long been an unstable category. Instead, one sees that in a range of areas, Americans argued over what mathematics could do for their political project. They made choices about what mathematics were best for participating in and understanding economic life—concrete arithmetic, spatial geometry, abstract analytics, and eventually, dynamic, time-oriented calculus. 3 The most cited text on this matter is Timothy Mitchell, “Fixing the Economy,” Cultural Studies, 12, 1 (1998): 82– 101. See also Daniel Breslau, “Economics Invents the Economy: Mathematics, Statistics, and Models in the Work of Irving Fisher and Wesley Mitchell” Theory and Society, Vol. 32, No. 3 (Jun., 2003): 379-411; Donald MacKenzie, Fabian Muniesa & Lucia Siu (eds.), Do Economists Make Markets? On the Performativity of Economics (Princeton: Princeton University Press, 2008); Mary S. Morgan, The History of Econometric Ideas (Cambridge: Cambridge University Press, 1990); Quinn Slobodian, “How to See the World Economy: Statistics, Maps, and Schumpeter's Camera in the First Age of Globalization” Journal of Global History, Vol. 10 (2015): 307-332; Yuval P. Yonay, The Struggle Over the Soul of Economics: Institutionalist and Neoclassical Economists in America Between the Wars (Princeton: Princeton University Press 1998). 2 In those contests, one finds a tension between democratic accountability and expert mystification, both based in claims to mathematical reasoning. “Mathematics” did not tip the scales to the latter; the people who won these conflicts, with their claims to a particular economic expertise, mystified both economic life and mathematics itself. Above all, one perceives clearly that the invention of the mathematical economy was a process, not an event. Only after a hundred years of contestation over mathematical knowledge would a universally rational economic man appear so self-evident, so inevitable, so that some could assume he had been there all along.4 Nineteenth century Americans built the preconditions needed for a mathematical economy to emerge in the early twentieth century. At the outset of the 1800s, they did not agree on what to include in their mathematical education, or even what mathematics was, in a rigid epistemic sense. To understand how the conditions of possibility for mathematical economy came to be—or, more correctly, were made—we have to understand mathematics as a historically contingent collection of knowledge. Mathematics is more than the arrangement of numbers. Its different fields represent fundamentally different ways of thinking. When Americans debated what kinds of mathematics should be used in business and commerce, and how, and by who, they were also debating how to understand, and participate in, economic life. Thus, the invention of the mathematical economy required more than quantification. It universalized a historically specific form of mathematical- commercial expertise, one formed by contests over political ideology, economic culture, business practices, and social difference—particularly gender. Indeed, the nineteenth century lines around 4 This is not to say that mathematics is the only way of understanding the tension between democratic accountability and expert mystification, nor that the United States is the only country whose history demands its explanation. See Ben Kafka, The Demon of Writing: Powers and Failures of Paperwork (New York: Zone Books, 2012). 3 what mathematics should be used in economic life were drawn primarily through ideas about what productive masculinity should look like in American society. Proud proclamations at the outset of the century touted every American man’s ability to learn mathematics, and thereby achieve economic self-ownership. Initial efforts to build a national mathematical tradition on the classical geometry of Old Europe conflicted with a political culture that valued practical utility over perfect reasoning. Mathematical fields that had once been central to a college education were criticized as ornamental, aristocratic, and effete. Antebellum political economic culture instead valued those mathematics understood to be needed in productive, manly work. Cultural and educational institutions and texts elevated the idea that in the United States, “mathematics” meant combining of theory and practicality, reason with rules. Americans wanted their mathematics to be useful, to harness its twin abilities to sharpen the mind and invent practical improvements, in service of national prosperity. Antebellum Americans thus defined mathematics by its ability to bring economic order and agency to a new political economy. Educational practices and ideological claims led Americans to understand “mathematics” as practical, manly reasoning, a shibboleth of self-ownership in a society ostensibly without hierarchy. The appeal of this understanding of mathematics in antebellum America, however, lay in its apparent ability to bridge the intuitive reasoning of an independent person with objective rules of commercial engagement, ones that “market society” seemed to otherwise lack. These competing visions of mathematical reasoning left a key question unanswered: who decided what mathematics to use in economic life? In response, new experts emerged, a “numerate elite” of mathematically educated men who consolidated a particular vision of economic expertise. These men claimed both the masculine productivity of trigonometry and arithmetic, and the independent reasoning of more 4 abstract fields. Numerate elites professed to hold states and corporations accountable to objective rules, then used their own expert reasoning to create new economic realities. Engineers, actuaries, accountants, and academic economists thus shifted Americans’ perceptions of mathematics. As numerate elites became increasingly skeptical of the public’s ability to understand their reasoning, they abandoned the idea that the public could comprehend the economic knowledge they produced, and began to privatize their methods, models, and knowledge. By the end of the nineteenth century, many Americans saw mathematics as difficult, abstract, and mysterious. Ultimately, these contests over when and how mathematics should be used in commercial settings helped define both the extent of, and the limitations to, participation in economic life in nineteenth century America. The incorporation of specific mathematical business practices created new economic systems and established the necessity of mathematical expertise in managing these systems. It was thus the contests and changes of the nineteenth century that created the conditions for the modern mathematical economy. At the end of the nineteenth century, an emergent group of social scientists universalized these nineteenth century contests over mathematical expertise and commercial power into a common economic man. After a century of growing interdependence between mathematics and business, these “economists” insisted that individuals were constantly calculating, meaning their behavior could be modeled. By erasing the debates over what types of mathematics were appropriate, the ways that specific mathematics had created material economic realities, and the longstanding conviction that economic mathematics were inherently masculine, economists alienated the mathematical economy from its historical foundations. “Visionary Calculations” argues that nineteenth century contests over the use and meaning of mathematics made our modern economy possible. Mathematical reasoning became integral to 5 claiming authority in nineteenth century commerce, and as a result, economic knowledge became tied to mathematics—its definition, its utility, and its cultural meaning. This dissertation aims to explain, through contests over the proper role of mathematics in economic life, how Americans became attracted to a mathematical economy, how commercial mathematics became increasingly specialized, and how people pushed back on this mystification. Long before academic economists adopted calculus, the ability to claim mathematical expertise had become essential in debates over what constituted a legitimate economic actor. It determined how economic knowledge was—or should be—made, and who could be trusted to make it. Rather than see the mathematical economy as originating in twentieth century economics departments, therefore, this project illustrates that it was instead made by possible by a hundred years of changes in business practices, mathematical pedagogies, social relations, and economic ideas. It was in those spaces, over the long nineteenth century, that Americans invented their mathematical economy. *** In 1837, South Carolina Democrat Hugh Legaré declared to Congress that he had “no faith in speculative politics.” A “theorist in government,” he warned his colleagues, was “as dangerous as theorist in medicine, or in agriculture.” Legaré insisted that anything “too complicated and too obscure for simple and decisive experiments” could not be theorized with mathematical principles, which to his mind included anything within the realm of political economy.5 In his skepticism toward the “speculative” aspects of mathematics, Legaré echoed other commentators of his time. 5 “Twenty-fifth Congress—1st Sess. Speech of Mr. H.S. Legaré, of S. Carolina” Richmond Enquirer, November 10, 1837, p. 1. The idea that experimental science was more democratic than deductive science can also be found in natural history during this period, as was the idea that it was more respectful of God’s omniscience. Andrew Lewis, Democracy of Facts: Natural History in the Early Republic (Philadelphia: University of Pennsylvania Press, 2011). 6 In antebellum popular discourse, commentators warned that mathematics was too “speculative” or “visionary,” by which they meant it was too abstract for real world applications. The title of this dissertation references this early criticism and indicates that much of the mathematics discussed herein would have likely seemed too visionary to Legaré. But it also gestures to the fact that these theorists would ultimately become the primary keepers of political economic knowledge. In that sense, though Legaré might have rejected it, we might consider them visionaries. The founding of the United States in the late eighteenth century attempted, among other things, to weave disparate ideals into a modern state: a classless society, an educated populace, a modern economy, a scientific government, and an illustrious future. Most of the initial leadership did not deal explicitly with the question of mathematics, only with “science” more broadly. They believed that scientific reason, in every aspect of government and society, would guide America to eternal freedom.6 As the decades passed, mathematical knowledge gained increasing importance in American life. In education, politics, and commerce, numbers and calculation became essential knowledge for Americans, though exactly how they should be taught and used remained a subject of fierce debate. But over time, one thing became clear: time and again, mathematics proved to be a uniquely potent tool to settle political economic nerves and disputes. Its ability to make absolute claims to objectivity, combined with its perceived democratic potential, made mathematics a more and more frequent source of economic authority. The mystification of modern economics was not an inevitable result of its use of mathematics. Rather, over the course of the nineteenth century, 6 The classic text on this subject is Brooke Hindle, The Pursuit of Science in Revolutionary America, 1735-1789 (Chapel Hill: University of North Carolina Press, 1956). On ideas about the relationship of science to democracy in the early American republic, see Andrew Lewis, Democracy of Facts (2011) and John C. Greene, American Science in the Age of Jefferson (Ames, IA: Iowa State University Press, 1984). 7 mathematics and economics were simultaneously made mysterious, by emerging experts whose claims to economic authority rested in their specialized mathematical skill. In the contests over how to number, count, measure, and evaluate the economic life of the country, Americans relied on their mathematical training. For some, this meant the arithmetic they had learned in common schools or at home, which had taught them to expect a market of static numbers, individual transactions, and perfect clarity. But others with different backgrounds had other ideas. Civil engineers, who came to manage the infrastructure projects on which the growing national economy relied, did not think of their projects in purely arithmetic terms. Instead, they relied on mathematical educations that dealt heavily with Euclidean geometry and trigonometry, the basis of surveying and construction. To these experts, the American nation was a Euclidean plane, and they arranged canals and railways to balance its centers of production. After the Civil War, insurance actuaries found themselves managing increasingly complex financial institutions that dealt in mortgages and investments as well as in life policies. Their statistical and probabilistic knowledge made them comfortable with algebraic variables, which they in turn used to invent and manage the complex financial instruments of the postbellum decades. It is these experts that I refer to collectively as “the numerate elite.” These were the groups, later professions, who emerged from the mathematical-commercial stew of the early republic and fashioned themselves into practical and experienced economic experts. Numerate elites often came from some privilege, but did not see themselves as “businessmen.” Indeed, they achieved their authority by explicitly positioning themselves as separate from their capitalist employers. They viewed themselves as disinterested scientists who merely consulted for capital, but were not part 8 of it.7 Many dismissed the investors and businessmen who hired them as too close to their profits to be objective about the work. They insisted that their mathematics served public prosperity, not individual gain. Engineers, actuaries, accountants, and eventually economists used mathematics to engender public trust in otherwise new and unfamiliar professions. Although they did not always coexist in perfect harmony—often disagreeing vehemently both within and between occupational groups—they reinforced the interdependence of mathematics and commerce. The numerate elite encouraged not only trust in numbers, but also trust in the mathematical expert. In most cases, the titles used herein—mechanic, accountant, engineer, actuary—primarily designated one’s occupation, but did not necessarily entail specific credentials. Most of these titles depended on general social acceptance, as professional credentialing did not exist for any of these occupations until the end of the nineteenth century. This fluid state of professional affairs put much of the emphasis on mathematical skill, both perceived and demonstrated. Thus, mathematics could provide an opportunity for advancement for people otherwise excluded from economic authority, if they could prove their mathematical skill; a workman quick with numbers, for example, might be promoted to engineer. But at the same time, the lack of official professional credentialing often simply reinforced extant social privileges, as such people found it much easier to convince others of their worthiness. In reality, most civil engineers were highly educated, especially those tapped to superintend complex and politically sensitive infrastructure projects. Many of them hailed from affluent families, and many had an engineer for a father. All were white men. 7 On “disinterestedness” in early American industrial science, see Paul Lucier, “Commercial Interests and Scientific Disinterestedness: Consulting Geologists in Antebellum America” Isis, Vol. 86, No. 2 (Jun., 1995): 245-267. 9 Furthermore, their economic authority did not merely give the numerate elite grounds to declare they believed business and commerce operated in a certain way, as professors of political economy did. Rather, because they were practical experts, centrally located in some of the biggest economic changes of their day, they were also able to direct and reshape the material course of economic life, even for those people outside their immediate influence. Long before the emergence of mathematical financial models in the late twentieth century, mathematical ideas and informal models created new economic realities. Members of the nineteenth century numerate elite made concrete decisions about where to put a canal, how to value a company, and with whom to transact business, all based on their mathematical educations. In this sense, these mathematical experts did not just imagine the mathematical economy; they invented it.8 Or, perhaps more accurately, they invented many overlapping mathematical economies: an arithmetic one, a geometrical one, an analytical one, and so on. Each of these stemmed from different mathematical models and created certain ideas, expectations, and realities for those who participated in them. These differing mathematical approaches meant that claimants to economic authority often conflicted—over the price of a canal, the cause of a panic, the solvency of a corporation, or best practices in commercial education. Despite their differences, however, they all contributed to the growing belief that mathematics was the primary field of knowledge that a person claiming economic authority should have. In periods of anxiety or moments of outright panic or crisis, the 8 This phenomenon is an early American iteration of what some historians of economics, particularly those trained in Science and Technology Studies (STS), now refer to as “performativity”: that while there is nothing natural about certain economic forms, the mathematical models used in economic activity can change the material reality of those situations, effectively making the models “true”. Donald MacKenzie, An Engine, Not a Camera: How Financial Models Shape Markets (Cambridge: MIT Press, 2006) and Donald MacKenzie, Fabian Muniesa & Lucia Siu (eds.), Do Economists Make Markets? On the Performativity of Economics (Princeton: Princeton University Press, 2008). 10 apparent steadying hand of mathematics was increasingly called upon to settle economic problems, from the individual to the national. But the consensus that mathematics should rule economic life was fragile. The more complex the mathematics behind economic life became, the more protective the numerate elite became of their own position, and the more critical some outsiders became of their secretive methods. The central paradox of the mathematical economy—between its initial democratic ideals and its disappointingly specialized reality—became more and more strained as the century progressed. And it was in the context of this crisis of faith in the mathematical economy that a new cadre of university economists emerged at the end of the century. Throughout nineteenth century American history, mathematics repeatedly emerged as a tool to settle anxiety or controversy, turning mathematical acumen, over time, into a proxy for economic authority. The mathematical economy was never an inevitable tool of obfuscation and mystification; on the contrary, it has most often been a participatory ideal—even, to a lesser degree, a reality. But the privatization of certain aspects, including data, methods, and expertise, undercut that ideal. It convinced mathematical experts that they alone possessed the knowledge and skills to safely manage the increasingly complex commercial systems. Over time, these numerate elites began to cope with the disconnect between their supposed accountability and their expert realities through a growing comfort with the notion that “the public” could not perform, and thus could not understand, the kind of mathematics they were doing. Indeed, the growing import of mathematics to economic life in the United States tracks quite closely with how difficult the subject was seen to be, in its most general sense, and how exclusive its practitioners would be. In particular, gender was a crucial and consistently bright line between what mathematical knowledge conferred authority and what was considered useless or rote. At the beginning of the 11 century, fields like arithmetic and plane geometry seemed eminently useful to the productive working man, while more abstract types of mathematics were deemed luxuries—ornamental, elite, even effeminate. As these more advanced mathematics gained greater utility in business, however, the boundaries of “useful” mathematics shifted away from hands-on trigonometry to more abstract analytics. As economic life grew in reach and complexity, formerly ornamental mathematical knowledge became useful. Masculinity came to lie not in the calculative self-ownership of engine- repair and bookkeeping, but in the mathematical expertise of the canal superintendent or the head actuary. In turn, the mathematics that was considered suitable or feasible for women to learn also shifted. By the end of the nineteenth century, many corporate offices comprised a male accountant with a female bookkeeping staff. Close attention to the history of mathematics reveals that keeping economic authority an exclusively male space over long periods required the frequent re-drawing of lines around gender, utility, and authority in mathematical knowledge. The way that Americans’ definitions of mathematics and understanding of its utility shifted and warped around changing gender norms is one key example of the way mathematics was made mysterious. Recent historians have pushed back on the old argument that American capitalism was born fundamentally democratic.9 They argue that mathematics mystified commercial life, turning “the economy” into something to be managed only by experts. Engineers who invalidated workers’ technical knowledge, actuaries who objectified racial inequality in their life tables, government 9 On the democratic origins of American capitalism, see Gordon Wood, “The Enemy Is Us: Democratic Capitalism in the Early Republic” Journal of the Early Republic, Vol. 16, No. 2, Special Issue on Capitalism in the Early Republic (Summer, 1996): 293-308. On numbers as democratic, see Patricia Cline Cohen, A Calculating People: The Spread of Numeracy in Early America (Chicago: University of Chicago Press, 1982); M. A. Ken Clements and Nerida F. Ellerton, Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics (New York: Springer, 2015); and Caitlin Rosenthal, “Numbers for the Innumerate: Everyday Arithmetic and Atlantic Capitalism” Technology and Culture, Vol. 58, No. 2 (April 2017): 529-544. 12 statisticians who institutionalized elite conceptions of property, and the professionalization of economic authority, including academic economics itself, have all been called upon to show how mathematical knowledge made economic life less democratic.10 These narratives are all crucial in understanding how economic authority was made. However, they tend to suggest that mathematics is fundamentally undemocratic. Just as historians of ready reckoners and decimal currency once implied the naturally democratic bent of arithmetic, so too do critics of the mathematical economy assume the inherent difficulty of advanced algebra, probability, and differential calculus, and thus place the onus of mystification mathematics’ innate qualities and powers. Yet if we turn our attention to the history of mathematics, rather than those of business or the economy, we find that no such linear inevitability exists. If we put aside the unsubstantiated belief that early America has no history of mathematics, we find that the growing acceptance and relevance of mathematical knowledge in managing an economy of numbers can help us understand how Americans located economic authority in a self-conscious, and self-delusional, democracy.11 10 Works that are explicit about this mathematical technocracy include: David F. Noble, America By Design: Science, Technology, and the Rise of Corporate Capitalism (New York: Knopf, 1977); Michael Zakim, “Inventing Industrial Statistics” Theoretical Inquiries in Law Vol. 11, No. 1 (Jan. 2010): 283-318; Dan Bouk, How Our Days Became Numbered: Risk and the Rise of the Statistical Individual (Chicago: University of Chicago Press, 2015). Others gesture to the mystification of economic life in the nineteenth century, though don’t dwell on mathematics specifically: see Jessica M. Lepler, The Many Panics of 1837: People, Politics, and the Creation of a Transatlantic Financial Crisis (Cambridge: Cambridge University Press, 2013); Jonathan Levy, Freaks of Fortune: The Emerging World of Capitalism and Risk in America (Chicago: University of Chicago Press, 2012); William G. Roy, Socializing Capital: The Rise of the Large Industrial Corporation in America (Princeton: Princeton University Press, 1997); and Jeffrey Sklansky, The Soul’s Economy: Market Society and Selfhood in American Thought, 1820- 1920 (Chapel Hill: University of NC Press, 2002). 11 The idea that there was no mathematics going on in the United States is more a result of scholarly omission than actual argument. For example, the American Mathematical Society (AMS) published its History of American Mathematics in 1988, on the centennial of the Society’s founding. It opens with a 1904 address by AMS founder Thomas Fiske, who argues that prior to the 1880s no research in “pure mathematics” existed in the United States, and gives only the briefest mention to Nathaniel Bowditch and Benjamin Peirce. Similarly, Karen Parshall and David Rowe’s The Emergence of the American Mathematical Research Community, 1876-1900 (Providence: American Mathematical Society, 1994) largely omits the antebellum era. International overviews of the history of mathematics also tend to omit the United States prior to the twentieth century. See: Carl C. Boyer and Uta C. 13 This dissertation contends that only by taking seriously the history of mathematical concepts and practices, not merely as proxies for a social privilege, but as scientific knowledge with contingent histories, can we fully understand how the economy became alienated from most of its ordinary participants. “Mathematics” did eventually deliver a hegemonic conception of economic life that placed its authority beyond the general populace. However, that definition of mathematics is not an ahistorical fact, but the result of a process defined by social relations and cultural changes. The numerate elite made mathematics mystified, not the other way around. In narrating the invention of the mathematical economy, then, my dissertation recounts the conflicts and instabilities in the democratic nature of numbers and calculation. On one hand, I take seriously the contention, frequently made by historian Theodore Porter, that modern quantification has largely been a “weapon of the weak.” In general, Porter has argued, individuals or groups who already possess political or economic power do not need quantification. On the contrary, applying fixed rules of calculation to their efforts often makes achieving their goals more difficult. Numbers became such an important part of governments, economies, and scientific institutions, according to Porter, because the public, in some form, demanded them to hold elites accountable.12 I argue that this basic impulse of democratic accountability is present in the invention of the mathematical economy, as people used mathematics to settle disputes over economic authority. Mathematical reasoning, particularly in its antebellum American definition of practical calculation, seemed to provide a kind of mechanical objectivity for commercial transactions. Merzbach, A History of Mathematics (New York: Wiley, 1989) and Morris Kline, Mathematical Thought from Ancient to Modern Times (Oxford: Oxford University Press, 1990). 12 Porter, Trust in Numbers (1996); see also Porter, “Objectivity and Authority: How French Engineers Reduced Public Utility to Numbers” Poetics Today, Vol. 12, No. 2, Disciplinarity (Summer, 1991): 245-265. 14 However, at the same time, I also illustrate that expertise in mathematics became its own form of claiming economic knowledge. As a result, specialized mathematical knowledge began to masquerade as numerical accountability while simultaneously concentrating economic authority in a diminishing number of hands. The line between trust in numbers and trust in calculation was never bright. Indeed, many Americans in the nineteenth century often viewed them as essentially the same. The reason numbers are more trustworthy, in Porter’s explanation, is their replicability, which in turn depends on calculative knowledge. But trust in calculation slid—sometimes easily, sometimes only in moments of crisis—into trust in calculators. Numerate elites therefore came to hold an anti-democratic power built out of a democratic impulse. Still, they were not a homogenous power, and tracking when and how their various iterations emerged can tell a social history of how the mathematical economy became its obscure modern reality. At the core of this paradox, in which calculation is expected to lead to a democratic market society, but mathematical knowledge removes the economy from the hands of ordinary people, is the role of mathematics in conceptualizing, participating in, and learning about economic life. The more numbers came to define certain aspects of people’s economic relationships, the more crucial mathematical knowledge and the ability to calculate—real or perceived—became. This fact alone did not necessitate that the mathematical economy would become either participatory or mystified, or that it would involve a specific field of mathematics, or that it would expand inexorably into everyday life. Rather, the historical processes by which Americans learned to think economically, to reason, calculate, and trade, defined the realities of mathematical economic life. For many years, the quasi-democratic idea that every man could learn to calculate, as an independent and competent economic actor, existed alongside the notion that business required management by a trustworthy 15 group with specialized calculative skill. The modern mathematical economy resulted not from the inherent nature of “mathematics,” but social decisions about how to define it. *** The emerging historiography on American capitalism, in the recent words of Gautham Rao, compels historians “to confront their longstanding ambivalent relationship with mathematics” on the grounds that understanding capitalism requires studying its methods.13 Efforts to conceptualize capitalist methods are well under way, and the impulse to extend them to mathematics is valuable. But in pursuing it, we should be careful not to treat “mathematics” as a necessarily capitalist form of economic knowledge. To do so would be to legitimize the deeply ahistorical claim that the first neoclassical economists made: that there can exist only one relationship between calculation and economic rationality, that of a utility-maximizing, game-theorizing, economic-law-abiding homo economicus. Mathematics may today have a uniquely close relationship with capitalism, but this seems even more reason to take seriously the complexity of its history. In particular, it is essential that historians not conflate the project of social quantification with economic mathematization, although those stories often intersect. The proliferation of numbers alone did not build an economic epistemology based in mathematical expertise and universal models. We know that people in the nineteenth-century experienced a rapid expansion in political and economic numeration—what Ian Hacking has called “an avalanche of numbers.”14 American 13 Gautham Rao, “Review: Tamara Plakins Thornton, Nathaniel Bowditch and the Power of Numbers: How a Nineteenth-Century Man of Business, Science, and the Sea Changed American Life” The American Historical Review, Vol. 122, No. 3 (June 2017), p. 835. 14 Ian Hacking, “Biopower and the Avalanche of Printed Numbers,” Humanities in Society, 5, nos. 3 and 4 (1982): 279-295. On the central role that quantification played in establishing social and economic modernity, primarily in the European context of the eighteenth and nineteenth centuries, see: Max Weber, The Protestant Ethic and the Spirit of Capitalism, trans. Talcott Parsons (New York: Scriberns, 1958); Tore Frängsmyr, J.L Heilbron, and Robin 16 historians have produced ground-breaking work on the processes that turned social relationships into supposedly objective numbers. They have shown how new accounting practices shaped the economic lives of northern laborers and southern slaves; the way that life insurance agents valued and commodified human life; the well-learned lessons in capitalist self-discipline of bookkeeping textbooks; governments’ use of statistics to conceptualize and invent new categories of race, labor, and wealth; and the process by which that each of these aspects of quantification encouraged the naturalization of a rational economic actor. These histories, often linked under the “history of capitalism,” have demonstrated that a history of and about numbers does not have to flatten our historical narrative, but instead reveal how numbers are produced, disseminated, and made socially real. This relatively new approach to telling the history of economic ideas and practices attempts to privilege neither names nor numbers, but understand them as twin processes.15 E. Rider, eds., The Quantifying Spirit in the 18th Century (Berkeley: University of California Press, 1990); M. Norton Wise (ed.), The Values of Precision (Princeton: Princeton University Press, 1997); Theodore M. Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton: Princeton University Press, 1996); and Nelson Espeland and Mitchell L. Stevens, “A Sociology of Quantification,” European Journal of Sociology 49, no. 3 (2008): 401-436. On the role of quantification in establishing modern capitalism, particularly in Britain, see: Margaret Schabas, A World Ruled by Number: William Stanley Jevons and the Rise of Mathematical Economics (Princeton, 1990); Porter, Trust in Numbers (1996); William J. Ashworth, “Memory, Efficiency, and Symbolic Analysis: Charles Babbage, John Herschel, and the Industrial Mind” Isis, 87 (1996): 629-53; Simon Schaffer, “Babbage’s Intelligence: Calculating Engines and the Factory System,” Critical Inquiry, Vol. 21, No. 1 (Autumn, 1994): 203-227; E. P. Thompson, “Time, Work-Discipline, and Industrial Capitalism” Past & Present, no. 38 (1967): 56-97. See also: James C. Scott, Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed (New Haven: Yale University Press, 1998). 15 On the role of numbers in the “new” history of capitalism, see: Eli Cook, The Pricing of Progress: Economic Indicators and the Capitalization of American Life (Cambridge: Harvard University Press, 2017); Stephen Mihm, A Nation of Counterfeiters: Capitalists, Con Men, and the Making of the United States (Cambridge: Harvard University Press, 2007); Frankel Oz, States of Inquiry: Social Investigations and Print Culture in Nineteenth Century Britain and the United States (Johns Hopkins University Press, 2006); Jessica M. Lepler, The Many Panics of 1837 (2013); Dan Bouk, How Our Days Became Numbered (2015); Jonathan Levy, Freaks of Fortune (2012); Jamie Pietruska, Looking Forward: Prediction and Uncertainty in Modern America (Chicago: University of Chicago Press, 2017). On numbers in the codependence of capitalism and slavery, see: Caitlin C. Rosenthal, “From Memory to Mastery: Accounting for Control in America, 1750-1880” PhD Dissertation, Harvard University (2012); Stephanie E. Smallwood, Saltwater Slavery: A Middle Passage from Africa to American Diaspora (Cambridge: Harvard University Press, 2008); Daina Ramey Berry, The Price for their Pound of Flesh: The Value of the 17 And yet, at the end of nearly every sentence in these works asserting that nineteenth century Americans were becoming increasingly comfortable with numerical calculation, and applying it to their economic lives, we find the same citation: Patricia Cline Cohen’s first book, A Calculating People. Cohen wanted to know why there seemed to be so many numbers, and so much talk about calculating and computing, in antebellum America, and could find nothing in existing books about the period, whether in histories of society, education, economic life, or elsewhere. To rectify this omission, she formulated an argument about American numeracy in the eighteenth and nineteenth centuries that tied calculation to democratic participation in the market, which in turn led to a wide acceptance among Americans of the inviolability of numbers, culminating in the book’s excellent dissection of the 1840 federal census. A Calculating People stands as the last full treatment of the relationship of nineteenth century mathematical education to economic participation in American history, but nothing about it suggests this was its intent. Indeed, the book raises as many questions as it answers: about mathematics other than arithmetic, women’s education, the use of calculation for economic pursuits other than market capitalism, and more.16 Enslaved from Womb to Grave in the Building of a Nation (New York: Beacon Press, 2017); Walter Johnson, Soul by Soul: Life Inside the Antebellum Slave Market (Cambridge: Harvard University Press, 2001). 16 Patricia Cline Cohen, A Calculating People: The Spread of Numeracy in Early America (Chicago: University of Chicago Press, 1982). Other histories of nineteenth century American mathematics tend to focus on its technical applications, eschewing questions about the larger nature of mathematics in favor of its practical uses. Relevant examples include Silvio A. Bedini, Thinkers and Tinkers: Early American Men of Science (New York: Charles Scribner's Sons, 1975) and Edward W. Stevens, Jr., The Grammar of the Machine: Technical Literacy and Early Industrial Expansion in the United States (New Haven: Yale University Press, 1995). On early American numeracy beyond Cohen, see Rosenthal, “Numbers for the Innumerate” (2017); Clements and Ellerton, Thomas Jefferson and his Decimals 1775–1810 (2015); Christopher J. Phillips, “An Officer and a Scholar: West Point and the Invention of the Blackboard,” History of Education Quarterly 55 (Feb. 2015): 82-108; Robin E. Rider, “Perspicuity and Neatness of Expression: Algebra Textbooks in the Early American Republic” in Apple et. al (eds.), Science in Print: Essays on the History of Science and the Culture of Print (Madison: University of Wisconsin Press, 2012). 18 While A Calculating People focused on “numeracy” and calculative ability alone, however, this dissertation aims to examine mathematics itself. Although some fields of mathematics do rely on numerical calculation, they tend to be the ones that some mathematicians might not consider to be mathematics at all, such as arithmetic and statistics. Indeed, ask any lay person to name some kinds of mathematics, and geometry and algebra are likely to crop up immediately. While neither field is entirely free of numbers, they both require much more than numerical calculation. Classical geometry, for instance, involves no numbers at all, only logical proofs of sameness or difference, while much of algebra can be done entirely in x’s and y’s. Historians of mathematics argue that types of mathematics represent different styles of reasoning, as different as biology and physics— more, even, given how recently modern scientific fields were divided. Thus, when applied to areas of human society, mathematical fields shape how systems are seen and understood. None of this is to say that calculation is not “real mathematics,” of course, merely that it is only a piece of the story. A full history of the invention of the mathematical economy requires analyzing the role of mathematical reasoning writ large, both with and without numbers. This project seeks to separate the vague field of “mathematics” into the concrete realities of how specific types of mathematics were used in economic life, by whom, and in what situations. It seeks to examine the United States’ history of mathematics, to explain how its definition shifted over time, how it changed—and was changed by—economic culture, and how it was taught. Thus, it treats “mathematics” as a historically contingent form of knowledge, one made up of varied ideas and practices that have changed over time and space. What emerges from these moments of intersection is a story of contest, change, and continuity. Using mathematics might mean adding or subtracting arithmetically, creating algebraic formula, using spatial geometrical reasoning, or 19 modeling numerical data. Rather than assume an objective hierarchy of difficulty in these fields, this dissertation aims to untangle their meaning at certain historical moments. It took a long time for anyone to consider a mathematical economy to be normal, and recovering that process requires an explicit engagement with the history of American mathematics. It seems likely that the primary obstacle to this work, and the reason it has not been done already, is mathematics itself. I do not mean that historians somehow “cannot do” mathematics. Many excellent histories of American economic life ably recreate business accounts, stock prices, insurance policies, even obsolete machines, by using calculation to analyze past numerical data. Instead, I suggest that the task of analyzing mathematics itself, as a historical form of knowledge, poses a challenge to historians. Historian of mathematics Amir Alexander has argued that in the early days of the history of science, mathematics formed the rational “skeleton” on which science operated (quoting historian George Sarton in 1937), thus ensuring its central role. But as the history of science began to move toward social and cultural explanations for changes in scientific ideas and practice, the notion of a rational core was abandoned, leaving mathematics a discipline without a history—or at least, without one of the sort that most historians recognize, based in context and contingency.17 As a result of this “ghettoization” of the history of mathematics, only a handful of recent scholars have interrogated mathematics as a historical field of knowledge whose meaning and standards have changed in concert with political and cultural factors.18 17 Amir Alexander, “The Skeleton in the Closet: Should Historians of Science Care about the History of Mathematics?” Isis, Vol. 102, No. 3 (September 2011): 475-480. 18 Such histories include Raviel Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History (Cambridge, UK: Cambridge University Press, 1999); Judith V. Grabiner, The Origins of Cauchy’s Rigorous Calculus (Cambridge: MIT Press, 1981); Amir Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (Palo Alto: Stanford University Press, 2002); Joan Richards, “Augustus de Morgan, the History of Mathematics, and the Foundations of Algebra,” Isis, Vol. 78, No. 1 20 This project does not seek to explain the development or invention of new mathematical knowledge, as a traditional history of mathematics might. It does, however, draw on some of the key insights of the history of mathematics about how to study the subject as a historically situated field of knowledge, not something that exists outside of human society. Of these, the most crucial is the idea that “mathematics” has always served as an umbrella term. Historians of mathematics argue that algebra, geometry, statistics, calculus, and arithmetic warrant different types of analysis, just as biology, chemistry, and physics (not to mention alchemy and phrenology) do. Like these sciences, mathematical fields bring certain epistemological values with them when applied outside their domain. But because it lacks the concrete content of a more inductive science, mathematics is particularly absorbent of whatever realm it finds itself in. A businessman who keeps arithmetic account books sees every transaction as a static and finite transaction. But a civil engineer trained primarily in geometry interprets problems through the lens of size, direction, and space. He seeks a static equilibrium of proportionality. Both are using tools of mathematical reasoning, but their different mathematics lead them to different economic conclusions.19 Disaggregating and historicizing “mathematics” allows us to begin to demystify it. In the United States, we are accustomed to using the term in the singular, creating a kind of homogenizing (Mar., 1987): 6-30 and Joan Richards, “Rigor and Clarity: Foundations of Mathematics in France and England, 1800-1840,” Science in Context, 4 (1991): 297-319. Substantial literature also exists on the history of probability and statistics, and tends to be more attuned to historical contingency than those of geometry and analysis: Lorraine Daston, Classical Probability in the Enlightenment (Princeton: Princeton University Press, 1988); Theodore M. Porter, The Rise of Statistical Thinking, 1820-1900 (Princeton: Princeton University Press, 1986); Ian Hacking, The Emergence of Probability: A Philosophical Study of Early Ideas About Probability, Induction and Statistical Inference (Cambridge, UK: Cambridge University Press, 1975); Gerd Gigerenzer, et al. (eds.), The Empire of Chance: How Probability Changed Science and Everyday Life (Cambridge: Cambridge University Press, 1989). 19 A relevant epistemological analogy is the idea of the “actant” in the history of technology. See Bruno Latour, Pandora's Hope: Essays on the Reality of Science Studies (Cambridge: Harvard University Press, 1999). 21 bubble around the subject. But the history of mathematics demonstrates that, especially before the twentieth century, different forms of mathematics possessed distinct identities, and thus, distinct cultural valences. Using different fields of mathematics in economic applications therefore did not merely advance the mathematization of economic life; it shaped the specific economic knowledge that was produced in these settings. The invention of the mathematical economy therefore cannot be told only as a story about the inexorable expansion of numbers. Quantification, the problem of what should be assigned a number, how, and by whom, is only the first step. We must also consider mathematics as a historically contingent and constitutive part of this story. Historicizing mathematics also allows us to see a national mathematical tradition in the United States. In Europe, the term “mathematics” had encompassed both applied (or “mixed”) and pure mathematics. The former included the numerical computations that merchants and mariners needed to conduct their daily business, and was primarily the province of the working and middle classes. The latter comprised Euclidean geometry and the knowledge that followed. Passed down from the Greeks, these mathematics seemed to many the highest form of knowledge: a method for absolute reasoning that could never yield an incorrect conclusion, a perfect exercise of the human mind.20 The United States’ early national mathematicians and intellectuals attempted to collapse this distinction between theory and practice as part of their political experiment. They sought to combine Enlightenment rationalism with a free society for white men, and quickly adopted market 20 On the tension between the two, see: Thomas Kuhn, “Mathematical vs. Experimental Traditions in the Development of Physical Science.” Journal of Interdisciplinary History, 7:1 (1976): 1-3; Lorraine Daston, “Enlightenment Calculations” Critical Inquiry, Vol. 21, No. 1 (Autumn, 1994): 182-202; Mordechai Feingold, “Mathematicians and Naturalists: Newton in the Royal Society” in Isaac Newton’s Natural Philosophy (Cambridge: MIT Press, 2004); and Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life (Princeton: Princeton University Press, 1985). 22 relations as providing the social coherence lost in the transition. But the tension between deductive reasoning and mechanical rule-following in mathematics remained, eventually embedding itself in the fabric of the mathematical economy, where it constantly reappears. Perhaps most essentially, disaggregating the constitutive parts of mathematics and studying its historical form provides a view into the “black box of rationality.”21 Economic rationality has long been loosely tied to of calculation, but in such a way that presumes that there is only one way of making economic calculations.22 Once we see mathematics not as a homogenous, unchanging standard, but as a heterogeneous knowledge grouping, we can explore the interactions between types of mathematical reasoning and the economic ideas and applications in which they were used. The individuals who first began to apply mathematics to economic life had a realm of options to choose from, each with its own cultural and intellectual variances. Once we see these many ways of calculating, “rational calculation” becomes a meaningless phrase. Understanding how historical actors came to use their numbers therefore belies the ahistorical economic man. By unearthing the entwined histories of these two insistently timeless disciplines, mathematics and economics, we can illuminate the instability of some of our most basic modern assumptions. *** 21 Caitlin Rosenthal uses this phrase in “From Memory to Mastery” (2012) to argue that dissecting past techniques of calculation can help historians better grapple with the vague and seemingly timeless concept of rationality. 22 In neoclassical economics, rationality has come to mean “individual behavior that maximizes benefits or minimizes costs in achieving some goals of individuals or of groups such as households or firms” and is therefore “a characteristic of the ideal-typical economic man,” as expressed by Arthur L. Stinchcombe, “Reason and Rationality” Sociological Theory, Vol. 4, No. 2 (Autumn, 1986), p. 160. However, the idea that reason and rationality are tied to mathematical calculation is not limited to modern economics, as the longstanding intellectual connections between mathematics and logic can attest. 23 In this dissertation, I present some of the most important points of contention, change, and choices taken (and not taken) during the long process of economic mathematization. I do not doubt that there are myriad other examples in this period in which mathematics and commerce intersected and clashed. I trust that those stories will eventually be unearthed and told. The invention of the mathematical economy was neither simple nor inevitable, but I hope the “visionary calculations” presented herein can begin to illustrate the complex, even paradoxical ways that nineteenth-century Americans grappled with the possibilities and constraints of their economic lives. By exploring how debates about the use and meaning of mathematics repeatedly found expression in commercial contexts, and how these debates made possible the development of the mathematical economy, this dissertation expands our knowledge of how education, expertise, and social difference helped to build, and continue to shape, our own mathematical economic lives. A note on terminology: as historians think more about the nature of the nineteenth century “economy,” they have embraced the diversity of terms and concepts that Americans applied to their economic lives.23 Though the terms ranged from “business” and “commerce” to “trade,” “the market,” and sometimes even “political economy,” together these formulations suggest that people were beginning to think more and more about their employment, incomes, fortunes, commercial relationships, and citizenship as a distinct aspect of life and work. Eventually this space would be dubbed “the economy,” but before the 1930s, its characteristics and limits remained undefined. Rather than impose the anachronistic term “the economy” on the subject that the characters in this project were debating, I try to remain true to contemporary terms. In many cases, these terms have 23 On the complexities of historical economic terminology, see Hannah Farber, “Nobody Panic: The Emerging Worlds of Economics and History in America” Enterprise & Society, Vol. 16 (Fall 2015), pp. 686-695. 24 valences that suggest a specific economic worldview. However, when speaking abstractly, I have opted to use “economic life” to describe this realm of human experience. In Chapter One, I chart the essential role of mathematics in the emerging political economic culture of antebellum America, what I term “the useful knowledge economy.” At the outset of the century, mathematics was touted as essential to the new nation’s future prosperity: American men would learn both the theory and practice of science so they might lead intellectually fulfilling lives, while still occupying economically productive jobs, thus fulfilling the nation’s republican dreams. The useful knowledge economy defined mathematics as a field on which to equate scientist and laborer. Its advocates linked the new nation’s political goals to an explicitly masculine conception of practicality, condemning those mathematics seen as too abstract as effeminate and aristocratic. Yet while elite celebration of mathematics in cultural discourse did little to shift the larger social hierarchy for working men, it provided an avenue for men with mathematical ability to begin to claim expertise in commercial matters based on their “scientific attainments.” Crucially, these men made the mathematical knowledge that working men merely used. In Chapter Two, I expand on the tension between making mathematics and using it through an exploration of antebellum arithmetic education. Arithmetic became a cultural obsession in the United States, as a signifier of how well prepared its children were for a “life in business.” In the 1820s and onward, a pedagogical debate emerged over whether arithmetic should be taught in the old way, through established rules, or through “mental arithmetic,” a new pedagogy emphasizing children’s innate calculative skills. Because antebellum arithmetic education was so tightly linked to commerce, this debate reflected a larger uncertainty about what a person should expect from a caveat emptor market society. Should a buyer place his trust in his own calculative abilities, as the 25 advocates of mental arithmetic argued? Or would he be safe in assuming that others were playing by common, objective rules? The debate over arithmetic education highlighted the problem with mathematical economic authority otherwise obscured by the discourse of useful knowledge. Did mathematics locate authority in the reasoned self, or in the common good? In Chapter 3, I narrate the rise of the United States’ first mathematical economic experts, civil engineers. Having been trained in advanced mathematics in the era of useful knowledge, and encountering a nation eager for infrastructure but conflicted over how (and how much) to pay for it, civil engineers claimed economic authority. They used their extensive mathematical educations and professed scientific disinterestedness to project apolitical expertise in deeply political debates over public works projects. However, although antebellum engineers achieved economic influence by promising to make states and corporations follow the rules, they became increasingly protective over their ability to define those rules through expert judgment. Trained in geometry for surveying and construction, they saw economic life as a rational space, to be managed by experts from above, and themselves as the gatekeepers of truly useful, masculine, productive knowledge. As a result, antebellum civil engineers built a geometrical economy of roads, canals, and railways, and turned fraught political contests over economic life into mathematical problems. In Chapter 4, I show how these ideas about mathematical expertise, public accountability, and commercial authority became privatized through emerging corporations. I focus on the rise of insurance actuaries during and after the Civil War as new members of the numerate elite, now with expertise in analytical algebra and statistics, which they used to build new financial instruments and markets. As actuaries began to define “useful” mathematics through its more abstract arenas, once seen as ornamental and effeminate, the discourse around mathematical knowledge changed. 26 Those men who were able, including engineers, embraced those mathematics that allowed them to claim belonging in the emerging algebraic-financial economy. As a result, arithmetic, once a badge of liberal self-ownership, became the task of menial laborers—many of whom were now women. At the same time, corporate calculators, particularly actuaries, began to insist that the public could not understand their calculations, and ceased trying to explain them to the public or government. As the status of commercial arithmetic degraded, corporate calculators’ privatization of economic mathematics further eroded its always-uneasy promise of accountability. In Chapter 5, I illustrate how the contests and changes of the long nineteenth century made possible, though not inevitable, the invention of the mathematical economy. The earliest American economists who wanted to use mathematics, primarily associated with the “marginalists” of Britain and Europe, upturned the historical school that then held sway in economics, through the apolitical power of mathematical models. At the same time, they muscled out the business interests that had helped define the professionalization of early economics, dismissing corporations as insufficiently disinterested to be true economic experts. The newly hegemonic vision of economic life that these economists invented drew on many of the previous century’s ideas about mathematical economic expertise, particularly the need for apolitical experts to interpret economic facts, and the idea that they necessarily acted in the public good. Crucially, however, they used differential calculus, with which they invented a universal economic man—a figure who could only have been imagined after a hundred years of making mathematical reasoning central to economic life. The universalization of homo economicus continued into the twentieth century, but at the time, his invention erased the century of choices, contests, and silences that had made him possible at all. 27 Chapter 1: The Useful Knowledge Economy On June 18, 1799, Thomas Jefferson wrote to a student who had sought his opinion on mathematical studies. William Greene Munford had just finished the first six books of Euclid, plane trigonometry, surveying, and algebra at the College of William and Mary, and desired to know if the Vice President thought he should go further. Jefferson agreed that the trigonometry Munford had learned in surveying was of the utmost importance to a man of the world, as was the calculation of square and cube roots and algebra to quadratic equations and logarithms. Any study beyond this, however, Jefferson deemed “a luxury… not to be indulged in by one who is to have a profession to follow for his subsistence.” These luxuries included conic sections, any curves or algebraic operations beyond quadratics, spherical trigonometry, and “fluxions,” by which he meant Newton’s calculus. Jefferson recommended that instead, Munford pursue some of the eminently practical sciences of the day, such as astronomy, botany, chemistry, natural history, anatomy, and natural philosophy—not to master them, but to gain familiarity with “their general principles and outlines” so that he might pursue any of them later in life.1 As to continuing in mathematics, Jefferson stressed that he believed that the human mind could always advance; the only people who made arguments to the contrary were “the present despots of the earth” and their allies. But he also asked Munford to consider which “acquisitions in science have been really useful to him in life, and which of them have been merely a matter of luxury”—again suggesting that beyond the “useful” mathematics he had already learned lay only 1 Thomas Jefferson, “On Science and Freedom; the letter to the student William Greene Munford, June 18, 1799” (Worcester, 1964). Rauner Special Collections Library, Dartmouth College (Hanover, NH). 28 an ornamental education unfit for the modest republican economy that Jefferson envisioned for the new nation. With somewhat false modesty, he depicted himself as a member of the “generation which is going off the stage,” and reminded Munford that the responsibility of keeping the republic belonged “to the generation of your contemporary.” To Jefferson, “freedom and science” were the only sure ways to ward off the return of despotism. “Science can never be retrograde,” he insisted; “what is once acquired of real knowledge can never be lost.”2 As the turmoil of the 1790s died down somewhat, and Americans began to consider what would come next, “science” loomed large.3 To American intellectuals like Jefferson, the United States had been founded as a deeply scientific project. The ideological leaders of the American revolution envisioned a new republic founded on scientifically rational principles of government. Jefferson and his peers imbibed deeply from European intellectuals who described governance and trade in scientific terms, comparing them to natural systems—what Linnaeus called an “economy of nature.”4 They hoped that a “science of society” might be discovered that would ensure peace and justice in conflict-prone Europe.5 To American intellectuals, who believed they held a fateful 2 Ibid. 3 The rescuing of American science from its old reputation as a vulgar backwater has been a positive development for American history and the history of science more generally. This project follows in the recent, but nevertheless well-established, tradition of taking American science seriously despite—or even because of—its commercial and non-research-oriented applications. Se Dan Bouk, “Review: Tocqueville’s Ghost” Historical Studies in the Natural Sciences, Vol. 42, No. 4 (September 2012): 329-339. See also the recent JER roundtable on early American history of science, Conevery Bolton Valencius et. al., “Science in Early America: Print Culture and the Sciences of Territoriality” Journal of the Early Republic, Volume 36, Number 1 (Spring 2016): 73-123. 4 Quoted in Emma Spary, “Political, Natural and Bodily Economies” in N. Jardine, J.A. Secord, and E.C. Spary (eds.) Cultures of Natural History (Cambridge: Cambridge University Press, 1996), p. 178. 5 Works on social scientific thought in European intellectual circles of the late eighteenth century are many and varied. I found these to be the most valuable as background for this chapter: Peter Buck, “People Who Counted: Political Arithmetic in the Eighteenth Century” Isis, Vol. 73, No. 1 (Mar., 1982), pp. 28-45; Harold J. Cook, Matters of Exchange: Commerce, Medicine, and Science in the Dutch Golden Age (New Haven: Yale University Press, 2007); Lorraine Daston, “Enlightenment Calculations” Critical Inquiry, Vol. 21, No. 1 (Autumn, 1994), pp. 182- 202; Fredrik Albritton Jonsson, “Rival Ecologies of Global Commerce: Adam Smith and the Natural Historians” 29 opportunity for political innovation, the possibilities seemed infinite. But to make the most of it, they needed the right conditions, and that meant focusing their energies on the simple, productive work of building a republic—and eschewing those “luxuries” that threatened to distract from that project, or worse, bring about the return of tyranny. It was through this political economic lens that Jefferson viewed Munford’s question about his mathematical studies.6 Was mathematics a luxury, or a necessary skill for a practical republican? What was its relationship to science, itself a very ill-defined term in the early nineteenth century? What would it mean for mathematics, or particular fields of it, to be useful? And how would it fit in with the American project? As American mathematicians and intellectuals developed a domestic tradition in mathematics for the new nation, they found themselves inverting many of older European ideas about the subject. Where European mathematicians had long celebrated “pure” mathematics, and dismissed “mixed” (or applied) mathematics as its illegitimate offspring, Americans in the early national and, especially, antebellum periods gravitated toward mathematical application. The most epistemically prestigious mathematical knowledge in early America was that with practical utility, especially commercial. Early republican political culture created deep foundations for this vision of mathematics, one that lasted well into the nineteenth century. Mathematics came to form the core of what I call the “useful knowledge economy.” This vision of national economic productivity The American Historical Review, Vol. 115, No. 5 (December 2010), pp. 1342-1363; Margaret Schabas, The Natural Origins of Economics (Chicago: University of Chicago Press, 2005); Spary, “Political, Natural, and Bodily Economies” (1996). On the intellectual project of the American Revolution, see Bernard Bailyn, The Ideological Origins of the American Revolution (Cambridge: Harvard University Press, 1967); Gordon Wood, The Creation of the American Republic, 1776-1787 (Chapel Hill: UNC Press, 1969); Drew McCoy, The Elusive Republic: Political Economy in Jeffersonian America (Chapel Hill: UNC Press, 1980). 6 On the aversion to luxury in early republican political economic thought, see Drew R. McCoy, The Elusive Republic: Political Economy in Jeffersonian America (Chapel Hill: UNC Press, 1980). 30 and prosperity, based in a common education, made science and mathematics useful, necessary economic skills in the early decades of American industrialization.7 As Americans considered what it would mean for mathematics to be a useful skill in their new republic, and they decided on a circumscribed role within practical science that emphasized a nation of practically educated working men. As a result, any higher or abstract mathematics outside this consensus was often perceived as unnecessary, and even counteractive, to a true republican society. The useful knowledge economy applied republican ideas about masculine productivity to the growing democratization of economic life. “Useful” knowledge was such when it combined experimental practice with mathematical theory to contribute to the prosperity and progress of the nation. Early American mathematics had value precisely because it could be applied productively and practically. It promised to make the working man into a man of science, and the man of science into a working man, to direct all knowledge toward the productivity and prosperity of the young nation. Jefferson’s distinction between utility and luxury created space for useful mathematics to become a prized economic skill and a productive, manly undertaking. However, while promising an idyllic nation of practical men, this definition of mathematics also planted seeds of technocratic economic expertise deep in early American political thought. 7 The literature on “useful knowledge” in industrializing America, especially as it relates to education, is wide. Examples include James D. Watkinson, “Useful Knowledge? Concepts, Values, and Access in American Education, 1776-1840” History of Education Quarterly Vol. 30, No. 3 (Autumn, 1990), pp. 351-370; Alexandra Oleson and Sanborn C. Brown, The Pursuit of Knowledge in the Early American Republic: American Scientific and Learned Societies from Colonial Times to the Civil War (Baltimore: Johns Hopkins University Press, 1976); William G. Shade, “The ‘Working Class’ and Educational Reform in Early America: The Case of Providence, Rhode Island” The Historian Vol. 39, No. 1 (November 1976), pp. 1-23; Charles Dorn, For the Common Good: A New History of Higher Education in America (Ithaca: Cornell University Press, 2017). 31 Domesticating Mathematics On June 5, 1810, Professor John Farrar wrote to Samuel Webber, president of Harvard University. Three years earlier, at age twenty-eight, Farrar had been named the Hollis Professor of Mathematics and Natural Philosophy at Harvard, and must have assumed that Webber would be sympathetic to his request, as he had preceded Farrar in the post. The young professor wanted to remind the university president that he had asked for books for his department: specifically, he wanted “[Colin] Maclaurin’s Algebra, [Leonhard] Euler’s Elements of Algebra, [and] [Edward] Waring’s Meditations Analytical.” All were European mathematicians of the eighteenth century whose work Farrar wanted to import to improve Harvard’s lackluster—to his mind— mathematics curriculum.8 Presumably Farrar received his books, because during the next fifteen years he would help lead the development of homegrown American mathematics. He and his peers endeavored not only to bring the latest in European mathematics to the United States, but also to carve out its appropriate role, and position the new nation in a complicated world. When John Farrar surveyed the Harvard mathematics department in the 1810s, the state of international mathematics was in disarray. Despite its modern reputation as a universal language, mathematics was deeply nationally segregated in the eighteenth century, particularly between the competing Continental and English visions that stemmed from opposing versions of the calculus.9 8 John Farrar to Samuel Webber, June 5, 1810. Box 1: Reports and Correspondence, Correspondence and Faculty Reports by John Farrar, Hollis Professor of Mathematics and Natural Philosophy, 1810-1831. Harvard University Archives (Cambridge, MA). 9 For a full description of the reasons and ramifications of the divergent mathematical traditions in eighteenth century England and France, see: Joan Richards, “Rigor and Clarity: Foundations of Mathematics in France and England, 1800-1840,” Science in Context, 4 (1991): 297-319; Stephen Shapin, “Of Gods and Kings: Natural Philosophy and Politics in the Leibniz-Clarke Disputes.” Isis, Vol. 72, No. 2 (Jun., 1981): 187-215; and Harvey W. Becher, “Radicals, Whigs, and Conservatives: The Middle and Lower Classes in the Analytical Revolution at Cambridge in the Age of Aristocracy,” British Journal for the History of Science, 28 (1995): 405-26. 32 Furthermore, Farrar did not just teach mathematics; he was also responsible for natural philosophy, the primary purpose of which in the early nineteenth century was to teach Newtonian mechanics. Farrar did not know, when he assumed his position, that one outcome of the French Revolution would be the reconciliation of French and English mathematics.10 Instead, Farrar believed himself responsible for bringing Harvard’s mathematics up to date. His initial requests for books favored British mathematics; he had, after all, been educated in Massachusetts, and now taught in deeply Anglophilic New England. To teach calculus, however, he adopted the Leibnizian notation, which, though reviled in Britain, Farrar saw as “undoubtedly” superior.11 Just as his peers in Britain and France sought a means of teaching and learning mathematics that matched the political and social culture of their national communities, so too did Farrar hope to domesticate mathematics in the new United States in such a manner that would be definitively American. If the United States was to fulfill its destiny as the world’s only nation guided by true rationality and scientific principles, as Farrar and other early republican intellectuals believed, it could not be content with inferior mathematics, or textbooks leftover from the nation’s colonial past. To that end, Farrar attempted to “compile a new course of mathematics,” drawn from the best extant materials, for use in American schools.12 The task, he discovered, was not an easy one. A 10 On mathematics and the French Revolution, see: Judith V. Grabiner, The Origins of Cauchy’s Rigorous Calculus (Cambridge: MIT Press, 1981); Bruno Belhose, “The École Polytechnique and Mathematics in Nineteenth-Century France” Changing Images in Mathematics: From the French Revolution to the New Millennium, ed. Umberto Bottazini and Amy Dahan Dalmedio (New York: Routledge, 2001); Harvey W. Becher, “Radicals, Whigs, and Conservatives: The Middle and Lower Classes in the Analytical Revolution at Cambridge in the Age of Aristocracy,” British Journal for the History of Science, 28 (1995): 405-26. 11 Farrar to Kirkland, Jan. 22, 1817. Although Leibniz’s larger proof of the calculus involving “infinitesimals” was made obsolete by Cauchy’s definition of the limit in the 1820s, his dy/dx notation proved useful, and lives on. 12 Florian Cajori, The Teaching and History of Mathematics in the United States (Washington: GPO, 1890), 127-8. 33 full year after the university approved his plan, he complained to Harvard’s new president John Kirkland that he had been “utterly unable to execute the plan proposed in any tolerable manner.” His efforts to write a substitute text for Euclid’s geometry had proved especially difficult, and he struggled to bring a “uniform character” to a French work on algebra. Nevertheless, even Farrar could not devote all his time to mathematics; he continued to also teach natural philosophy, chemistry, and astronomy. For all the time and effort that he and his fellow American mathematicians put into adapting and translating the subject for their students, the Harvard curriculum remained focused on the classical liberal arts. The university had instated a mathematics requirement for entry in 1802, but applicants needed little more than addition and subtraction. And should they attend, they would find their mathematics classes “confined to the two lower class during the term” and “given by the two junior tutors.”13 After that, students could be “excused” from mathematics, or if they chose to persevere, they could be excused from further language study and instead introduced to the “higher parts of algebra [and] trigonometry” as well as introductory calculus. Harvard’s mathematical texts might have begun to incorporate the latest in French mathematics, but in general, its students were destined to become lawyers, physicians, or clergymen—not exactly the sort to use algebra in daily life. Rather, Farrar and other mathematicians argued that what American students needed out of college mathematics was “a specimen of clear and close reasoning” that only mathematics could deliver.14 In 1814, Yale professor Jeremiah Day published An Introduction to Algebra, as he had 13 Reports on the Department of Mathematics, 1825. Farrar Papers, Harvard University Archives (Cambridge, MA). 14 Farrar to Kirkland, June 23, 1817. Box 1. Correspondence and Faculty Reports by John Farrar, Hollis Professor of Mathematics and Natural Philosophy, 1810-1831. Harvard University Archives (Cambridge, MA). 34 become frustrated with his students’ English textbooks. Day believed that, even if the English texts were theoretically “intended for beginners,” they were organized as outlines for a tutor to expand upon, and thus tended to be too concise for students to learn from directly. Day wanted to “put into the hands of a class, a book from which they are expected of themselves to acquire the principles of the science to which they are attending” and attend class well-versed in the material. Thus, he decided to provide a more comprehensive and detailed textbook, and he decided to provide it. Day argued it was “the logic of the mathematics which constitutes their principle value” for students, rather than any specific content or useful application. He argued that “no other subject affords a better opportunity or exemplifying the rules of correct thinking.”15 That mathematics should be used to teach reasoning was not a uniquely American idea; it had been the main justification for learning and studying mathematics, especially geometry, for centuries. But American intellectuals reframed it through their current political culture, believing successful republican governance relied on the reasoned judgment of independent citizens. In this view, mathematics could encourage public virtue, because it made “no room for authority, nor for prejudice of any kind, which may give false bias to the judgement.”16 Algebra and geometry were necessary to develop students’ reasoning faculties, and the future of the nation depended upon a people capable of independent reasoning. While all advocates of liberal education saw independent thought as the goal, mathematicians argued that no subject could be “more favorable to the exertion 15 Jeremiah Day, An Introduction to Algebra, Being the First Part of A Course of Mathematics, Adapted to the Method of Instruction in the American Colleges (New Haven: Howe & Deforest, 1814). 16 Thomas Kelt, The Mechanics’ Text-Book and Engineer’s Practical Guide: Containing a Concise Treatise on the Nature and Application of Mechanical Forces (Boston: Phillips, Sampson and Company, 1853). On virtue in early republican political economic thought, see Drew McCoy, The Elusive Republic (1982). 35 of the reasoning powers, to the continuance of their action.”17 They hoped mathematics would “produce a habit of methodical arrangement of the thoughts” and in turn “strengthen, expand, and improve the reasoning powers” and “guard the mind against the reception of error.”18 In a political system based on reasoned choice, nothing could be more important. To these intellectuals, for whom the creation of a national political culture was bound up in their academic pursuits, the spread of mathematics beyond the university appeared essential to the future of the republic.19 From Jefferson on, they established a discourse around mathematical pedagogy and content that linked the discipline firmly to what, as Farrar explained it to Kirkland, “the state of the college and of the country requires.”20 They had not yet considered how the subject would intersect with economic life, only that it, like most other ideas and practices Americans had imported from Europe, should be put to use in the project of nation-building. Mathematics would have value insofar as it bolstered the national project. The idea that the United States would hold mathematics in special esteem proved surprisingly resilient, even as the primary figures and ideas 17 John Playfair, Dissertation Second: Exhibiting a General View of the Progress of Mathematical and Physical Science, since the Revival of Letters in Europe (Wells and Lilly: Boston, 1817). 18 Halsey R. Wing, Essay on the Moral and Intellectual Effects of Studying the Mathematical and Physical Sciences; and on the Application of these Sciences to the Arts (Albany: Young Men’s Association, 1834). 19 The idea that mathematics is deeply intertwined with human reasoning is a relatively widespread historical claim, and the subject of many histories of mathematics, ranging from the sixteenth century to the twentieth. See Lorraine Daston, Classical Probability in the Enlightenment (Princeton: Princeton University Press, 1995) & “Enlightenment Calculations” Critical Inquiry, Vol. 21, No. 1 (Autumn, 1994), pp. 182-202; Joan Richards, “Rigor and Clarity: Foundations of Mathematics in France and England, 1800-1840,” Science in Context, 4 (1991), pp. 297-319; Peter Dear, “Miracles, Experiments, and the Ordinary Course of Nature” Isis, 81:4 (1990), pp. 663-683; and Christopher J. Phillips, The New Math: A Political History (Chicago: University of Chicago Press, 2015). This dissertation hopes to interrogate how mathematics and economic reasoning affected one another in nineteenth century America. 20 Farrar to John Kirkland, Jan. 22, 1817; Farrar to Kirkland, Jan. 26, 1817. Box 1: Reports and Correspondence, Correspondence and Faculty Reports by John Farrar, Hollis Professor of Mathematics and Natural Philosophy, 1810-1831. Harvard University Archives (Cambridge, MA). 36 of the early republican period receded. Debates over mathematics would continue to be framed by the question of whether it met what the “state of the country” required. “Dear Miss Anna Lytical” The idea that mathematics afforded students the tools to master “correct thinking” appealed to mathematicians like Day and Farrar. For them, mathematics embodied the liberal education, and pushed for it to be included not only in college classrooms, but secondary schools as well. As educational institutions of various levels were founded across the United States, discussions about who should learn mathematics, how, and why, spread beyond Harvard and Yale.21 As they did, so too did the cultural concerns at the heart of the discipline. During the antebellum years, two visions emerged about what mathematics was and what role it ought to play in society. On the one hand, it might be useful, profitable, and masculine. On the other, it risked becoming abstract, ornamental, and effeminate. Where and how that line would be drawn was not at all clear, but once the debate over the meaning of mathematics moved beyond mathematicians, it became bound up in ongoing arguments about the nature and future of republican political economy. The intellectual and economic changes of the second quarter of the nineteenth century re- framed the debates around the appropriate use and role of mathematics. The decline of Federalist politics, the expansion and masculinization of political participation, and the increasing emphasis on the public role of working class men began to force many Americans to confront the realities of social class in the republic. Whereas the founding generation had worried about political elitism, 21 Harvard and Yale were not the only educational institutions deeply invested in mathematics education; the U.S. Military Academy at West Point also debated their mathematics curriculum during this period, and engaged in many of the same conversations about reason and judgment that their New England colleagues did (see Chapter 3). 37 Americans before and after Andrew Jackson’s presidency began to concern themselves more with the potential perils of economic inequality.22 This shifting discourse affected the way Americans talked about mathematics. Whereas Farrar and Day had envisioned a national mathematical project that emphasized the right-reason of geometry, the growing political concern with class burdened the discipline with new issues. In the antebellum period, mathematics became a site of class-based critique. As American political culture shifted into something its partisans called “democracy,” some began to argue that geometry should not central to the education of a nation of working men. Mathematics became a site to contest the political economic future of the nation. This conversation was not only happening in the United States. The economic and political forces driving it, particularly the way that technological advances of the industrial revolution made practical science an economic priority, occurred in a transatlantic context, most visibly an Anglo- American one. Many mechanics’ handbooks and advice manuals published in the United States in the antebellum decades were reprints of English texts. An English mathematics professor recalled, in the 1870s, that fifty years ago “a strong current arose in favour of useful knowledge,” when “the machinery of lectures, mechanics’ institutes, and cheap literature, was employed for the diffusion of this useful knowledge among the humbler classes.”23 These processes were mirrored directly in the American context. Nevertheless, despite these connections to England, Americans saw their 22 On the emergence of political discourse around class inequality, see, briefly: Martin J. Burke, The Conundrum of Class: Public Discourse on the Social Order in America (Chicago: University of Chicago Press, 1995); Stewart Davenport, Friends of the Unrighteous Mammon: Northern Christians and Market Capitalism, 1815-1860 (Chicago: University of Chicago Press, 2008); Harry L. Watson, Liberty and Power: The Politics of Jacksonian America (New York: Hill and Wang, 1990); Paul E. Johnson, A Shopkeeper's Millennium: Society and Revivals in Rochester, New York, 1815-1837 (New York: Hill and Wang, 1978); Sean Wilentz, Chants Democratic: New York City and the Rise of the American Working Class, 1788-1850 (New York: Oxford University Press, 1984). 23 Isaac Todhunter, The Conflict of Studies and Other Essays on Subjects Connected with Education (London: MacMillan, 1873). 38 debates over the proper role of mathematics as profoundly tied to their national project. Arguments for, as well as criticisms against, mathematics education were most frequently framed through the lens of the nation’s success and the appropriate education of its citizens. Indeed, some antebellum Americans viewed education in mathematics as a remnant of European despotism, and argued that it belonged to an old world that the new republic had been specifically designed to eliminate. In the 1820s and 1830s, some American observers began to criticize mathematics as impractical, too difficult, overly abstract—even aristocratic, un-Christian, or effeminate. Whereas Farrar and Day had argued that mathematics should serve as a tool to instill republican virtues in the citizenry, these antebellum commentators argued instead that it threatened to teach students exactly the wrong kind of reasoning. Instead of undergirding good judgment, they worried it would lead students to look for absolute truth in all things, and disrupt their ability to weigh unreliable evidence. The American Revolution had supposedly banished absolute rule from the borders of the United States; surely such an abstract, totalizing, difficult, and impractical subject as mathematics should be done away with too. Instead, these critics argued, Americans should learn only the useful and practical applications of mathematics. In October of 1834, Thomas Smith Grimké addressed the fourth annual meeting of the Western Literary Institute and College of Professional Teachers, in Cincinnati Ohio. Grimké was an educated man, hailing from the South Carolina gentry, but as he told the assembled teachers, he felt “little hesitation in saying, as the result of my experience and observation, that the whole body of pure mathematics is ABSOLUTELY USELESS to ninety-nine out of [every] hundred, who study them.” If he had his way, Grimké claimed, he “would banish to-morrow… the whole body of pure mathematics out of our system” and end forever the notion that “a knowledge of pure 39 mathematics is necessary to a right understanding” of, and ability to perform, the calculations necessary for certain professions.24 To Grimké and other opponents of mathematics education, the problem was not finding the point at which algebra and geometry ceased to be useful: to them, the whole subject was useless—and worse, a threat to the republic. He wanted to see the entire subject excised from the “scheme of general education in our country.”25 If mathematicians like Farrar had seen their subject as foundational to right reasoning and thus to the future of the republic, Grimké believed instead that it threatened republican reasoning as he understood it in the 1830s. He too framed his address in explicitly nationalist terms. Contrary to the idea that the right-reasoning skills of mathematics were essential to a republican education, Grimké demanded, “can it be [denied] that [mathematics] are just as fit a part of education in a despotism, or an aristocracy, as in a republic?” For such critics, mathematics epitomized the central flaws of the American education system as it existed in 1834: it lacked both utility and religiosity, and it was too concerned with subjects not “purely American.” Like the ancient languages of Latin and Greek, which Grimké also lambasted for similar reasons, mathematics could be eliminated from American schools with no ill-effects. Rather, he argued that mathematics and classics were relics of eighteenth century despotism that should have been cast off with the monarchy. Certainly now, in an increasingly democratic country, was time to do so.26 24 Grimké did not want to get rid of arithmetic, as he did believe that basic calculation skills were useful for children. The place of arithmetic in American economic culture is the subject of Chapter 2. 25 On Grimké, see the extensive literature on his more famous sisters, Sarah and Angelina: Catherin H. Birney, The Grimké Sisters (New York: Kessinger Publishing 2004); Mark E. Perry, Lift Up Thy Voice: The Grimke Family's Journey from Slaveholders to Civil Rights Leaders (New York: Viking Penguin, 2002); Grace H. Long, “The Grimkes, Southern Iconoclasts” Peabody Journal of Education, Vol. 20, No. 6 (May, 1943): 359-364. 26 Thomas Smith Grimké, Oration on American Education, Delivered Before the Western Literary Institute and College of Professional Teachers, at their Fourth Annual Meeting, October, 1834 (Cincinnati: Josiah Drake, 1835). 40 For opponents of mathematics education like Grimké, using mathematics to teach students reasoning was counterproductive, because it would lead them to form a rigid view of an uncertain world. They argued that this inflexibility limited mathematics’ applications. Grimké lamented that in classrooms, “the logic of mathematics is cultivated as [though] it were the logic of actual life[,] whether public or private” when in fact it was “the logic of neither.” To apply it as such, he argued, would be a “complete misapplication of the geometrician’s art.”27 Mathematical proofs threatened to “contract the mind,” as the North American Review had argued in 1821.28 These critics argued that mathematics would have a constricting effect on students’ reasoning. Would it not lead them to look for absolute veracity where none existed? Even Jeremiah Day admitted that it would be “unwise to form our general habits of arguing” on a discipline that relied so much upon “absolute certainty; while the common business of life must be conducted upon probable evidence.” But he believed that when students learned to apply mathematics in science, would they learn to use its lessons in daily life, a proposition Grimké and others found unconvincing. The absolute certainty of mathematics proved an emotional sticking point for its opponents. Not only did mathematics fail to be suitably republican, they said, there was also nothing inherently Christian about it. Surely, Grimké asked, mathematical laws were as applicable in countries where the “religion of Fohi, of Brama, or of Mahomet exists”? Others went further, suggesting that not only was mathematics not specifically Christian, it might in fact be anti-religious. They fretted that its claim on absolute truth made it “disposed to exalt itself presumptuously, to refer all to itself as 27 Grimké, Oration on American Education (1834). 28 Quoted in Todd Shallat, Structures in the Stream: Water, Science, and the Rise of the U.S. Army Corps of Engineers (University of Texas Press, 1994), p. 103. 41 the author” rather than leading students to “new revelation in the wisdom of the omnipotent Creator of man.”29 These accusations struck at the core of mathematics, something that its defenders could not change. Mathematics did promise absolute certainty in anything to which it was applied. That claim to near-divine truth meant that anywhere mathematics was used, would become a place of absolute right and absolute wrong. Surely a nation that had thrown off absolute rule in its politics should be skeptical of a subject that promoted rigidity in all things? Mathematics’ perceived elitism in the antebellum decades was not limited to its connection to despotic rule. Due to its abstract and its sometimes-difficult content, some argued that it was the province only of elites who had a lot of time to learn a subject that would not help them win gainful employment, because they did not need to be employed. Just as its absolute nature mimicked the absolute rule of European aristocrats, they argued, so too did its emphasis on theorizing instead of practical use or application make it the appropriate province of the gentry, not the republican. Even university students themselves often dismissed mathematics this way: they were conscious of their particular educational status, and understood the subject as one they needed to graduate, but not to prosper. Sometimes, this fact frustrated and angered college students, as the next section will show, but it also proved to be a source of resigned amusement. Once they had completed their two years of required mathematics, which was the standard course at most liberal colleges, students reveled in the idea that they would never use most of the material again. These ideas, although born in the republican political culture of the early republic, proved to have remarkable staying power in critiques of mathematics. They can be seen even in the 1850s, 29 “Intellectual Education: Letter IV” American Annals of Education (Jul. 1832), p. 318. 42 in eulogies that sophomores at Dartmouth College composed to celebrate the end of their required mathematics courses. At the end of the school year, a student, apparently chosen by committee, would deliver a lecture: two such titles were “Eulogy at the Burial of Mathematics” and “Remarks on the Burial of Mathematics.”30 The speakers joked that they had been chosen for the “melancholy pleasure of bidding these sacred relicts a last adieu” as the class bade cheerful farewell to their required mathematics courses, and spoke of the discipline like a departed elder.31 The “eulogies” were also a chance for the boys to show off their knowledge of classical poetry and history; both speeches were laden with classical references, to texts such as Milton’s Lycidas and Horace’s Ars Poetica. But lower references were used, too: an English nursery rhyme lamented the departure of a friend who had apparently failed his course in algebra: Who killed Rogers? I says Analytical With my ‘Elements of Integral’ I killed Rogers.32 As the doggerel suggests, the Dartmouth sophomores apparently possessed a special hatred for algebra and analytics, a sentiment many of their university peers shared. They rarely mentioned geometry, perhaps preferring the more concrete nature of the subject to algebra’s abstractions. But they also complained about the increasing prevalence of mathematics in college courses, and the growing requirements of young men enrolled in American colleges, noting the “alarming increase 30 “Eulogy at the Burial of the Mathematics,” c. 1852 and “Remarks at the Burial of the Mathematics, The Class of ’56 in Dartmouth College” at Rauner Special Collections Library, Dartmouth College (Hanover, NH). These appear to be the only two manuscripts that have survived (the eulogies do not appear to have ever been published) but they follow such similar themes and styles that they appear to be part of a longer tradition, but how long is unknown. 31 “Eulogy at the Burial of the Mathematics,” c. 1852. Rauner Library, Dartmouth College (Hanover NH). 32 “Remarks at the Burial of the Mathematics” Rauner Library, Dartmouth College (Hanover NH). The verse mimics the format of the verses of the nursery rhyme, “Who Killed Cock Robin?” 43 of Mathematical drudgery in the attainment of what the Faculty are facetiously disposed to term, ‘a liberal education,’” as one of the eulogizers put it. “Year by year,” he warned, perhaps somewhat presciently (if a bit histrionically), “this poison is slowly insinuating itself into the very vitals of a college education, and in long it will permeate the whole system.” 33 Furthermore, both eulogizers picked up a thread from earlier critiques of mathematics that had been latent but rarely explicit: that it was effete, even effeminate. Both presented mathematics as a flighty, cruel woman, tormenter of earnest young men. One spoke of “the marked similarities” of different types of mathematics “to certain feminine characters, which we meet in life”: analytics, a smiling “coquette” who ultimately gave only “ambiguous answers” and then deserted men when they “most need aid and comfort and consolation, just as one’s knowledge of Analytical forsakes him at the dread hour of Examination”; calculus, who too “plys her seduction arts” but in the end “more expressions fall from her lips which you cannot understand”; and algebra, akin to those “stony-hearted, matronly ladies” ready to dole out punishment for every minor transgression.34 For “dear Miss Anna Lytical,” the young men could not bring themselves to weep.35 They had survived the “flirtations,” exercises, punishments, and doubts of their mathematics courses and now, they believed, would never have to engage Chase’s Algebra again. These students did not refer to mathematics as women because they thought women were natural or talented mathematicians. Rather, they echoed the growing criticisms of mathematics that it was ornamental, impractical, demanding, and inscrutable—a kind of obstacle to be overcome on 33 Ibid. 34 “Remarks at the Burial of the Mathematics” Rauner Library, Dartmouth College (Hanover NH). 35 “Eulogy at the Burial of the Mathematics,” c. 1852. Rauner Library, Dartmouth College (Hanover NH). 44 the way to adulthood, just like a flirtatious woman. The linking of useless knowledge to effeminacy was not entirely new; Jefferson had gestured to it in his correspondence with William Munford when he called higher mathematics a “luxury,” itself a deeply gendered term that garnered men with humble, productive rationality and women with flighty, wasteful irrationality.36 But in linking mathematics to a particularly gendered version of political economy, the Dartmouth sophomores implicitly made the case that for mathematics to support the American national project, it had to be the province of productive men. Indeed, one can read the eulogies as the students performing, and mocking, their own economic privilege, suggesting their awareness that they were out of step with the larger economic culture. In sloughing off mathematics, they were freed from the domestic, feminine confines of their schooling, ready to become real American men.37 When Jefferson had referred to advanced mathematics as a luxury in 1799, he did not necessarily intend the word in its most pejorative sense. But in using it, he nevertheless linked the discipline to ornamental education reserved only for the few—in essence, an aristocratic education, intended for those whose work would be done for them, by those who had not received the same 36 On women in republican political thought, see: Linda Kerber, Women of the Republic: Intellect and Ideology in Revolutionary America (Chapel Hill: University of North Carolina Press, 1997); T.H. Breen, The Marketplace of Revolution: How Consumer Politics Shaped American Independence (New York: Oxford University Press, 2004), pp. 172-182. Many domestic economy texts from the antebellum and Civil War period echo Revolutionary-era concerns about women’s wasteful spending, including Harriet Beecher Stowe (writing as Christopher Crowfield), who complained that “it’s the fashion to talk as if all the extravagance of the country was perpetrated by women.” Christopher Crowfield, House and Home Papers (Boston: Ticknor and Fields, 1865). 37 On manhood in antebellum America, see Amy Greenberg, Manifest Manhood and the Antebellum American Empire (Cambridge: Cambridge University Press, 2005). By the 1850s, the feminization of teaching at the elementary and secondary levels had begun to make schools seem to many like a more domestic space than in the past, though whether this translated to the university, where all faculty were men, is hard to say. On the feminization of teaching, see Richard Bernard and Maris Vionovskis, “The Female School Teacher in Ante-Bellum Massachusetts,” Journal of Social History (10) (1977): 332-45; Nancy Hoffman, “‘Inquiring after the Schoolmarm’: Problems of Historical Research on Female Teachers” Women's Studies Quarterly Vol. 22, No. 1/2, Feminist Teachers (Spring - Summer, 1994), pp. 104-118. 45 level of instruction, and were therefore consigned to work. Antebellum critics picked up on this idea to argue that if mathematics became too abstract and divorced from application, it threatened to undermine not only good judgment, but also the underpinnings of the republic itself. Their opposition to mathematics education heightened the need for a clear justification for the subject among even its staunchest defenders. As a result, teachers and mathematicians themselves moved to respond to the criticisms by creating a circumscribed role for mathematics, one that specifically sought out the line between theory and application that would make mathematics appropriate for an educational system dedicated to practicality over luxury. “Any ordinary intellect” As they entered their sophomore year, the Yale University Class of 1832 looked at their upcoming mathematics course with growing horror. Under the presidential tenure of Jeremiah Day, the mathematics curriculum in the sophomore year was considered the most difficult of any subject in any year. The Class of 1832 had begun to worry even in their freshman year, and took little comfort in the intense relief that juniors expressed about having completed it. In July of 1830, the sophomores began the dreaded course on conic sections: the study of ellipses, parabolas, and other quadratic shapes. These students’ fears were compounded by the recent introduction of the blackboard: whereas prior students had relied on the figures in the appendixes of their textbooks in previous mathematics courses, particularly in conic sections, they were now asked at random to come to the blackboard and “demonstrate the figure.” Five years earlier, sophomores had risen up in aggrieved unison when their conic sections tutor had promised to skip the course, only to renege 46 during a gap in the schedule. These students had been pacified by changes to the schedule. But in 1830, no such reprieve awaited the new class of sophomores.38 On July 28, a student committee petitioned the Yale faculty to allow students to “recite” figures with their textbooks, rather than demonstrate on the blackboard. They insisted that their request “arose not from a desire to render the study easier” but because there would not be enough time left in the semester to properly learn such a difficult subject. The faculty rejected the petition. When the sophomores next convened for class, their tutor drew names from a bowl to perform the exercises on the blackboard. One by one, the students refused to answer, until the ninth, at which point the tutor ended the session and complained to the faculty. The nine students who had stayed silent were promptly suspended. The rest of the sophomore class expressed their opposition to this measure by rioting. For nearly a week, the sophomores broke windows, tormented freshman, and, in a few cases, assaulted their tutors. Once the riot had played itself out, all forty-four members of the sophomore class were expelled. None were readmitted to Yale, and many never managed to enroll in another American university. Even Andrew Calhoun, son of then Vice President John C. Calhoun, found himself blacklisted from the likes of Harvard and Princeton.39 38 On the two “Conic Sections Rebellions” at antebellum Yale see: Clarence Deming, “Yale Wars of the Conic Sections” The Independent, Vol. 56 (January-June, 1904); “A Circular, Explanatory of the Recent Proceedings of the Sophomore Class, in Yale College. New Haven, August, 1830” Yale University Archives (retrieved online); Andrew Fiss, “Professing Mathematics: Science and Education in Nineteenth-Century America” PhD Dissertation, Indiana University, 2011. On the introduction of the blackboard to American classrooms, see Christopher J. Phillips, “An Officer and a Scholar: Nineteenth-Century West Point and the Invention of the Blackboard” History of Education Quarterly, Volume 55, Issue 1 (February 2015): 82-108. Conic sections are shapes that can be formed out of cones (circles, ellipses, parabolas, and hyperbolas) and represented on a Cartesian plane with quadratic equations. They are usually considered part of algebra or, today, pre-calculus. 39 Fiss, “Professing Mathematics,” pp. 2-3. 47 The ringleaders of the “Conic Sections Rebellion” explained, in the wake of the revolt, that the trouble had occurred because the course in conic sections was simply “unattainable, during the hours prescribed by the laws, to any ordinary intellect.” In fact, they argued, the curriculum had never given enough time to conics, and every year the material remained “beyond the capacity of the vast majority of any class” of Yale students. The students repeatedly emphasized the lack of time devoted to such a difficult subject, pointing to the faculty’s own claims that mathematics required close study, daily practice, and clear instruction “until the student is at length reduced to the beneficial process of committing his mathematics to memory.”40 According to these students, conic sections was simply impossible to learn under the present curriculum. They implored the faculty to see past “the clouds of prejudice” and instead recognize, through “the cold calculations of utility” that their students had been asked to learn too difficult a subject in too short a time, to then be evaluated by means deemed unfamiliar, unfair, and impractical.41 While the Yale sophomore class may have had selfish reasons for rejecting a difficult subject, they were not alone in appealing to the “cold calculations of utility” in evaluating what kind of mathematics should be learned, and how. Like their peers at Dartmouth, albeit somewhat more sincerely, they challenged their mathematics professors to tell them why they should learn a subject for which they believed they would never have a practical use. Like Grimké, they argued that the subject was untethered from reality, and served no useful purpose. For their mathematics professors, many of whom also wrote mathematics textbooks for secondary—and, increasingly as the century progressed, grammar—schools, this challenge had to be met. The solution mattered 40 “A Circular, Explanatory of the Recent Proceedings of the Sophomore Class” pp. 3-4. 41 Ibid., p. 13. 48 not only to collegiate education, but the American vision for education overall. If mathematics was to be a useful subject, needed by anyone “who is to have a profession to follow for his subsistence,” as Jefferson put it, then it must be taught in schools. If it was a luxury, it could remain ensconced in universities, or even be excised from the curriculum altogether. Even Jeremiah Day argued that all American schools should adopt courses in mathematics “for the purpose of forming sound reasoners, rather than expert mathematicians.”42 Although he focused heavily on the former, his distinction mattered. Day hoped some students might develop a special taste for the subject and pursue it to higher levels, but that was independent of his belief that introductory algebra and geometry should be required for American students. He argued that basic mathematics was critical to any education, but he agreed that at some point along the way it stopped being useful and became a luxury. But where exactly did that line fall? As Day and others set about answering this question, they gravitated toward the idea that mathematics that could be applied practically should be included, and anything more would be optional. Even Farrar, as he compiled a textbook to teach his students the Elements of Euclid, fretted that the subject would be too abstract for his students if it were not “applied to material nature and to the arts.”43 Mathematics threatened to separate the ornamentally educated elite from hardworking but “ordinary” citizens, as the Yale sophomores put it, only when it became overly abstract. Mathematics moved slowly into secondary education in the United States. In 1843, Horace Mann, then Secretary of Education in Massachusetts, reported that 463 students were enrolled in 42 Day, Introduction to Algebra (1814). 43 Farrar to Kirkland, June 23, 1817. Box 1. Correspondence and Faculty Reports by John Farrar, Hollis Professor of Mathematics and Natural Philosophy, 1810-1831. Harvard University Archives. 49 geometry and 2,333 were studying algebra in the state’s public schools. But in the same year, more than ten thousand students in Massachusetts were learning American history in school.44 The gap likely stemmed from reluctance to teach mathematics outside of high school, which many students never attended. Algebra and geometry did eventually become part of a general curriculum beyond private seminaries for both boys and girls, but they remained little studied relative to other subjects in American public schools in the antebellum period. The algebra tended to be what contemporary mathematicians referred to as “general arithmetic”—adding and subtracting with variables instead of numbers—and the geometry was strictly plane. In 1839, Charles Augustus Murray, a Scotsman visiting the United States, opined that British pupils were far more advanced “in respect to classics and pure mathematics” than their American peers, and believed Americans would agree, given, as Murray saw it, “the limited attention they bestow upon these studies.”45 The search for a bright line between utility and luxury also made space for mathematicians of more practical education to enter the fray. In 1830, surveyor and engineer Amos Eaton published the second edition of his popular Art Without Science, which promised to explain surveying techniques without the “speculative principles and technical language of mathematics.” Eaton was a surveyor and land agent, and at the time of publication, a mathematics teacher at the Rensselaer School, one of America’s first technical schools. In his book, he recommended “most emphatically, the common course in Euclid, Algebra, &c.” But he also dismissed “cloistered mathematicians,” and noted approvingly that all around him, he saw that in mathematics and science, the “cloister 44 Edward W. Stevens, Jr., The Grammar of the Machine: Technical Literacy and Early Industrial Expansion in the United States (New Haven: Yale University Press, 1995). 45 “Art I. Travels in North America” American Annals of Education (Dec. 1839), p. 529. 50 begins to surrender to the field, where things, not words, are studied.”46 He likely would have agreed with Murray that Americans lagged behind their British peers in “pure mathematics,” but to him, that meant that American education was on the right path. Even some traditional mathematics professors allowed that some of the criticism of their discipline was fair. In November 1835, mathematics professor George Keely of Waterville College wrote to Rowland Gibson Hazard, a Rhode Island manufacturer and intellectual.47 In response to Hazard’s criticism of mathematics as a field of study, Keely hastened to explain that he feared Hazard had received “a very wrong impression” about the nature of Keely’s work. “If you think I am devoted to Mathematicks as such you are entirely mistaken,” he informed Hazard. “The mere Mathematician is in my opinion a narrow-minded man.” Rather, Keely explained, he appreciated mathematics “as a workman loves his tools.” Even as a mathematics professor, he insisted that any work in mathematics that did not lead to a greater understanding of “nature” did not interest him. Rather, he said mathematical studies occupied as much of his time as it did because of he believed that “no one is able to form an independent opinion on any question in Science without a sound knowledge of Mathematicks.”48 Although certain mathematicians could be “narrow-minded,” and fail to see this as the purpose of their studies, Keely blamed the men, not the subject. If mathematics led to rigidity in thinking, he argued, the fault lay with the user, not the tool. 46 Amos Eaton, Art Without Science: or, Mensuration, Surveying and Engineering, Divested of the Speculative Principles and Technical Language of Mathematics, Second Edition (Albany: Wester and Skinners, 1830). 47 On Hazard, see Caroline Elizabeth Robinson, The Hazard Family of Rhode Island, 1635-1894 (1896), pp. 122- 123; on his intellectual contributions to the history of American philosophy, see Peter H. Hare, “Rowland G. Hazard (1801-88) on Freedom in Willing” Journal of the History of Ideas Vol. 33, No. 1 (Jan. - Mar., 1972), pp. 155-164. 48 George W. Keely to Rowland Gibson Hazard, November 1, 1835. Rowland G. and Caroline (Newbold) Hazard Papers, box 2, folder 20. Rhode Island Historical Society (Providence, RI). 51 Keely’s defensiveness about his chosen discipline reflected the wider conversations around mathematics taking place in the antebellum decades. In general, even mathematicians agreed: one could study mathematics to improve his scientific reasoning, but should not become obsessed with the abstractions of the discipline itself. Mathematics could be a helpful ‘tool’ for understanding how the natural world operated, but as a subject in and of itself, it lacked utility and practicality. Even those who pushed for its inclusion in a liberal arts education and its importance in teaching independent reasoning wanted to see it curtailed to its most useful forms. Surveying, navigation, and engineering all required a basic knowledge of Euclidean geometry, plane trigonometry, square and cube roots, parabolic equations, and of course arithmetic. Beyond these and other immediately practical mathematical subjects, abstract or pure mathematics seemed outside the direct project of American education—even to some mathematicians themselves. Whereas “right-reasoning” had been sufficient for Farrar and Day, new political concerns convinced antebellum mathematicians to defend the practicality of their discipline. Throughout the period, it constituted “useful knowledge” so long as it was confined to showing the principles of fundamentally experimental or practical science, so that it remained in the service of practical and productive work. Mathematics’ role in useful knowledge essentially became an argument over class: learned correctly, mathematical knowledge would be an equalizer, ensuring that every man would be both intellectual and producer, scientist and worker. Whereas critics had alleged that it was aristocratic and useless, and threatened to separate Americans into classes of intellect and therefore of profession, the new argument for mathematics promised social mobility for working American men, fulfilling the original ideals of the early republic. This promise, like most made by 52 American elites in this period, was a largely inaccessible ideal, but it does help to explain how and why mathematics began to spread through a somewhat skeptical society. “I am sure my father does not intend me for a Carpenter” In 1834, Halsey R. Wing addressed the Young Men’s Association of Albany. A judge from nearby Glen Falls, Wing had come to speak to one of the capital’s useful knowledge associations, which regularly hosted lectures on subjects ranging from phrenology to philosophy.49 He began with a story of an English university student, who had just been handed Euclid’s Elements in his mathematics class. The student protested to his tutor that learning geometry would be a waste of time, boasting, “I am sure my father does not intend me for a carpenter.” Wing warned his audience that this “prejudice against mathematical studies” existed in the United States too, but mainly as a remnant of British aristocratic pretensions. Over there, he said, students viewed geometry as useful only for mechanics, and as a result was “scornfully pronounced to be unworthy of the notice of those, whose pride and pretensions lay claim to that, which, by the proud and pretending only, is regarded as a more exalted rank in society.”50 But an even greater problem prevailed in the United States, said Wing: too often, mechanics, mariners, and surveyors, the people who used mathematics in their daily working life, adhered too strictly to the tables and charts that “scientific men” had produced for them, because they could not understand the original mathematical principles. Wing allowed that precise calculations were of course essential to these men’s professional work, but he lamented that a sole focus on “approved guides” meant that these 49 The New York State Register for 1845: Containing an Almanac for 1845-6 with Political, Statistical, and Other Information Relating to the State of New York and the United States (Disturnell, 1845), p. 476. 50 Wing, Essay on the Moral and Intellectual Effects of Studying the Mathematical and Physical Sciences (1834). 53 hardworking men eschewed mathematical reasoning altogether. The “complicated, yet beautifully regular relations” of mathematics became no more than pat rules, thus denying these men the most important part of mathematical education: deductive reasoning. Wing condemned each of these prejudices, “which either assumes to look down on upon mathematical knowledge as something of mere mechanical utility,” as indicated by those men who only followed tables and charts, “or fears to attempt an examination of its principles, as a task too mighty for any but the great in mind.” The best citizens, Wing argued, would be those “intelligent mechanics, who carried into their business a theoretical mind as well as a skillful hand.” Through Euclid, Albany’s young men would become the thoughtful citizens and skilled mechanics on which true republican political economy needed to rest. They would not be ‘mere mathematicians’ bogged down in abstraction, but neither would they be unthinking calculators. With mathematics, they would be equally essential to the prosperity of the nation, whether they became astronomers or carpenters. They all would be both workingmen and mathematicians, thereby erasing the distinction between the two. Men like Wing insisted that knowledge of the mathematical principles that undergirded the manuals, tables, and charts of everyday labor would elevate mechanical work into scientific, reasoned, and above all, useful knowledge. In the first half of the nineteenth century, independent associations devoted to the spread of what was popularly termed “useful knowledge” sprang up around the United States, especially in populous urban centers.51 These societies professed their dedication to “the great moral, and 51 On useful knowledge societies in America, see: Bruce Sinclair, Philadelphia's Philosopher Mechanics: A History of the Franklin Institute, 1824–1865 (Baltimore: The Johns Hopkins University Press, 1974); Jonathan Lyons, The Society for Useful Knowledge: How Benjamin Franklin and Friends Brought the Enlightenment to America (New York: Bloomsbury Press, 2013); Lawrence A. Peskin, Manufacturing Revolution: The Intellectual Origins of Early American Industry (Baltimore: Johns Hopkins University Press, 2003); Ralph S. Bates, Scientific Societies in the 54 economical importance of diffusing useful knowledge throughout society.”52 Affluent city leaders pooled some of their capital to establish free lending libraries, sponsor lecture series, and publish journals designed to spread useful knowledge throughout their surrounding communities. Many, including the Young Men’s Association of Albany, focused their attention on unmarried young men. At that stage of life, the Boston Society for Useful Knowledge explained, “when the mind is active and the passions urgent, and when the invitations to profitless amusements are strongest,” young men should be furnished, “cheaply and invitingly,” with “useful information” that would expand their “general intelligence” and prepare them for work.53 Libraries dedicated to young men proliferated. The Apprentice’s Library of Philadelphia was founded in 1820; similar institutions soon appeared in New York, Boston, Salem, Portland, Trenton, and Detroit.54 In 1841, a second branch of Philadelphia’s Apprentices’ Library opened for young women.55 Antebellum “useful knowledge” was fundamentally tautological: for knowledge to qualify as useful, it had to be perceived as something that people would use, often in a commercial context. However, its specifics were never clearly well defined. One Boston lecture series included talks about the life of Benjamin Franklin, the effects of clean water on public health, a history of western United States, 3rd edition (Cambridge: MIT Press, 2003); John C. Greene, “Science, Learning, and Utility: Patterns of Organization in the Early American Republic” in Oleson and Brown, The Pursuit of Knowledge in the Early American Republic (1976); Joshua Greenberg, Masculinity, Organized Labor, and the Household in New York, 1800-1840 (New York: Columbia University Press, 2010). 52 Memorial to the Legislature of Pennsylvania, 1821?. Apprentices Library Company of Philadelphia records, 1820- 1948, box 1, folder 2. Historical Society of Pennsylvania (Philadelphia, PA). 53 “Boston Society for the Diffusion of Useful Knowledge,” Box 1829. Massachusetts Historical Society (Boston, MA). 54 Edith Sarmberton to Ernest Spofford, 1919. Apprentices Library Company of Philadelphia records, 1820-1948, box 1, folder 6. Historical Society of Pennsylvania (Philadelphia, PA). 55 “An historical sketch of the Apprentices’ Library Co. of Philadelphia”. Apprentices Library Company of Philadelphia records, 1820-1948, box 1, folder 2. Historical Society of Pennsylvania (Philadelphia, PA). 55 civilization, animal biology, the moral sciences, “sensation as a source of knowledge,” and the historical constancy of human nature.56 Sometimes the topics included as “useful knowledge” might be grouped under the notion of “science,” another word that lacked precise meaning in this period. Certainly, subjects like chemistry and biology would be considered science, but so might engineering, history, political economy, even rhetoric. One lecturer tried to define it in 1833 as “knowledge acquired by the thoughts and the experience of many, and so methodically arranged as to be comprehended by anyone.”57 In the complex educational discourse of the early republic, “useful knowledge” and “science” often had slippery, intersecting meanings. Ultimately, “useful knowledge” was a self-evident good: some field of learning that could connect intellect and skill to bolster a republican system of self-owned political economic actors. Most of all, useful knowledge was seen as such because it lay foundations for prosperity through individual improvement—both intellectual and professional. Urban elites hoped that those cities with the “most skillful and best informed workmen” would flourish in art and industry, which meant spreading useful knowledge was both charitable and self-interested.58 “It is to her mechanics that Philadelphia must look for a large share of her future prosperity,” explained banker Clement Biddle, a board member of Philadelphia’s Apprentice’s Library.59 Science, broadly defined, would enlighten the populace, and prosperity would follow. In an address to the Mechanics’ Institute of 56 List of lectures. Boston Soc. for Dif. II: Papers, 1830-1843, Folder 2, #7-11. Massachusetts Historical Society (Boston, MA). 57 Gulian Verplanck, “A Lecture, Introductory to the Course of Scientific Lectures before The Mechanics’ Institute of the City of New York” (New York: G.P. Scott & Co, 1833). 58 Clement C. Biddle, “The Apprentice’s Library of Philadelphia” Feb. 6, 1821. Apprentices Library Company of Philadelphia records, 1820-1948, box 1, folder 4. Historical Society of Pennsylvania (Philadelphia, PA). 59 Ibid. 56 Philadelphia, engineer William Rankine reminded his audience that “knowledge is a fit coadjutor of virtue,” but he simultaneously assured them that from scientific learning, “pleasure or profit is alike desirable.”60 Urban economic elites promised that accessible scientific education, in the form of schools, libraries, and lectures, would ensure that every American was intellectually equipped to contribute to the nation’s economic prosperity. Many reformers agreed: labor activist Frances Wright told a Buffalo audience in 1829 that useful knowledge, by way of national public schooling, would lay “the true foundation of practical republicanism.”61 During a moment in which both urban patricians and labor reformers advocated “useful knowledge” as an inherent good to a republic, mathematics continued to live in an uneasy space between pointless abstraction and menial obedience. The purpose of geometrical education, in the old vision, was to train students’ reasoning faculties. But new American advocates of mathematics education emphasized the practical and applicable: arithmetic, algebra, plane trigonometry, simple analytics. No one advocated for men to simply read numbers off a chart or apply rules without an understanding of where they came from. But at the same time, no one wanted navigators to rewrite their tables every time they set sail. In the old world, mathematicians had made tables and workers had used them, a vision that no antebellum Americans advocated. In reality, despite Halsey Wing’s disdain, most working people used practical short hands or premade tables to carry out everyday labor. But a system in which some made mathematical knowledge, and others followed it, implied 60 William J. M. Rankine, Address [to mechanics’ institute], 1845/1846. Miscellaneous Manuscripts Collection, 1668-1983, Mss.Ms.Coll.200. American Philosophical Society (Philadelphia, PA). 61 Frances Wright, “An Address to the Industrious Classes; a Sketch of a National System of Education” (New York, Free Enquirer: 1830). Library Company of Philadelphia (Philadelphia, PA). 57 one in which a few controlled the levers of American prosperity. No public figures in antebellum America wanted to publicly encourage such a dire political economic system. Wing, for his part, skirted this problem by arguing that the theory and principles of science, which would be eminently useful for apprentices, artisans, and working people of all stripes, could only be learned through mathematics. Wing’s position was not exactly original; the concept that “every workman must be better fitted for his business, by understanding the theory of his art” had circulated widely among advocates of useful knowledge education by the time he spoke in 1834.62 It centered on the idea that by elevating the working man with a theoretical education to back up his practical art, the republic would be secured. Some went so far as to advise that “every mechanic and labourer… be made acquainted with Euclid, particularly the first six books; also algebra; the properties of conic sections; and the doctrine of fluxions.”63 However, others, especially in public lectures, omitted the word “mathematics,” perhaps because the term itself remained divisive. Still, “theory” and “principles” usually meant mathematics, from plane geometry needed for surveying to Newtonian mechanics for constructing and fixing engines. The association between theory and mathematics can be found in the libraries dedicated to useful knowledge, which contained shelves of handbooks dedicated to geometry and algebra, by both American and English authors. Titles promised formulae and calculations for the “Engineer, Mechanic, Machinist, Manufacturer of Engine-work, Naval Architect, Miner, and Millwright” and contained lessons in arithmetic, plane and solid geometry, and some basic algebra, mostly as 62 Clement C. Biddle, “The Apprentice’s Library of Philadelphia” Feb. 6, 1821. Apprentices Library Company of Philadelphia records, 1820-1948, box 1, folder 4. Historical Society of Pennsylvania (Philadelphia, PA). 63 Thomas Kelt, The Mechanics’ Text-Book and Engineer’s Practical Guide (Boston: Phillips, Sampson and Company, 1853). 58 needed for geometry, as well as reference information like “Tables of Squares, Cubes, Square and Cube Roots of Numbers,” “Specific Gravity,” “Proportions of the Lengths of Semi-Elliptic Arcs,” and more.64 Others covered simple mechanics, explaining the mathematics behind the strength of materials, torsion and twisting, falling bodies, velocity of water wheels, of pumps and engines, and properties of liquids.65 Some advertised their “pocket” size, perhaps in hopes that workingmen would take their formulae and tables into their workshops and factories, or at least that they would be able to buy the small text. One British text, in its first American edition, celebrated that in both England and America, “that much-wished-for time appears to be at hand, when Mechanics shall not only be acknowledged cunning artificers, but men of science.”66 The importance of utility in mathematics extended to its teaching in schools as well. One New York observer noted in 1843 that although geometry was a recent addition to the curriculum, it had already produced great results. According to him, geometry was “a favorite subject among pupils”; the promise of a geometry lesson was supposedly enough to encourage students to finish their other lessons, cure truancy, excite the interest of “boys of the rougher sort from the streets and docks” to focus on their studies, and even get students to request to come in on Saturday to do more geometry. The “secret” for such enthusiasm, the commentator insisted, “is, in one word,— employment.” Not only were students’ eyes and hands occupied and their brains engaged, the claim 64 Oliver Byrne, The Practical Model Calculator, for the Engineer, Mechanic, Machinist, Manufacturer of Engine- work, Naval Architect, Miner, and Millwright (Philadelphia: H.C. Baird, 1852). 65 Julius W. Adams, Templeton’s Engineer, Millwright, and Mechanic’s Pocket Companion (New York: Appleton & Co, 1852). 66 Robert Brunton, A Compendium of Mechanics, or Text Book for Engineers, Mill-Wrights, Machine-Makers, Founders, Smiths, &c. Containing Practical Rules and Tables (New York: Carvill, 1830). “Men of science” was the preferred nomenclature of the early nineteenth century for the group of people we today would call “scientists.” 59 went, but geometry also produced “visible, tangible, appreciable fruits” that resulted directly from the students’ own labors.67 For these boys, geometry was not an abstract concept, but rather a productive and necessary exercise to give them practical skills that they would need later in life. Approving commentators encouraged this perception of mathematics, and continued to push for greater inclusion of algebra and geometry as public schooling expanded. Whether there was another geometry class for girls, this New York observer did not say. Women’s mathematical education in antebellum America is woefully under-studied in the annals of educational history, but what research does exist suggests a general parallel to the overarching discourse around mathematical education, with a few key caveats. Women who attended private academies and seminaries in these years encountered courses very similar to what their male peers would have seen, which meant courses in geometry, algebra, astronomy, and natural philosophy. Furthermore, the rationale for teaching those girls was, professedly, the same as for boys: to teach them to “THINK—to reason, investigate, compare, methodize, and judge,” in the words of an ad for the Petersburg Female College in Virginia.68 Charles Murray observed that these schools made less distinction between “male” and “female” subject materials than their English peers, preferring to teach a broad overview to all pupils. According to Murray, educated American women were 67 “New York Public Schools” Common School Journal [reprint, The Christian Advocate and Journal] (Oct. 16, 1843), p. 305. 68 Quoted in Mary Kelley, Learning to Stand and Speak: Women, Education, and Public Life in America’s Republic (University of North Carolina Press: Chapel Hill, 2006), p. 92. References to women’s mathematical education are scattered throughout Kelley’s book, although the subject does not receive a specific analysis. More to the point is Kelly’s demonstration that “reason” was still a primary justification to educate women in the antebellum period. For a more direct analysis of women’s mathematical education in the antebellum period, and the general goal of providing them the same education as men, see Chapter 7, “Science for Women: The Troy Female Seminary” in Edward W. Stevens, Jr., The Grammar of the Machine: Technical Literacy and Early Industrial Expansion in the United States (Yale University Press: New Haven, 1995). 60 generally “more conversant with meta-physics, and… speculative writings than English women” but fell behind in subjects “more peculiarly feminine.”69 But the notion that women’s mental faculties might differ from men’s was also becoming more entrenched in this period, and some argued that not only did women not need mathematics, they were biologically incapable of learning it. These ideas seem to have gone hand in hand. The fact that women had no need for so-called useful mathematics, because they were not “destined to be Navigators, nor Opticians, nor Almanac-makers, nor Practical Mechanics, nor Miners, nor Engineers, nor Doctors in Medicine” mingled with ideas about their actual ability to learn the subject at all. Despite plenty of pushback from women, and the founding of female academies in every region, including the technical Troy Female Seminary in 1821, the general belief that “time bestowed on the more abstruse and severe studies, by young women, is time wasted,” persisted— and indeed, grew.70 Perhaps ironically, accusations of femininity leveled at mathematics ultimately pushed women out of the subject, as mathematicians and advocates reacted by emphasizing the masculinity of useful knowledge. By linking mathematics to self-ownership and productive work, they helped it gain acceptance by making it primarily a province of men. Still, the threat of abstraction and aristocracy could not be fully vanquished. Supporters of mathematics as useful knowledge, who celebrated linking “the accomplished speculative projector and the successful practical machinist” admitted that “all purely speculative science” was always in danger “to wander into visionary abstractions, to shroud itself in abstruse technicalities.” Such subjects, like mathematics, sometimes preferred “to substitute words of learned length, and rules 69 “Art I. Travels in North America” American Annals of Education (Dec. 1839), p. 529. 70 “A Friend to the Ladies” Independent Chronicle & Boston Patriot (August 20, 1825), p. 2. 61 or maxims of arbitrary authority, to simple and intelligent reason.”71 These pejoratives—visionary, speculative, arbitrary—continued to haunt mathematics education. They implied theory divorced from practice, the presumption of truth without material evidence, and a kowtowing to unearned authority. And, now that mathematics had become so tightly linked to mechanics and workingmen, the fear emerged that mathematics might lead young men toward “vain speculations in visionary schemes” instead of staid, productive industry.72 But, on the other hand, without mathematics, men would work as thoughtless drudges instead of republican citizens. The solution lay somewhere between “visionary abstractions” and uniform obedience: a balance that, when correctly achieved, could lead to a practical scientist. This idea was advanced by useful knowledge advocates’ constant feting of people like Benjamin Franklin and inventor Robert Fulton, names familiar to many antebellum Americans. The idolization of America’s most famous practical scientists made a vague idea about marrying theory and practice central not only to the political future of the nation, but also to an economic culture centered on educated and productive mechanics. The achievements of “Franklin and Rittenhouse and Whitney and Fulton and Perkins” had less to do with their mathematical genius, and more with their dedication to hard work and practical knowledge.73 In an address to the American Institute of the City of New York, H.C. Westervelt claimed that while “the financial policy of Alexander Hamilton was of invaluable importance subsequent to the revolution, nevertheless… the genius of Franklin, and the practical 71 Gulian Verplanck, “A Lecture, Introductory to the Course of Scientific Lectures before The Mechanics’ Institute of the City of New York” (New York: G.P. Scott & Co, 1833). 72 Thomas Kelt, The Mechanics’ Text-Book and Engineer’s Practical Guide: Containing a Concise Treatise on the Nature and Application of Mechanical Forces (Boston: Phillips, Sampson and Company, 1853). 73 Verplanck, “A Lecture, Introductory to the Course of Scientific Lectures” (1833). 62 and mechanical knowledge… were infinitely superior.”74 To the purveyors of useful knowledge, men like Franklin and Fulton proved that a virtuous government could be based in ordinary people, so long as hard work and a good education were valued among all classes. Perhaps no one received more effusive praise for his mathematical acumen than Nathaniel Bowditch. Born into modest wealth in Salem Massachusetts in 1773, Bowditch spent his childhood learning accounting and navigation, in preparation to become a mariner like his father and maternal grandfather. He also served as a record-keeper and calculator in the 1794 survey of the Salem coast alongside Harvard professor William Bentley and local captain John Gibault.75 Soon after, his rise to fame began in earnest. Frustrated with the errors in the navigational text that most American sailors had used in the eighteenth century, John Hamilton Moore’s Practical Navigator, Bowditch wrote The American Practical Navigator—a book of navigational tables, calculations, and charts for sea travel. First published in 1802, the Practical Navigator immediately became a staple in American navigation, and made Bowditch a familiar name for anyone connected to the industry. In addition to being more numerically correct than Moore’s text, Bowditch’s Practical Navigator emphasized simple methods of calculation, “appreciable by men of limited education,” which furthered its popularity.76 In 1818, six thousand copies sold for 30¢ each.77 74 H.C. Westervelt, “Address.” Scrapbook Volume, Printed Items (circulars, pamphlets, tickets, forms), 1845-1856. Records of the American Institute of the City of New York for the Encouragement of Science and Invention, 1808- 1983. New York Historical Society (New York, NY). 75 Original Field Book for Land Survey of Salem, undated [1794]. Bowditch Family Papers, 1726-1942: Series 1, Box 1, Folder 7. Phillips Library, Peabody Essex Museum (Salem, MA). 76 “Sailors Revere Bowditch,” Boston Sunday Globe, July 5, 1903. Bowditch Family Papers, 1726-1942: Series 1, Box 1, Folder 17. Phillips Library, Peabody Essex Museum (Salem, MA). 77 Edward M. Blunt to Nathaniel Bowditch, August 14, 1818. Bowditch Family Papers, 1726-1942: Series 1, Box 1, Folder 3. Phillips Library, Peabody Essex Museum (Salem, MA). 63 Bowditch’s work mirrored that of Farrar and Day, by employing mathematics in a national project, but he achieved far more fame.78 During a public lecture in 1831, Edward Everett told his audience that few mariners, who looked to their Practical Navigators “for the calculations with which he finds his longitude in mid-ocean” knew that the calculations had been produced by someone “who started at the same low point in life” as them—and fewer still knew that those same calculations had led their author to a position of “equality with the most distinguished philosophers of Europe” and situated his name alongside “those of Newton and La Place.”79 Here Everett was most likely referring to Bowditch’s translation of French mathematician and astronomer Pierre- Simon Laplace’s Mécanique Celeste into English, a task he began in 1800 and continued until his death in 1838. In all likelihood, almost none of those who fawned over Bowditch’s achievement actually read it, but the fact of a self-taught American mariner translating an opus of European mathematics made Bowditch an American hero to the advocates of useful knowledge.80 He, much more than any academic mathematicians, embodied American mathematics. With some fudging of his biography, Bowditch could be—and was—held up as a self- taught mathematical genius of humble origins, who harnessed his intrinsic numerical talents to provide American sailors and merchants with knowledge that was crucial to both science and 78 On the use of more popular educational productions in the early republican nation-building project, see Jill Lepore, A is for American: Letters and Other Characters in the Newly United States (New York: Vintage, 2002). 79 Edward Everett, An Address delivered as the introduction to the Franklin Lectures, in Boston, November 14, 1831 (Boston: Gray and Bowen, 1832), p. 21. 80 Everett, like most Americans who talked about Bowditch like this, exaggerated: while many British and European mathematicians and scientists certainly respected Bowditch, his genius primarily lay in correction and translation, not in original mathematical research. See, especially, Tamara Plakins Thornton, Nathaniel Bowditch and the Power of Numbers: How a Nineteenth-Century Man of Business, Science, and the Sea Changed American Life (Chapel Hill: University of North Carolina Press, 2017). 64 commerce. Those who praised Bowditch both during and after his life took note of his essential American-ness: certainly, they emphasized his modest origins and self-education, but they also took pride in the fact that Bowditch had directed his talents to something “useful”—and his case, explicitly commercial. The translation of the Mécanique Celeste might have swelled the pride of American intellectuals who wanted to see their new nation rise to Europe’s scientific heights, but as Everett said, the mathematical knowledge that Bowditch used to translate a great work had originated in his calculations for the Practical Navigator. Thus, Bowditch was not some “mere mathematician,” as George Keeley had put it. He combined theoretical knowledge with practical experience to improve the lives and livelihoods of his fellow seamen. Bowditch died in 1838, in a period of great enthusiasm for useful knowledge. Obituaries ran in the papers of every seaport; a New York paper called him “first mathematician of the new world, probably the first of the age,” while the midshipmen of the U.S. Naval School in Norfolk, Virginia, wore black armbands in mourning. A Boston eulogizer spoke to a packed house at the Odeon theater, most of whom belonged to the city’s Mechanic Association, and reflected on the appropriateness of addressing that body on the “life and character, the labors and services of the son of a poor ship-master and cooper.” Yet another paper boasted that “it was left for America to furnish a Bowditch who could faithfully interpret the great work of the Mécanique Celeste of La Place, which the Edinburgh Review said not twelve men in Europe could understand.” Most of all, the Philadelphia National Gazette crowed, the great mathematicians of France, Germany, and England had been astonished by Bowditch, because they could not believe “that a man in active 65 business should have found time to become so learned a mathematician.”81 Not only, the Gazette implied, was the utilitarian-bent of American mathematics more socially beneficial, it could also lead to genius just as effectively as the education of European aristocrats. Men like Everett and Halsey Wing pointed to Bowditch as embodying the theoretical mind and the skillful hand, a symbol of equal opportunity by way of mathematics. How much they truly believed that this outcome was possible, and how much the philosophy intended to merely present the image of possible classlessness without disrupting the socioeconomic status quo, is impossible to say. “Useful” mathematics accorded with ideas about republican manhood, industriousness, and national prosperity. Nevertheless, it also did little to change distributions of education, wealth, or power, except for a very distinct few, like Bowditch. The social inequities in education, property, and legal rights in early America of course played a large part in preventing the kinds of mobility that urban elites touted. Even as a theory, however, this argument for mathematical mobility rested on unstable ground. In his Albany address, Wing had condemned the “mere mechanical utility” of relying on premade tables. And yet, his and his peers’ hero, Nathaniel Bowditch, had achieved his fame and fortune by writing those tables, not using them. This tension, between making and using mathematics, ultimately became the core of the useful knowledge economy. “Cui bono?” In a speech to the Delaware County Institute of Science in the early 1820s, Robert Maskell Patterson—professor of mathematics at the University of Pennsylvania, like his father—admitted 81 Misc. newspaper clippings. Bowditch Family Papers, 1726-1942: Box 1, Folder 16: Newspaper Clippings, Mostly Obituaries, 1838. Phillips Library, Peabody Essex Museum (Salem, MA). 66 that he heard the criticism of science. He claimed that when people looked at theoretical scientists, like Franklin with his kite or Newton and his soap-bubbles, they tended to “sneer at the trifling occupation” and demand, “cui bono? what is the use of all this?” Patterson’s answer took up the rest of his long, winding speech: he talked about how science had led directly to the invention of gunpowder, the lightning rod, the telescope, and how each of these had furthered not only human knowledge, but prosperity as well. Mineralogists did not crack open rocks, nor botanists linger by the side of the road, for their own amusement.82 Everyone benefited from scientific discovery; it undergirded the machines and calculations that made business possible, whether by ensuring ships got where they were going or by providing new things for them to carry. Meanwhile, a few years earlier, Patterson’s father had received a letter from James Austin, a resident of a small Pennsylvania town about 130 miles from Philadelphia. After apologizing for “the presumption of a stranger who writes to you for no other reasons, than, the wish of obtaining knowledge,” Austin informed Robert Patterson Sr. of a recent idea of his. Assuring Patterson that this idea had “entered [his] mind, without any human assistance” Austin explained that he believed he had found “a method of obtaining the sum of a number of rectangles, by transferring one factor of each, under the digits agreeing with its other,” and helpfully included a graphical representation of what he meant. This method, Austin insisted, would make summing unlike quantities easier, by providing an easy way to find a common multiplier and relieve the calculator of performing many individual computations, and could be used to improve surveying techniques. He concluded that he would be “exceedingly happy” to receive Patterson’s opinion of his method, and provided his 82 Robert Maskell Patterson, “A defense of curiosity, delivered to the Delaware County Institute of Science” (c. 1825). Robert Patterson Papers, 1775-1853, Series 1, Box 3. American Philosophical Society (Philadelphia, PA). 67 address in Northumberland County to facilitate the reply.83 Despite his son’s later lauding of the benefits of practical mathematics, however, Patterson did not respond. The experiences of the two Pattersons at the end of the early national period point to the twin impulses of the antebellum embrace of practical mathematics. On one hand, elite advocates of useful knowledge argued that mathematics benefited the nation, and looked toward a future in which it could direct science into prosperity, erasing class distinctions by establishing a nation of “thinkers and tinkers.”84 In this vision, scientific theory elevated the mechanics beyond a laborer, into a man of science. Equally importantly, it turned men of science into laborers, thereby ensuring that they would contribute something useful to society and national prosperity. On the other hand, however, men like Austin readily took note of speeches that promised that “no person should be deterred from the profits and gratification of investigating the practical utility of natural science.”85 To them, mathematics promised not only a comfortable life, but also a potentially rich future. In the initial decades of the nineteenth century, the American Philosophical Society was inundated with letters like Austin’s, whose authors had a much less general answer to the younger Patterson’s question. They wanted the nation’s benefit to also be their own. 83 James Austin to Robert Patterson, June 15, 1815. American Philosophical Society Archives: Manuscript Communications, box 1. American Philosophical Society (Philadelphia, PA). 84 This phrase taken from Silvio A. Bedini, Thinkers and Tinkers: Early American Men of Science (New York: Charles Scribner’s Sons, 1975). Bedini shows the many small scientific inventions devised by Americans between the 1660s and the 1830s, arguing that the United States’ early history of science could be found in these “little men of science” who were, in contrast to European men of science, primarily “practitioners” who pursued science for need and profit, but made important inventions and discoveries nonetheless. While much more work has been done on early American science since then, Bedini is still one of the only historians to include mathematics in this depiction of colonial and early American science, particularly in navigation. 85 Wing, Essay on the Moral and Intellectual Effects (1834). 68 In the antebellum decades, the ideal of linking of practical science to theoretical principles, in the service of national prosperity, laid the foundation for a new American political economic vision: what I call the “useful knowledge economy.” According to its advocates, while individuals could profit from new inventions, only the combination of scientific knowledge and reasoned judgment could contribute to the national good. “Useful knowledge” provided the foundation for a new political economy, one that applied older republican ideals about masculine productivity to the growing democratization of economic life. Central to useful knowledge were the mathematical principles that supported scientific advance. At the same time, however, advocates of the useful knowledge economy also made sure to remind their listeners that science should not be used to try and rapidly change their positions in life. For all the radical potential of a political economy based entirely in scientific education, rather than any other marker of social identity, its elite boosters did not want to see fundamental disruption to American society. The useful knowledge economy thus contained a central irony: a classless ideal, achieved through the distribution of mathematical skill, which in reality created a narrow path to mathematical economic authority. Elite-produced texts and lectures of the antebellum period promised the young mechanic that he might at any moment find “some brilliant discovery, which will speedily conduct him to fortune and fame,” yet they also strenuously warned such a man away from purposefully pursuing “visionary schemes” that might lead to financial ruin.86 In this, they admitted what men like James Austin had long been aware of: that mathematics, by way of scientific principles, was a possible ticket to wealth, but they stressed that it would be a risky journey. Most such texts expressed their 86 Thomas Kelt, The Mechanics’ Text-Book and Engineer’s Practical Guide (1853). 69 preference that individuals improve themselves into the singular, idealized class of educated, self- sufficient, practical scientists. Speculation, risk-taking, quick wealth—all seemed vaguely related to mathematics, even as financial speculation had yet to become a mathematical science. The useful knowledge economy instead linked republican political culture to the liberal economic spirit of the antebellum years by promising to keep both political aristocracy and economic dependence at bay. Whether this ideal delivered a material reality seemed not to trouble its largely conservative advocates; indeed, they seem to have preferred that it did not. Furthermore, the association between mathematics and commercial knowledge reinforced the masculinity of science and mathematics.87 The socio-political association of theoretical and productive science with young, practical men on the make overwhelmed any potential claims by other kinds of people, especially women, to join mathematics’ narrow ladder of upward mobility. The United States’ ideal economic citizen, in the useful knowledge economy of the antebellum decades, was defined by the theoretical mind and the skillful hand. The result was that the need to learn mathematics, and the ability to do so, became mutually reinforcing. Those who worked with their hands were understood to need to learn science and mathematics, to apply them to their work. By being the sort of person who applied mathematics to their work, therefore, they were presumed to possess the ability to learn it. Those who were not supposed to work, on the other hand, would learn mathematics only ornamentally. Over time, intellectual efforts to solve the problem of class reinforced the masculinization of American mathematical practice. 87 Cohen, A Calculating People (1982), p. 8. Cohen also argues that the association between mathematics (especially arithmetic) and commerce during this period further masculinized mathematics, but somewhat differently than I do here. I deal more fully with the gendered meaning of arithmetic calculation in the next chapter. 70 Meanwhile, however, those Americans perceived as particularly mathematically inclined increasingly found themselves in positions of practical or commercial significance. Not all of them were Fultons or Bowditches; many simply realized that their knowledge was in demand. These men recognized that the marriage of the skillful hand and the theoretical mind operated in two directions. The useful knowledge economy called upon those with scientific and mathematical learning to apply those skills in the service of the national economic project, which in turn offered such people a claim to economic authority. John Farrar joined civil engineer Loammi Baldwin in his survey of the Merrimac and Connecticut Rivers, part of planning of the Middlesex Canal.88 Nathaniel Bowditch offered his mathematical services to insurance, first at the Essex Fire and Marine Insurance Company, and later, to the Massachusetts Hospital Life Insurance Company, a proto-investment bank for New England’s early capitalists.89 And during the antebellum period, hundreds of young men joined the national Coast Survey, under the direction of military engineers, using mathematical calculations to literally define the new nation.90 As a result, the growing importance of mathematical principles to antebellum economic culture began to create space for a nascent technocratic elite, as practical mathematicians found that their “scientific attainments” opened doors to economic authority. The national effort to create scientist-laborers focused rhetorically on the elevation of laborer to scientist, but the reverse had 88 Caleb Butter to Loammi Baldwin, 5 February 1816. Folder #22: Middlesex Canal, Incoming Letters, 1812-1822; Box 1, Part II: Incoming Letters, 1791-1854; Baldwin Family Business Papers, 1694-1887. Baker Library (Boston, MA). 89 Tamara Plakins Thornton, “‘A Great Machine’ or a ‘Beast of Prey’: A Boston Corporation and Its Rural Debtors in an Age of Capitalist Transformation” Journal of the Early Republic, Vol. 27, No. 4 (Winter, 2007): 567-597. 90 Hugh R. Slotten, Patronage, Practice, and the Culture of American Science: Alexander Dallas Bache and the U. S. Coast Survey (Cambridge: Cambridge University Press, 994); Nathan Reingold, “Alexander Dallas Bache: Science and Technology in the American Idiom” Technology and Culture Vol. 11, No. 2 (Apr., 1970): 163-177. 71 major consequences as well, as the useful knowledge economy lay the groundwork for scientific professionals to claim economic expertise. The more important that using mathematics became to national prosperity and economic citizenship, the more authority those people who could create mathematical knowledge acquired. Advocates of mathematical education and useful knowledge more generally elided this uncomfortable distinction. Perhaps they glimpsed the irony that their efforts to distribute economic self-ownership through scientific knowledge had created conditions for mathematics to become a specialized avenue to commercial authority. James Austin seemed to have understood it as early as 1815, but he did not appear to have benefited from his foresight, relying as he did on the approval of men like the Pattersons. The implied answer to Patterson’s question of mathematics and science, “cui bono,” was everyone. His description of practical science relied on discoveries that benefited the public in some way, not ones that had made their inventors notably rich or famous. The near-deification of people like Bowditch and Fulton did suggest that individuals could gain pecuniary benefit from applied science and mathematics. But antebellum conversations about how mathematics should be defined did not focus on specific applications, or even on stories that emphasized personal wealth. Rather, mathematics provided the useful knowledge economy with a path to classless prosperity. By combining science and labor, certain mathematical knowledge would create equal opportunity and widespread economic self-ownership. Through a delicate balance between the masculine and the effete, the menial and the abstract, the concrete and the speculative, useful mathematics would distribute the nation’s prosperity throughout society. Yet, by elevating the commercial prestige of mathematical science, the useful knowledge economy contained a fundamental tension: between 72 those who made mathematics, and those who used it. Ultimately, the true beneficiaries of the useful knowledge economy would be those who laid claim to being the former. “Practical philosophers” In 1829, British mathematician Charles Babbage wrote Nathaniel Bowditch to thank him for sending part of the translated Mécanique Celeste. Congratulating Bowditch on bringing the French work into “our common language,” Babbage sighed ruefully that “however I feel that the parent country ought to have performed this service to science, I hope she will never be too proud to follow any example either in knowledge or benevolence.”91 At the time, Babbage was preparing to publish his “Reflections on the Decline of Science in England,” in which he complained that his native land had fallen behind its European neighbors in “the more difficult and abstract sciences.” The Mécanique Celeste, he wrote, had finally been translated into English—but in America, not England.92 Having never had great faith in British mathematics, Babbage increasingly came to see the United States as the discipline’s new frontier. More than two decades later, he told Alexander Dallas Bache that he believed that mathematics was best left to “younger heads and more vigorous hands than my own—to the practical philosophers of a younger country.”93 In the pairing of head and hand, theory and practice, idea and invention; in the deification of “practical philosophers”; in the lectures of useful knowledge societies; in practical handbooks 91 Charles Babbage to Nathaniel Bowditch, n.d., c. 1829. Charles Babbage selected correspondence, 1827-1871. American Philosophical Society (Philadelphia, PA). 92 Charles Babbage, Reflections on the Decline of Science in England: and On Some of Its Causes (London: B. Fellowes, 1830). 93 Charles Babbage to Alexander Dallas Bache, October 20, 1851. Alexander D. Bache Papers: Miscellaneous Incoming and Outgoing Letters. American Philosophical Society (Philadelphia, PA). Babbage was fifteen years older than Bache, but actually ended up outliving him by four years. 73 and textbooks for mechanics and millwrights; and in hundreds of letters from hopeful inventors, we can see that, in practice, the emerging culture of invention, entrepreneurship, and science in the United States in the early nineteenth century made mathematics essential to the American project. But what exactly mathematics would entail was not entirely clear. In the project of building a national political economy, Americans found themselves trying to untangle the nature of the discipline itself. What types of mathematics were useful, and which were simply knowledge for the sake of knowledge? Then as now, this posed a problem for advocates of science, and the useful knowledge economy presented a possible solution. For American mathematicians, commentators, teachers, artisans, and mechanics, it brought the best of republican political economy into a new world of industrialization, technological invention, and entrepreneurship. Perhaps because so many writers and speakers eschewed the actual term “mathematics” in favor of “theory” or “principles,” American histories of science have largely ignored its ubiquity in discussions and debates over useful knowledge. But understanding early American mathematics this way also expands our understanding of the relationship between science and commerce during the antebellum period. Mathematics was part of American political economy: it seemed able to bridge work and science, and thereby deliver a classless republic of reason. Many Americans of the period retained an open but skeptical view of mathematics, and although they differed about what kinds of limits should be placed on its application, they generally agreed with Jefferson that limits should exist. Almost no one argued that mathematics was suitable as an end in itself, at least for most Americans: it had to be used and applied to some practical end. Otherwise, it was worse than useless; it threatened to undermine the American political project. 74 Mathematics has nearly always vacillated between near-divine claims to truth on one hand, and practical or mechanical application on the other. Rather than allow both ideas to continue in separate realms, however, antebellum Americans sought to bring these competing mathematical identities together. Their attempted goal was to solve the growing problem of class distinction in early American political economy. In the muddled discourses around work, wealth, and economic citizenship, mathematics emerged as a tool to distribute economic authority in a republican society. Educators and commentators emphasized the practical mathematics of applied science, while also holding onto the scientific prestige of mathematical reasoning. Mathematics did not make work prestigious; work made mathematics prestigious. As a result, mathematics became a crucial site of antebellum discourse about the new nation’s future prosperity—and about who would benefit, and how, from the emerging mathematical economy. 75 Chapter 2: Commercial Arithmetic In August of 1826, Professor Robert Mattel Patterson, at the University of Pennsylvania, received an irate (and unsigned) letter, likely from one of the college’s students or his father. The author insisted that “the science of figures stands preeminent for its antiquity” and that “it never has and never will change.” Philosophical queries about the history of mathematics aside, however, Patterson’s correspondent actually had a much more specific purpose: getting out of his tuition payment. Having established the privileged position of arithmetic as one of the only unchanging things in existence, upon the ageless principle that “two and two make four,” the writer reasoned that, “three months is only the half of six months, and if six months’ services be worth $30, three months’ services cannot be worth more than $15.” Thus, he determined that “if $30 be paid to a master for six months’ tuition, and at the end of three months he dismisses his scholar, the scholar will be entitled to receive back $15.” Patterson, he said, owed him money.1 These truths, the writer asserted, could not be denied, “and a few equations will prove them beyond all controversy.” Clearly, he believed that a numerical relationship had been established between the time of study and the cost of tuition. That only half the time of study was completed should mean that only half the tuition was required. That transaction did not only involve the two individuals and their contract. The letter writer believed that the principles of arithmetic held them both to some external standard by which all commercial transactions could be made objective. He appealed to the authority of calculation more than the fact of the numbers themselves. And he 1 Anon. to Robert Mattel Patterson, August 4, 1826. Robert Patterson Papers, Mss.B.P275.n: Series I, Box II (American Philosophical Society, Philadelphia PA). 76 insisted that, in this time and place, he could expect the same from those with whom he transacted. Under his logic, a commercial transaction did not necessarily mean paying an agreed-upon sum. It meant that both parties had entered an arithmetic relationship, and the rules of their commercial transactions would be subject to those immutable, universal laws. During the antebellum period, arithmetic proved a popular way for ordinary Americans to engage positively with a society defined more and more by commercial transactions—as well as to defend themselves against charlatans created and sustained by that society. The obsession with arithmetic was not just a reaction to the realities of business life. Rather, textbooks and pedagogical debates around arithmetic show that many Americans invested their attention deeply in the proper relationship between business and mathematical calculation, and gravitated towards mathematics that promised a rational, but also accessible, form of commercial practice. Many believed that the ancient truths of arithmetic could be used to make commercial practice fairer and more equal. Common education in arithmetic, they said, would ensure that every American could both manage his own business, and hold his partners accountable. According to many commentators, calculation was central to participating actively and correctly in “business life” in early America. Over time, this idea developed into a popular belief in commerce as inherently arithmetic, and arithmetic as the primary science of commercial life. By 1865, an arithmetic textbook could state unreservedly that “Money has intrinsic reports, and is controlled by natural laws.”2 2 E.E. White et al, Bryant and Stratton’s Commercial Arithmetic, in Two Parts (New York: Oakley and Mason, 1865). Historical arguments about the relationship between “democracy” and “capitalism” are extensive, wide- ranging, and sometimes heated. This chapter basically accords with the argument, most famously articulated by Gordon Wood in “The Enemy Is Us: Democratic Capitalism in the Early Republic” Journal of the Early Republic, Vol. 16, No. 2 (Summer, 1996), pp. 293-308, that capitalism in early America can be understood, at least in part, as a bottom-up social formation, driven by ordinary people trying to get ahead, rather than by already powerful elites. In the case of arithmetic, this argument helps explain why so many people read and used the textbooks described 77 In embracing the idea that all arithmetic was practical, textbooks collapsed mathematical and commercial knowledge into a single form of human reasoning. Fellowship, interest, discount, annuities, and other commercial practices built from social relations, economic risks, or political power mixed with addition, proportion, and ratio in schoolbooks. The separation of economic ideas and mathematical rules disappeared, as each became the other. This process did not happen out of sight or mind: it was embraced, almost fetishized in arithmetic textbooks as they boasted of their practical, utilitarian credentials. The idea that individuals should be constant calculators became central to arithmetic textbooks. They taught Americans to think mathematically about “business,” turning the exchange of goods and labor for money into a mathematical process. However, contests over how to teach mathematics revealed a problem in the arithmetic market. People like Patterson’s correspondent did not only trust their own calculations; they also wanted objective rules to hold others accountable. They thus raised the question: in an increasingly caveat emptor market, did authority lie in the individual, or the community? Should a man trust his own calculations, or could he assume others would follow the same mathematical rules that he did? While American intellectuals advocated the marriage of theoretical science and practical work to determine what kinds of mathematics to teach, this debate over how to teach mathematical skill, particularly arithmetic calculation, revealed a more fundamental tension in the roots of the mathematical economy. Although almost no one disputed the basic claim that all children should learn arithmetic, two distinct pedagogies emerged: one based in rules, the other in intuition. Both herein. It does not follow, of course, that the result necessarily benefited these people, but the idea helps explain the popularity of arithmetic. See also Caitlin Rosenthal, “Numbers for the Innumerate: Everyday Arithmetic and Atlantic Capitalism” Technology and Culture, Volume 58, Number 2, April 2017, pp. 529-544. 78 claimed superiority in teaching children useful skills, but they embodied different ideas about how Americans should consider their positions in an increasingly numerical marketplace. Those who advocated for “mental arithmetic” in the middle decades of the nineteenth century argued that arithmetic came naturally to children, and accorded with their intuition. But others maintained that people needed a rule-based pedagogy to maintain the communal standards that Patterson’s correspondent implicitly called upon in his letter. Each implied a fundamentally different view of economic participation, even as arithmetic and commerce became synonymous. Even as the useful knowledge economy obscured the difference between making and using mathematics, antebellum commercial arithmetic muddled the meaning of calculation itself. Arithmetic in the New Nation By the time Patterson received his letter in 1826, arithmetic had become a major cultural and pedagogical fixation for Americans. Textbooks, curricula, commentators, and educators began to treat arithmetic as the fundamental way by which children would learn necessary commercial knowledge. Whatever debates they may have had around the appropriateness of a mathematical education for children in geometry and algebra, almost no Americans disagreed about the utility of arithmetic for commercial purposes. Even Thomas Smith Grimké, who wanted the elimination of almost all mathematics from American schools, admitted that he would “retain so much of common arithmetic, as it is valuable for the business of life.”3 After being relatively little learned in eighteenth-century curriculum, the “science of figures” took center stage in the early nineteenth 3 Thomas Smith Grimké, Oration on American Education, Delivered Before the Western Literary Institute and College of Professional Teachers, at their Fourth Annual Meeting, October, 1834 (Cincinnati: Josiah Drake, 1835). 79 century conversation about how to prepare students for national economic and civic participation, as Americans grappled with the role of mathematics in their society. The useful knowledge economy of antebellum America emphasized the practical counting and algebraic skills of applied mathematics over the prestigious, but largely abstract, geometrical reasoning of an earlier pedagogy. Arithmetic, the execution of computational operations (adding, multiplying) on concrete numbers, had long been considered distinct from mathematics, as it did not share the non-numerical, proof-based deduction of geometry. But as Americans came to value mathematics for its practicality and not for its reasoned prestige, they also began to envision arithmetic as just as mathematical as any other field. Indeed, many began to argue that it could be just as valuable for training children’s logical faculties. Early American mathematics valued any effort to elevate fields that Europeans (they believed) considered common and vulgar. Some even began to argue that geometry held too much pedagogical influence, when arithmetic was “no less effectual” in the pursuit of right-reasoning.4 Rather than the computational exercise it had been in the prior century, arithmetic no longer needed to “fear comparison with her more favored sister.” In precision, utility, certainty, and even in “the sublime deductions of the most interesting truths,” arithmetic could lead to right-reasoning just as effectively as geometry.5 The idea that arithmetic calculation should be as widespread in education as basic literacy and writing skills did not emerge in North America until the early nineteenth century.6 Even in the northeastern district schools of the late eighteenth century, arithmetic was not taught during regular 4 Alfred Holbrook, The Normal: or Methods of Teaching the Common Branches, Orthoepy, Orthography, Grammar, Geography, Arithmetic, and Elocution (New York: Barnes & Burr, 1860). 5 Roswell C. Smith, Practical and Mental Arithmetic on a New Plan (Philadelphia: Marshall Clarke & Co., 1833). 6 Cohen, A Calculating People (1982), pp. 118-123. 80 hours. If students wanted to learn arithmetic or mathematics, they had to petition the schoolmaster to hold additional evening hours.7 In general, teachers believed that arithmetic was too difficult for children younger than twelve to learn, especially in a classroom setting. As a result, most were reluctant to teach it except to a small group of students who had already professed their interest in the subject. If students could not persuade their schoolmaster to hold these “cyphering schools,” they would either have to either acquire a private tutor, or attend a private academy after the age of twelve. Otherwise, they went without further mathematical education. Bronson Alcott, born in Massachusetts in 1799, recalled that in his boyhood, “no studies have been permitted in the day school but spelling, reading, and writing” and that arithmetic was taught only by select instructors one or two evenings a week. But despite “the most determined opposition,” he observed as an adult that “arithmetic is now permitted in the day school.”8 The emergence of the useful knowledge economy created a major shift in attitudes toward the study of arithmetic in the United States. Rather than an unrefined and menial task confined to the counting house, arithmetic began to seem like a useful tool for training citizenship in the new republic. If American mathematical education would focus on the practical over the speculative, then nothing could be more central for its youngest learners than the building blocks of numerical calculation. In discussing the cultural tools used to educate children into good American citizens, historians have overlooked arithmetic in favor of reading, writing, and spelling.9 But widespread arithmetic 7 “Evening Studies” The American Annals of Education (Feb 1834), p. 276. 8 Alcott quoted in Florian Cajori, The Teaching and History of Mathematics in the United States (Washington: GPO, 1890), 9. 9 See for example, Jill Lepore, A Is for American: Letters and Other Characters in the Newly United States (New York: Vintage Books, 2007); Margaret A. Nash, “Contested Identities: Nationalism, Regionalism, and Patriotism in Early American Textbooks” History of Education Quarterly Vol. 49, No. 4 (November 2009), pp. 417-441; Lorraine 81 education emerged in the early republic, and was deeply influenced by the political and economic concerns that attended the cultural project of nation building. In the burgeoning print culture of the early republic, arithmetic textbooks joined other print media—such as newspapers, broadsides, and literature—in establishing American nationalism.10 Arithmetic textbooks proliferated in the publishing free-for-all of the early 1800s. The domestic print market allowed professors, schoolteachers, accountants, engineers, and mechanics to present their expertise in the teaching of arithmetic. Each argued that their way of teaching the subject was the most practical, the most useful, and would prepare students most effectively for a life “in business,” while also bolstering their moral character. In 1799, the first copies of Nathan Daboll’s Schoolmaster’s Assistant were published; it would become one of the most popular arithmetic texts in the nineteenth century, going through repeated updates and re-editions until after the Civil War. Domestically published arithmetic textbooks provided yet another way that the United States could distinguish itself from England. Just as the new nation’s coterie of mathematicians had set out to produce domestic translations of classic European texts, its more common educators and citizens sought to educate the populace in distinctly American arithmetic. Smith Pangle and Thomas Pangle, The Learning of Liberty: The Educational Ideas of the American Founders (Lawrence: University of Kansas Press, 1993); Bernard Bailyn, Education in the Forming of American Society (New York: Random House, 1960). For a larger retrospective on early republican education, see Siobhan Moroney “Birth of a Canon: The Historiography of Early Republican Educational Thought” History of Education Quarterly Vol. 39, No. 4 (Winter, 1999), pp. 476-491. 10 This literature is vast, but see: Trish Loughran, The Republic in Print: Print Culture in the Age of U.S. Nation Building, 1770-1870 (New York: Columbia University Press, 2007); Frankel Oz, States of Inquiry: Social Investigations and Print Culture in Nineteenth-Century Britain and the United States (Baltimore: Johns Hopkins University Press, 2006); Francois Furstenberg, In the Name of the Father: Washington’s Legacy, Slavery, and the Making of a Nation (New York: Penguin Random House, 2007); David Waldstreicher, In the Midst of Perpetual Fetes: The Making of American Nationalism, 1776-1820 (Chapel Hill: University of North Carolina Press, 1997); Jeffrey L. Pasley, “The Tyranny of Printers”: Newspaper Politics in the Early American Republic (Charlottesville: University of Virginia Press, 2002); Lara Langer Cohen, The Fabrication of American Literature: Fraudulence and Antebellum Print Culture (Philadelphia: University of Pennsylvania Press, 2011). 82 Nowhere was the emphasis on nation-building clearer in arithmetic textbooks than in their fixation with the new federal money. Most American arithmetic textbooks, especially from the early nineteenth century, boasted in their titles that their system was “adapted to federal money” or the “federal currency”—and specifically that the text would present the new currency with decimals, thereby doing away with the painful calculations of the eighteenth century based in the various denominations of the English pound, which turned simple commercial problems into arithmetic nightmares. The argument for a decimal currency, based in powers of ten, was advanced as early as the 1790s. Erastus Root, in his An Introduction to Arithmetic for the Use of Common Schools, argued that the new nation should abandon the old “British intricate mode of reckoning”: “Let them have their own way—and us, ours.” Root advocated for a decimal system of currency because, as he put it, “Republican money ought to be simple, and adapted to the meanest capacity.” Marrying currency to decimal fractions, as many textbooks did, linked simple, republican currency with simple, republican calculations for commercial ease and utility.11 Arithmetic education invested heavily in language of independence and self-ownership, in both politics and economic life. Early arithmetic educators proclaimed that their discipline would imbue young Americans with the ability to think independently, essentially bringing the benefits of a mathematical education to the nation’s youngest citizens. If children were going to grow up into successful participants in the commercial prosperity of the nation, advocates argued, they had to begin learning mathematical building blocks at an early age. To that end, American arithmetic textbooks, particularly from the 1820s onward, devoted themselves almost entirely to explaining 11 Erastus Root, An Introduction to Arithmetic for the Use of Common Schools (Norwich, CT: Thomas Hubbard, 1796). 83 the subject through commercial examples. Arithmetic problems were those about commerce, and business principles explained through arithmetic. Just as mechanical mathematics in early America proposed to harness mathematical utility by teaching the working man the theory behind his labors, arithmetic promised self-ownership in an increasingly market-oriented nation. Efforts to develop a robust curriculum in arithmetic therefore linked the nation-building project of early American education to the socioeconomic goals of the useful knowledge economy. Arithmetic’s civic importance meant that it was taught to almost all schoolchildren, even those for whom its commercial focus seemed less useful. The evening classes that had taught arithmetic during the eighteenth century admitted both boys and girls, and that tradition continued into the next century. In 1820, the New York Free Schools stipulated that the arithmetic taught in the boys’ school “is applicable in all its parts to the girls’.”12 By midcentury, even conservatives agreed that women “should understand Practical Arithmetic, though not Mathematics.”13 This consensus meant that schools taught arithmetic to girls through the lens of commercial practice. A Philadelphia student, Martha Penrose, had the problem, “How much barley at 30 cents per bushel rye at 36 cents and wheat at 48 cents must be mixed with 12 bushels of oats at 18 cents to make a mixture worth 22 cents per bushel?”14 If “every female” was to have “considerable acquaintance 12 “Manual of the Lancastrian System of Teaching Reading, Writing, Arithmetic, and Needle-Work, as Practiced in the Schools of the Free-School Society of New York” New York: Published by Order, and for the Benefit of the Free School Society. Samuel Wood and Sons: 1820. Library Company of Philadelphia (Philadelphia, PA). 13 “Bedford Female Academy” Richmond Enquirer, 3 November 1837 p. 1. 14 Martha T. Penrose Ciphering Book, 1832. Historical Society of Pennsylvania (Philadelphia, PA). 84 with Arithmetic,” as part of the larger effort to build an industrious and virtuous American nation, then schoolgirls would learn arithmetic through bushels of barley.15 The arguments for women learning arithmetic sometimes included an acknowledgement that, under certain circumstances, women might have to perform some bookkeeping or commercial transactions, whether to best assist their husbands, or in the unlikely event of becoming feme sole traders.16 But some insisted that “females bitterly complain” about learning arithmetic. 17 Others claimed that they had never met a woman who was “either fond of arithmetic, or the least proficient in that invaluable science.”18 These observations suggest that the commercialization of arithmetic made it a dispiriting pursuit for female pupils. Catherine Beecher complained that students at the Hartford Female Seminary deemed arithmetic “the most difficult and abstruse subject,” and she struggled to convince her female students of its benefits.19 But part of the fault was likely her own. Beecher admitted that “in most cases a lady finds but little use for any but the simpler rules of arithmetic.” Yet female students never encountered problems outside of the commercial paradigm; even Beecher’s own Arithmetic Simplified, explicitly intended for female students, used problems of currency exchange, interest, discount, fellowship, and annuities. 15 Joseph Emerson, “Female Education, a Discourse, Delivered at the Dedication of the Seminary Hall, in Saugus, Jan. 15, 1822” (Boston: Samuel T. Armstrong, 1822). 16 Becker, A Treatise on the Theory and Practice of Book-Keeping by Double Entry (1847). On women merchants, see Patricia Cleary, “She Merchants” of Colonial America: Women and Commerce on the Eve of the Revolution (Chicago: Northwestern University Press, 1989); Ellen Hartigan-O’Connor, The Ties That Buy: Women and Commerce in Revolutionary America (Philadelphia: University of Pennsylvania Press, 2009). 17 Becker, A Treatise on the Theory and Practice of Book-Keeping by Double Entry (1847). 18 “Female Education, Its Importance, and In What It Should Consist” Common School Assistant (Jun 1839): 43. 19 Catherine Beecher quoted in Cohen, A Calculating People, pp. 145-146. 85 Of course, Beecher must have known that her “ladies” had servants, men and women, who would need to have some calculative knowledge to represent their mistresses and households at the market, and in some cases to keep the family account books. But in general, as in conversations about mathematics education generally, rationales for mass education in arithmetic tended to elide conversations about class, identity, and labor, instead suggesting the fair distribution of economic practice and power through mathematical knowledge. Arithmetic’s appeal to the new nation lay in both its simplicity and its power to encourage reason in what one natural science professor called “the only rational, political association on the globe.”20 Rather than prepare children for a specific profession, or improve their competency in it, arithmetic began to seem like a more elemental skill. For this reason, it became central to children’s education. By 1850, Benjamin Greenleaf, principal of the Bradford Teachers’ Seminary in Massachusetts, could state that “Arithmetic is, and ever must be, a very important branch of study pursued in all our schools. Probably no subject receives so much attention, or consumes so much of the time, of the pupil, as this.”21 The fascination with arithmetic education in antebellum America both stemmed from and redefined the useful knowledge economy. Though European mathematicians might have had some qualms about thinking about arithmetic calculation as a branch of mathematics, Americans did not share this attitude. On the contrary, Americans defined mathematics primarily by its utility, not its classical origins, and as nothing was more useful than arithmetic, it cleared the bar. But arithmetic 20 “Natural Science in Common Schools: Essay on the Introduction of the Natural Sciences Into Common Schools. Read at the Meeting of the American Lyceum, in May, 1833, by Prof. Dewey, of Pittsfield” American Annals of Education (July 1835), p. 304 21 Benjamin Greenleaf, The National Arithmetic, on the Inductive System; Combining the Analytic and Synthetic Methods, Together with the Canceling System; Forming a Complete Mercantile Arithmetic (Boston, 1850). 86 also seemed even more fundamental to the American political project. Not only was it elemental to the mathematics of the useful knowledge economy, it was itself an essential skill for American citizens, boys and girls alike. Above all, arithmetic seemed to provide the skills to participate in commercial life. Unlike the specialized skills of the carpenter or millwright, arithmetic offered the ability to survive and thrive in an increasingly market-oriented society. Having long been a key skill for anyone working in a counting house, arithmetic remained fundamentally commercial even as it became part of the general education.22 In this, arithmetic augmented the interdependence of mathematics and business developing in antebellum economic life. “Designed as a practical work” In 1822, Uriah Parke, a Virginia schoolteacher, published The Farmers’ and Mechanics’ Practical Arithmetic through a local publisher. The book, he explained in its preface, had been “especially designed as a practical work; calculated to meet the wants of the man of business.” His reasoning for adding to the nation’s extant collection of arithmetic textbooks was “this class of our citizens” rarely had “sufficient leisure to acquire an extensive knowledge of Mathematics” and needed an “abridged course” in a cheap, accessible form.23 That arithmetic should be primarily business oriented, for all classes of citizens, had become educational orthodoxy by the 1820s. But among the flood of arithmetic handbooks, they differed relatively little in content. Most textbooks presented an image of “business” that had more to do with an idealized market than with concrete information about a specific profession or about the workings of a particular economic sector. 22 On the long, European history of commercial arithmetic, see Natalie Zemon Davis, “Sixteenth-Century French Arithmetics on the Business Life” Journal of the History of Ideas Vol. 21, No. 1 (Jan. - Mar., 1960). 23 Uriah Parke, The Farmers’ and Mechanics’ Practical Arithmetic (Winchester: Samuel H. Davis, 1822). 87 Rather, by explaining “business” through computational rules, books like Parke’s homogenized Americans’ economic experiences into a single conceptual model. The profound interdependence between arithmetic textbooks and commercial knowledge in antebellum America defined a key aspect of the emergent mathematical economy of nineteenth century America. Debates over the purpose of learning mathematics as a wider discipline revolved around concurrent disagreements about the nature of work, science, class, and national prosperity. But arithmetic textbooks contained none of these vagaries. From the 1820s until at least the 1860s, every arithmetic textbook for American children emphasized the utility of arithmetic in what was most often called “business life” or “a life in business.” From early textbooks’ emphasis on federal decimal money, through hundreds of textbooks in the following decades that uncritically combined arithmetic calculation with commercial terms and rules, arithmetic became the American science. Until at least the Civil War, it remained a subject about which educators and commentators fought vehemently, because its importance and utility was apparent to all. Antebellum textbooks authors sometimes admitted that “treatises of Arithmetic have not been wanting” in recent years, but each promised greater clarity, accessibility, and utility.24 And yet, while arithmetic textbooks inundated the American market, they actually varied quite little in terms of their content, at least until the 1870s. Tables of contents delineated some combination of: definitions; numeration; addition, subtraction, multiplication, and division; bills of parcels and book debts; compound arithmetic; the ever-present Rule of Three; vulgar fractions and decimals; simple and compound interest; commission and brokerage; discount; equation; barter; profit and 24 B. Bridge, The Southern and Western Calculator: or, Elements of Arithmetic Adapted to the Currency of the United States. For the Use of Schools (Philadelphia: Key and Mielke, 1831). 88 loss; single and double fellowship; alligation (weighted averages); arithmetic and geometric progressions, or series; permutations and combinations; involution and evolution (exponents and logarithms); finding square and cube roots; duodecimals (decimals in base twelve rather than ten); mensuration; and exchange in currencies, weights, and measures. Essentially no textbooks made any distinction between “pure” and “practical” arithmetic knowledge, and thus did not distinguish between which were laws of mathematics, and which of economic life. The organization of nineteenth century arithmetic textbooks did not vary greatly, despite their authors’ frequent claims of originality. Each section usually began with a rule, followed by its explanation, and then a series of practical problems for the student. Some, especially those published earlier in the century, might include a rigorous proof, but most authors did not consider proofs necessary for students. Utility in business was their primary concern, not rigor.25 Many assumed no prior knowledge of arithmetic, and began with the symbols +, —, x, and ÷, explaining each in turn. When commercial concepts appeared, some would be explained in detail, especially when expanding on another, simpler concept (e.g., the relationship of double fellowship to single), but often authors seem to have expected that their readers knew what interest, annuities, alligation, and fellowship meant—or else assumed that children would learn the arithmetic and pass over the concepts, while also making the book useful to innumerate adults. Despite political enthusiasm for 25 Earlier textbooks, as well as re-prints of English texts, are more likely to include “proofs” or “demonstrations”; see, for example, Benjamin Workman, The American Accountant; or, Schoolmasters’ New Assistant (Philadelphia: Printed for William Young, 1793); Samuel Webber, Mathematics, Compiled from the Best Authors, and Intended to be the Text Book of the Course of Private Lectures on These Sciences in the University of Cambridge Second Edition (Cambridge: William Hilliard, 1808); James Robinson, Jr., The American Arithmetick: In which the Science of Numbers is Theoretically Explained and Practically Applied (Boston: Lincoln & Edmands, 1825). 89 decimal currency, many textbooks continued to set problems in both American federal money and British pounds sterling, a feature that lasted well into the nineteenth century. That arithmetic would be the science of business, and therefore that business would be no more complex or unpredictable than arithmetic, found expression in every American arithmetic textbook of the antebellum period. Economic utility was the ultimate object of arithmetic. Parke explained that the rules in his textbook were “generally simple” and any more complicated ones had been omitted, “not because they were difficult, but because a knowledge of them is no use to any person in common business.”26 Textbooks laid out arithmetic rules “to correspond with the occurrences in actual business,” and to present “fully the appellations of arithmetic to actual business.”27 As appetites for arithmetic expanded, textbooks drew less and less distinction between which rules belonged to arithmetic and which to business. Some would reject certain concepts based on an individual author’s prejudice, but in general, textbooks erased any explicit distinctions between arithmetic concepts and commercial concepts. In doing so, they contributed to the cultural work of defining antebellum “business” and the commercial marketplace. In the eighteenth century, when American children learned arithmetic, they did so through a series of rules. Young Robert Bailey wrote in his commonplace book that arithmetic “shews the dependence of one Rule upon another throughout the work.”28 No rule held more importance than 26 Parke, The Farmers’ and Mechanics’ Practical Arithmetic (1822). 27 Smith, Practical and Mental Arithmetic (1833); E.E. White et al, Bryant and Stratton’s Commercial Arithmetic, in Two Parts (New York: Oakley and Mason, 1865). 28 Robert Bailey School Book, Box 1, Volumes 1-6. Historical Society of Pennsylvania Schoolbook Collection, 1710-1872. Historical Society of Pennsylvania (Philadelphia, PA). 90 the “Rule of Three,” sometimes called the “golden rule.”29 The way eighteenth century children learned the Rule of Three looks impenetrable to modern eyes because it relied on a pedagogical logic that privileged rules over reason. It was, simply, a “method of finding a fourth proportional from three numbers given.” Students today would probably solve these problems through cross multiplication, but for eighteenth century merchants, these questions were too important, given the variety of units involved in a single transaction, to be done with mathematical reasoning, which they believed beyond the comprehension of an ordinary counting house assistant. Instead, everyone preparing for a career in mercantile trade learned the Rule of Three. In its simplest form, it read: “Multiply the second and third terms together, and divide their product by the first: the quotient is the answer of the same name and kind with the second.”30 What did that mean? Take, for example, the problem: “If 3 yards cost 9 shillings, what will 6 yards cost, at the same rate?” Under the eighteenth-century method, the problem had to be set up just so, and each figure in the problem would be assigned a term number; in this case, 3 is the first term, 9 is the second term, and 6 is the third. Students were instructed to lay out these numbers in a dedicated form, so that they would not forget which term was which: 29 For a recent, complete treatment of the widespread use and appeal of the Rule of Three in the early and antebellum Atlantic world, see Caitlin Rosenthal, “Numbers for the Innumerate: Everyday Arithmetic and Atlantic Capitalism” Technology and Culture, Volume 58, Number 2 (April 2017): 529-544. 30 Benjamin Workman, The American Accountant; or, Schoolmasters’ New Assistant (Philadelphia: William Young, 1793). 91 Figure 1. Example of Rule of Three from Benjamin Workman, The American Accountant or, Schoolmasters’ New Assistant (Philadelphia: William Young, 1793) Then, according to the Rule, the student would multiply 9 and 6 (the second and third terms) to get 54, and then divide by 3 (the first term), to get the answer, 18—or, more precisely, 18 shillings.31 Assuming a student lays out the problem correctly, only a few simple calculations had to be done. Most crucially, he would not need to think about why the answer works out, or why he did the operations in that order. According to the logic of the time, that lack of “reasoning” was the primary appeal of the Rule of Three—the rule would produce the right answer, and the merchant could move on with his business. The same logic applied to all arithmetic teaching: one rule dependent on the next. In the Rule of Three as in the rest of arithmetic, rules demonstrated the general perception of arithmetic as a primarily mechanical, rather than reasoned, form of thought. Its purpose was to get to an accurate answer, not to understand the process. The first American textbooks of the nineteenth century tended to follow the same thought process that had informed eighteenth century arithmetic education. Authors still organized each 31 Because of the immense import of keeping units straight (in this as in all applied mathematics), the Rule of Three is designed so that the quotient has the “same name and kind with the second” term, meaning that the problem must always be arranged so that the answer will share the unit (in this case, shillings) of term in the middle position. 92 section of their textbooks by introducing the rule, sometimes giving an explanation of the rule’s derivation, and then explaining how and when to apply the rule. Some rules, like the Rule of Three, were calculative instructions, but others were more like numerical tricks. Daboll's Schoolmaster recommended finding interest with the rule: “Multiply the shillings of the principal by the number of days, and that product by 2, and cut off three figures to the right hand, and all above three figures will be the interest in pence.”32 A theoretical understanding of the subject did not seem necessary to early national educators. Rather, given arithmetic’s close association with the counting house, the central imperative remained to get an accurate answer as quickly as possible. Understanding the process was a project for geometry, and for those who had the time and resources to study it. Arithmetic meant finding an answer and moving on to the next calculation. Certainly, people employing these rules in “practical business” had to set up the problems correctly, which required some knowledge of how the rules operated. But for the most part, they assumed that calculators had no way to intuit whether the answer made sense or not. They could get an accurate answer, but they would not know, in any genuine sense, that the answer was correct. Arithmetic education based in rules represented an older commercial world in which computation was understood to be inherently different than mathematical reasoning. But as Americans began to reframe the relationship between reasoning, mathematics, and calculation in the first half of the nineteenth century, ideas about how children should learn arithmetic shifted. Some began to argue that rule-following alone was insufficient for a nation of independent citizens. Given arithmetic’s place as a science of commerce, moreover, the pedagogical arguments that emerged over the nature 32 Samuel Green, Daboll’s Schoolmaster’s Assistant (Utica: Gardner Tracy 1837). 93 of arithmetic reasoning after the 1820s necessarily shaped concurrent hopes and fears about how Americans should navigate their increasingly market-oriented lives. “He could not put the fat under any rule” The idea that American children were not thinking enough about their mathematics did not first emerge in the antebellum decades. Indeed, educators’ frustration with their students’ lack of retention, and a desire for a pedagogy of arithmetic that relied less on memorization and more on reasoning, reach back into the eighteenth century. In 1797, Thomas Jefferson received a letter from “Academicus” who complained that, “with respect to the method of teaching Arithmetic,” he often saw boys who had devoted long hours to going through the “common rules” and proven “very ready in the use of numbers… agreeably to the rules and down in their books.” But when he asked these boys to apply their lessons, he found their knowledge was now so poor, it was as though “they had never known figures” at all. Academicus blamed this situation on a “wont of a sufficient knowledge of the reasons of these rules.”33 Nevertheless, it would take another two decades for arithmetic to become a focal point of American education, and for a pedagogy to emerge that put knowing “the reasons of these rules” at its forefront. If any person can be credited with starting the shift in the pedagogical discourse around arithmetic in antebellum America, it would be Warren Colburn. Colburn had worked in factories and as a machinist in southern Massachusetts during his early life, but in 1816, at the age of twenty- three, he enrolled at Harvard University to study mathematics. Upon graduating, he wrote a text- 33 “Academicus” to Thomas Jefferson, “Plan for the Education of Youth” c. 1797. Box 1: A-Col, American Philosophical Manuscript Communications. American Philosophical Society (Philadelphia, PA). 94 book in arithmetic for a friend who taught at a female academy. Impressed, his friend encouraged Colburn to get the book published, thinking others might want to use it. In 1821, the textbook was published with the title First Lessons in Arithmetic. It was an instant success. Contemporaries and historians alike pointed to it as having a massive impact on American education, becoming central to schools nationwide. One estimate from the late nineteenth century suggests it may have sold upward of three and a half million copies.34 Colburn’s “excellent little work,” as one contemporary described it, did not look like a revolution, but its impact was enormous.35 At the heart of First Lessons lay a fundamental reversal of rule-based education. Rather than set out to explain to a pupil what arithmetic is, as most textbooks did, it began by asking what likely seemed to most children to be very simple questions: “How many thumbs have you on your right hand? How many on your left? How many both together?” From there, it then asked, “John gives one apple to his sister, and one apple to his cousin; how many apples did he give away in all?” and “If you take away one of two books, how many will remain?”36 First Lessons guided students toward an understanding of arithmetic not by explaining rules, but by emphasizing their intuition. First Lessons took as its premise the idea that humans, including as children, were natural calculators. To many, the potential impact of this strategy was extraordinary. Supporters enthused that Colburn’s work could enable children as young as seven to solve arithmetic problems, without 34 Cajori, The Teaching and History of Mathematics (1890); Cohen, A Calculating People (1982). 35 “First Biennial Report of the Trustees and Instructer of the Monitorial School, Boston” (Boston: Wait and Son, 1826). One commentator also noted that Colburn’s First Lessons had come to him “highly recommended by Professor Farrar of Cambridge” which he in turn recommended to others. Joseph Emerson, “Female Education, a Discourse, Delivered at the Dedication of the Seminary Hall, in Saugus, Jan. 15, 1822” (Boston: Samuel T. Armstrong, 1822). 36 Warren Colburn, First Lessons in Arithmetic on the Plan of Pestazzoli with Some Improvements (Cummings, Hilliard & Company: Boston, 1825); Cajori, The Teaching and History of Mathematics (1890). 95 a slate, “which would exceed the powers of many a decent scholar of fifteen.” With Colburn, they insisted, the pupil “has learned and understood the reasons of the operations.”37 First Lessons suggested that arithmetic was the numerical science that most closely aligned natural human reasoning. In subsequent years, the argument that arithmetic could be taught to very young children became omnipresent, on the grounds that their intrinsic reasoning abilities would allow them to understand it. Educators, textbook authors, and commentators argued that, rather than being inherently difficult, basic calculation was simple, and should be taught to children as early as possible. Effective manuals and other teaching aids would make “the youngest persons capable of giving attention to the fundamental truths of mathematics” and thereby gain “accurate knowledge of the inherent elements” of the science.38 Rather than lead with rules, many textbooks began to gravitate toward Colburn’s method of beginning with questions. Even the Rule of Three was not safe from reform. “What will 3 yds of cloth come to at 20 cents a yard?” one text asked at the start of its section on proportions. “What will 5 yards? Will 7? 8? 12?”39 Only after the pupil was to have figured out the proportions on his own, did the textbook explain the principle behind finding the answer in every case: the ratio or proportion of the first and second numbers must match that of the third and the unknown. According to the author, this method was “thought to accord with the natural operations of the human mind.”40 This pedagogy sought to push back on the reasoning that students and young clerks had been asked to perform in 37 “Natural Science in Common Schools” American Annals of Education (July 1835), p. 304. 38 “Circular to the Visitors of the Franklin Institute” 1850 (Library Company of Philadelphia, Philadelphia PA). 39 Smith, Practical and Mental Arithmetic (1833). 40 Ibid. 96 the past, in which they had strung rules together based on instruction rather than a fundamental understanding of the calculations at hand. The pedagogical methods that became popular in the years following the publication of First Lessons came to be known as “mental arithmetic.” Those educators who subscribed to this philosophy believed that ultimately, students would be able to do arithmetic problems without copying them onto a slate. That is, children—and the adults that they would eventually grow into—would be able to think through arithmetic problems completely in their heads. They, not the textbooks, would hold calculative authority. This shift in arithmetic education, from a pedagogy based primarily in rules to one that attempted to teach students the reasoning behind those rules, has been briefly noted by those few historians of early American mathematical education, but little analyzed.41 Meanwhile, historians of early American economic life have often preferred to examine the capitalist self-discipline that such texts taught Americans of various ages.42 But the shift from “rules” to “reason” in arithmetic education, especially when placed in the context of arithmetic textbooks’ heavy emphasis on the necessity of the subject in economic life, sheds light on a widespread struggle to articulate how a person should best participate in economic life. The argument that arithmetic should be employed to improve children’s reasoning faculties is difficult, if not impossible, to extract from arguments 41 One such example is: National Council of Teachers of Mathematics, A History of Mathematics Education in the United States and Canada (Washington, DC: NCTM, 1970), pp. 25-26. 42 Discipline, especially through book-keeping, has been central to American historians’ growing understanding of the role that numbers and calculation played in the establishment of industrial capitalism, in how economic rationality had to be taught. See Michael Zakim, “Producing Capitalism: The Clerk at Work” and Jean-Christophe Agnew, “Afterword: Anonymous History” in Zakim and Kornblith, Capitalism Takes Command: The Social Transformation of Nineteenth-Century America (Chicago: University of Chicago Press, 2012); Caitlin Rosenthal, “From Memory to Mastery: Accounting for Control in America, 1750-1880,” Enterprise & Society (December 2013); Brian Luskey, On the Make: Clerks and the Quest for Capital in Nineteenth-Century America (New York University Press: New York, 2010). 97 about how an arithmetic market should operate. In arguing about whether students should prioritize rules or reason, they also debated how to think about economic life. The idea that there was something inherently natural about arithmetic calculation, nearly unknown in the eighteenth century, expanded rapidly in the 1820s and 1830s. New textbooks emphasized that arithmetic was a reasoned and deductive science, and that its “truths and principles should be derived by logical processes” based in perfect accuracy. Throughout the antebellum period, the role of arithmetic as “a fine field for the cultivation of the reasoning faculties” in children supplemented its earlier purpose as solely a means of understanding the commercial world. Textbook authors disagreed on certain pedagogical points, especially surrounding the role of “rules” in how students learned mathematical principles. But even then, nearly all accused their opponents of not preparing students for a business life as well as they could. Even more so than deciding what mathematics to teach, deciding how to teach it occupied an enormous amount of space in the minds of everyone with opinions about American education. “The study of mental arithmetic is introduced into our schools more and more, each succeeding year,” one commentator observed in 1848, in one of the nation’s many new journals dedicated to education. “From the nature of the exercise it is interesting to all pupils.”43 The new philosophy dictated that if arithmetic was going to be practical, it had to be based in intuition, not memorization. “How can they expect that such great knowledge will be of any use?” another writer demanded of rule-based arithmetic. “The great thing aimed at with teachers, seems to be the ready recitation of the rule from memory, rather than the ready application of it to practical purposes.”44 43 B.N.S., “Mental Arithmetic” Common School Journal (Jan 15, 1848), p. 22. 44 “Study of Arithmetic, No. II” Common School Assistant (Sep 1836): 70. 98 If arithmetic was supposed to be practical, which had long been orthodoxy, and if it did align with the “natural operations of the human mind,” and if not learning it properly would set a person up for failure in later life, then how to best teach arithmetic became a passionate subject for teachers, parents, and pedagogues alike. Colburn held significant appeal: he introduced a new, individualist ethos into a subject whose importance was universally recognized, but had previously relied on what many now viewed as the seemingly arbitrary authority of rules. The introduction of mental arithmetic into American arithmetic education also changed the relationship between arithmetic calculation and expectations for economic life. Whereas in the prior century, arithmetic had been used as a tool for obedience and accuracy, proponents of the new methods emphasized how much more effectively business would operate if everyone became familiar with mental calculations, and used their inherent intuition in commercial life rather than following external rules. They argued that commerce was no longer only the province of a few urban merchants, and therefore, neither was mathematical reasoning. In a universal marketplace, advocates said, businessmen needed to think mathematically. The idea that humans were natural calculators contributed to the growing idea that every adult would be involved in business, in one way or another. It would not be enough to learn the right rules and apply them correctly when the need arose, many now argued. Children needed to be taught arithmetic in a way that trained them to think like businessmen, so they would all prosper in their future lives. The idea of using reason and intuition in commercial transactions, moreover, seemed to fit with some Americans’ view that the market was a dynamic place that required more than a simple, static computation. One author in the Common School Assistant, a journal aimed at schoolteachers, related a cautionary tale about a young man of seventeen who boasted that he, having gone through 99 Daboll’s three times over the winter, could “do any sum in the hardest ciphering book you can bring.” Amused, the author did not disagree; he told the boy that “did not doubt but what he could mechanically obtain the answer of almost any sum he could find in a book, set down under a rule.” Instead he asked, “What will 20 pounds of beef come to at 12 cents per pound, provided the beef is two-thirds fat?” The boy protested the new information, and ultimately proclaimed that he had been given an “unfair sum” unlike any in a book. His tormenter concluded triumphantly that the “unfortunate lad had never brought the business of the world on to the slate… No: that two-thirds fat he could not understand—he could not put the fat under any rule.”45 Proponents of mental arithmetic insisted that “men in business scarcely recognize any other” while at work. They claimed that businessmen eschewed “formality of statements” except when they needed to double-check something they had figured out for themselves using practical reasoning.46 Arithmetic became another useful subject in which “practice should be blended with the theory” and serve both “the cultivation of the reasoning faculties” and children’s education as reasoned, prosperous citizens.47 Far from being seen as the difficult and painful calculations of the eighteenth century, by the 1840s Americans understood arithmetic as both naturally in accordance with the human mind, and the means by which business operated. Double-entry bookkeeping and other commercial tools emphasized the stability of the marketplace, teaching self-discipline and homogenizing transactions into impersonal exchanges. But proponents of mental arithmetic, while many certainly saw the market as a natural and beneficial organizer of human behavior, also saw 45 “Study of Arithmetic, No. III” Common School Assistant (Oct 1836): 73. 46 Smith, Practical and Mental Arithmetic (1833). 47 Parke, The Farmers’ and Mechanics’ Practical Arithmetic (1822); Holbrook, The Normal, or: Methods of Teaching (1860). 100 it as a space of constant movement and complexity. They considered it a place of opportunity, so long as participants always remained attuned to the fat in the meat. Not everyone preferred these new methods, however. Some argued that people, especially children, were not capable of figuring out mathematical rules on their own, and greatly needed the intervention of organization and authority. “Some writers would have us dispense with all rules in arithmetic, and give us nothing but a book filled with examples, leaving the pupil to make the rule and determine what examples come under them,” teacher B. Bridge fulminated. “The present writer does not adopt this plan, because he doubts very strongly whether the pupil, if left to himself, will make the necessary rules, or arrange and fix the principles systematically in his mind.” Without a clear organization of explicit rules, “his knowledge will be a complete jumble, neither satisfactory nor available for the purpose of actual business.”48 Even some commentators who generally advocated mental arithmetic also asserted that students would eventually need to name the principles that they had learned. Teacher and textbook author Roswell C. Smith dismissed the idea that a pupil, “when it actual business,” would have to repeatedly stop his work “to trace a train of deductions arising from abstract reasoning.” As useful as arithmetic might have been for right- reasoning, many educators agreed that it still had to produce accurate work. To Bridge, the idea that people would have time to re-discover the laws of arithmetic while on the job was nonsense. To others, however, mental arithmetic appealed as a pedagogy to instill arithmetic reasoning in pupils, so that they would never have to look up the rules again, in the 48 B. Bridge, The Southern and Western Calculator: or, Elements of Arithmetic Adapted to the Currency of the United States. For the Use of Schools (Philadelphia: Key and Mielke, 1831). 101 same way that they would not have to use a dictionary to read.49 Teachers complained often of children’s lack of retention in arithmetic, and fretted that this would surely hinder them in their working life. Students who had ostensibly “gone through” arithmetic classes would seem to have forgotten it all when they next went to study it. To actually make use of their arithmetic knowledge, that as an adult they would “be able to supply his knowledge and powers readily and profitably” students had to know the reasons behind what rule to use and when. Knowledge would not be sufficient: without reason, a businessman’s mind would be “a mere storehouse.” When it would matter most, “before the necessary knowledge can be looked up, the occasion for its application” would pass by.50 Even if students could fully master the logic of arithmetic commercial life, these commentators argued, they still needed to know when to apply what rule. The acolytes of Colburn’s First Lessons saw the market as a dynamic place. This fact made it risky, even a little dangerous, but also a space of great opportunity. And for all its pitfalls, “life in business” seemed to accord with the natural calculative faculties of the human mind. By this logic, success would always be possible for the prepared. For children to succeed, they had to learn that, eventually, rules would not be enough. More than learning to apply what rule, when, they had to learn to think like a man of business, to intuit the arithmetic truth behind transactions. No matter how much book-learning they acquired, there would always be fat in the problem. However, a problem remained, even for some of the strongest supporters of mental arithmetic. The critique expressed by Bridge and others, that children could not possibly be expected to perform original 49 This dilemma is a version of the larger problem of cognition and “the external mind” in the philosophy of science: that is, whether something recalled or understood only through outside cues is truly “known” or not. See Andy Clark and David Chalmers, “The Extended Mind” Analysis 58 (1998), pp. 10-23. 50 “Natural Science in Common Schools” American Annals of Education (July 1835), p. 304. 102 mathematical reasoning, nor would it be practical for them to do so on the job, presented a deeper problem for all those who wanted arithmetic at the heart of economic life. If all rules were banished from arithmetic education, how would participants know how to participate? How could someone be successful in business if everyone was operating by his own rules? “To guard against being cheated” For proponents of mental arithmetic, learning arithmetic at an early age promised the best means of entering business life. They insisted that children had to learn to think on their feet; that in the rapid-fire world of business they would have no time to consult their textbooks for the proper rule and then painstakingly do the problem out by hand. Mental arithmetic, and the mental discipline that it encouraged, proved popular for this reason. It adopted the old link between arithmetic and mercantile know-how into an educational philosophy in training students to reason commercially. But they could not get rid of rules entirely. Linking arithmetic and commercial education portrayed a specific kind of market, one that followed rules of arithmetic in a way that was accessible and transparent to all. Arithmetic seemed to provide more than a way for Americans to access market society; it was also presented as a means by which they could control a seemingly unruly system. Without rules, how would people be able to hold one another accountable in market transactions? How could they predict another person’s actions? “By business,” one accountant emphasized in 1848, “I mean habit. Paradoxical as it may appear at first sight, business is nothing in the world but habit, the soul of which is regularity.”51 51 William P. Ross, The Accountant’s Own Book, and Business Man’s Manual (Philadelphia: Zieber & Co., 1848). 103 Amid the excitement about the potential for a natural and universal world of business that would allow every American to find his fortune lay, as many historians have shown, an immense amount of anxiety, even among the optimists.52 This combination of excitement and anxiety sustained a persistent desire for “regularity” in arithmetic education and commercial life—in other words, for rules. As much as many antebellum educators wanted students to think like businessmen, many of them also wanted to hold onto the community standards that rules had promised. In the changing commercial world of the nineteenth century, arithmetic rules suggested more than accuracy. They seemed to provide a way for businessmen to hold one another accountable, even when transacting with a stranger. These competing pedagogies—which some educators seemed to deny were really at odds—led to a shaky consensus around participation in the market. This consensus emphasized that arithmetic commerce was both something that individuals could naturally intuit, and something that had to be held to high standards of objective rules so that businessmen could always protect themselves from swindlers and charlatans. Even the most basic education in arithmetic would enable Americans “to guard against being cheated in their dealings” by some nefarious swindler or con-man given life by the growing trade among strangers.53 The opportunity—and the imperative—of every businessman to keep his own accounts and ensure that he calculated correctly, continued to shape the discourse around arithmetic education. Daboll’s 52 For more on the culture around uncertainty and failure in nineteenth century America, see Scott A. Sandage, Born Losers: A History of Failure in America (Cambridge: Harvard University Press, 2006). Other cultural historians have dealt with the various material and social ways that Americans attempted to combat the perceived threat or unpredictability of “market society” in the nineteenth century. See in particular: Karen Halttunen, Confidence Men and Painted Women: A Study of Middle-class Culture in America, 1830-1870 (New Haven: Yale University Press, 1982); James Cook, The Arts of Deception: Playing with Fraud in the Age of Barnum (Cambridge: Harvard University Press, 2001). 53 “Calculation: Number and Magnitude” Common School Assistant (Apr 1840). 104 Arithmetic warned that people “employed in the common business of life, who do not keep regular accounts, are subjected to many losses and inconveniences”—but promised that these that could be avoided with the book’s “simple and correct plan” of arithmetic.54 Failure lurked around every corner in antebellum American economic culture, whether by one’s own faulty bookkeeping, or by being tricked by a nefarious stranger. But arithmetic rules promised a way to avoid both fates, and the humiliation and hardship of failure in business that attended them. Many textbooks in the nineteenth century presented problems that reminded students to think a commercial situation all the way through, rather than jump to a seemingly sensible, but ultimately incorrect, answer. Edward Brooks, a high school mathematics teacher in Philadelphia, laid out the following question in his Methods of Teaching Mental Arithmetic, in the book’s last section of “amusing” problems, “A and B went to the market with 30 pigs each. A sold his at 2 for $1, and B at the rate of 3 for $1, and they, together, received $25. The next day A went to the market alone with 60 pigs, and, wishing to sell at the same rate, sold them at 5 for $2, and received only $24. Why should he not receive as much as when B owned half the pigs?55 On the surface, a reader might assume that A selling his pigs at 2 for $1 and B selling his at 3 for $1 would not differ from A selling 5 for $2: the same number of pigs (five) are sold for the same overall price ($2). But, a relatively simple calculation shows that the average price per pig on the first day was 41!"¢ (half at 50¢ and half at 33#"¢). But on the second day, the average price per pig was only 40¢ ($2÷5)—a difference that cost A his dollar.56 54 Green, Daboll’s Arithmetic (1837). 55 Edward Brooks, Methods of Teaching Mental Arithmetic (1860). 56 ! Thus, the difference in average price per pig, 1 ¢, multiplied by 60 pigs, equals 100¢ or $1.00. " 105 The pig problem demonstrated to students that a careless businessman could lose money if he did not possess a thorough understanding of the arithmetic, simply by his own error. But an even greater threat appeared to exist in the perception that numbers and calculation could be used as a tool of deception against an honest man. A Boston schoolteacher posed a problem in 1825 to demonstrate how arithmetic might be used to trick rather than to reassure: “An ignorant fop wanting to purchase an elegant house, a facetious gentleman told him he had one which he would sell him on these moderate terms, viz., that he would give him a cent for the first door, 2 cents for the second 4 cents for the third, and so on, doubling at every door, which were 36 in all: It is a bargain, cried the simpleton, and here is a guinea to bind it; Pray, what did the house cost him?57 The answer, which the book provided immediately, is $687,194,767.35.58 Its message is clear: “facetious gentlemen” existed, and would swindle any “ignorant fops” who did not use or possess basic mathematical faculties. Americans fretted constantly, especially because they were constantly being warned, that dishonest people could make a dollar as easily, perhaps even more so, than honest ones. Fear of trickery necessarily implicated arithmetic in the worrying. Numbers could be “used as a means of security by the honest,” but just as easily as “an instrument of fraud by the dishonest.”59 But the numbers themselves did not lie, only the people using them. An honest man should be able to avoid deceit by doing his own calculations. And yet, no matter how well a man could calculate, he needed other participants to follow the rules. Holding others accountable 57 James Robinson, Jun., The American Arithmetick: In which the Science of Numbers is Theoretically Explained and Practically Applied (Boston: Lincoln & Edmands, 1825). 58 #'( ) This problem is probably best solved with the formula for the sum of a finite geometric series, 𝑎( ), with the #'( first term a=$0.01 (for one cent), the rate r=2 (because it doubles) and the final term n=36, which gives: #'!/0 $0.01( ) = – $0.01(1 − 2"4 ) = $687,194,767.35 #'! 59 “Art II. What is Education?” American Annals of Education (Apr 1832), p. 152. 106 with arithmetic required some communal, calculative agreement. Commercial arithmetic therefore suggested the existence of an objective standard, without actually naming it. The business world envisioned by arithmetic textbooks was one of both homogeneity and complexity. Proponents of mental arithmetic emphasized the role of natural intuition, suggesting that market transactions were among the most natural of human interactions. But the perceived perils of transacting with strangers also continued to make space for rules. Problems and warnings about swindlers suggested that the arithmetic market was not only one of individuals and singular transactions, but also a community with expectations about how individuals would behave, and how they would treat one another—ones that stemmed from arithmetic rules. Schools and teachers helped invent an arithmetic economy that combined a communal project of national prosperity with individual calculators who had the natural ability to intuit their own books and, at the same time, check one another. In each, calculation promised to prevent the perils of a business life. The useful knowledge economy had promised to distribute prosperity across classes, but the arithmetic one promised individual self-ownership in a united national marketplace. The new pedagogical norms of arithmetic education became popular in more direct forms of commercial education. Bookkeeping manuals generally relegated “commercial calculations” to a final section, under the assumption that youths or adults who wanted to learn account principles would have learned arithmetic in school and would need a section on arithmetic “merely to refresh his memory.” But enthusiasm for mental arithmetic did not go unheeded there, either. New book- keeping manuals of the 1840s and 1850s emphasized that, to learn to keep good accounts, students would have to practice them. By providing blank spaces in the manual, or a separate key to be used alongside it, a student would be “compelled to advance in his work by the aid of his judgment and 107 reasoning powers.”60 Older instruction in bookkeeping had relied on exercises “written up by the authors themselves, and the learner is required to copy.” New texts were instead arranged “without definitions, rules, or explanations.”61 Even here, in the most disciplined part of commercial life, some saw an opportunity to advance trust in the self over dictated rules. The idea that arithmetic textbooks would teach students to be smart and careful business- men also pushed educators to include more non-mathematical concepts into their textbooks. If the purpose of arithmetic education was not only to teach children the necessary rules of economic life, but also to think like a businessman, then it made sense to treat the most important concepts that they were likely to encounter. Arithmetic textbooks therefore did more than teach American children that life in business followed arithmetic laws; they also naturalized economic concepts by attributing arithmetical truth to them. To many educators and commentators, this was an essential part of teaching students to think like businessmen. Both advocates and critics of using rules mixed commercial and arithmetic information at will, in agreement over the central purpose of this form of mathematical education. Commerce made arithmetic practical, and it promised prosperity for its users, whether through the reasoned self-ownership of the mental arithmetic partisans, or the stabilizing, managerial vision of those who still advocated for rules. 60 George J. Becker, A Treatise on the Theory and Practice of Book-Keeping by Double Entry (Philadelphia: George Charles, 1847). Bentley Collection, Boston Public Library (Boston, MA). Bookkeeping manuals and arithmetic textbooks were distinct cultural products in the antebellum period, despite their apparent overlap. Bookkeeping manuals often relegated arithmetic knowledge to a final section, which presumed readers had covered this material in school and just needed a refresher. They focused much more on handwriting, correspondence, behavior, and other social markers necessary for a presumably upwardly mobile clerk. For more on clerks and bookkeeping, see Luskey, On the Make (2010) and Michael Zakim, Accounting for Capitalism: The World the Clerk Made (University of Chicago Press, forthcoming). 61 Joseph H. Palmer, A Treatise on Practical Book-Keeping and Business Transactions (New York: Pratt Woodford & Co, 1852). Bentley Collection, Boston Public Library (Boston, MA). 108 For example, many textbooks contained problems about calculating insurance, especially as the century progressed. Whereas earlier students had generally been given very simple problems of marine insurance, many nineteenth century students saw questions about life insurance, often with some editorializing. “Contracts of this kind are important to society,” Benjamin Greenleaf said of life insurance in his 1850 textbook. “Every man whose income depends on his own life or exertions, and on whom others are dependent,” must acknowledge that, through a small regular free, he could “provide against the casualties of life.” Though nothing can be more uncertain than the continuance of an individual life, yet nothing is more invariable than the duration of life in the mass; consequently, the exact value of life insurances can be calculated without any uncertainty whatever, and a man by effecting an insurance secures to his family, against risk of accident, the advantages they would have from enjoying his exact proportion of the average duration of life. Such transactions provide against destitution, and tend directly to the accumulation of capital.62 Greenleaf then showed two life expectancy tables, one from the Massachusetts Hospital Life Insurance Company and one from the New York Life Insurance Company, and explained how they were arranged and how, in brief, they to use them. He then set arithmetic problems, based on the table: “What premium will the Massachusetts Hospital Life Insurance Company require for the insurance of a life for 1 year for $1728, the person being 30 years of age?” Here, life insurance and arithmetic provide the same comfort: an appearance of protection against the “casualties of life” and a sense of ownership and control over risk. Moreover, by providing the numbers that real insurers used, textbooks like Greenleaf’s appeared to make the calculation of life insurance transparent, further emphasizing its safety and naturalness. 62 Greenleaf, The National Arithmetic (Boston, 1850). 109 Nowhere was this naturalness more emphasized than in textbooks’ treatment of currency, as a tangible object and as a concept of exchange. When it came to money, arithmetic promised a natural world of business. Students learned that money could be treated by simple or compound interest, and thus obeyed the arithmetic laws of series: one arithmetically (simple) and the other geometrically (compound). These laws allowed no variance or chance. Just as mathematical rules for series were the same in every instance, so too money did follow the laws of interest. Textbooks presented money as the sole arbiter of exchange; as the century progressed, arithmetic problems moved away from converting currencies toward paying for commodities, and ultimately to paying for labor. “A laborer engaged to work for 16 days on these conditions,” wrote Charles Davies in 1856. “For every day he labored, he was to receive 4 shillings, and for each day that he was idle he was to pay 2 shillings for his board; at the end of the time he received 52 shillings; how man days did he work, and how any days was he idle?”63 His tone suggested that the two days off, for fourteen days on, might still have qualified as overly “idle.” For many years, arithmetic texts and bookkeeping manuals presented interest and discount as the same thing because both treated differences in initial price and eventual payment. However, in the middle of the century, some textbook authors began to go out of their way to explain the difference. As one put it, using interest and discount interchangeably was “obviously erroneous” because the discount was an allowance made when advancing or lending money, while interest as payment on money already due. The textbook defined the discount by stating that a “sum of money due at any future period, is certainly worth less than at the present moment, than so much ready 63 Charles Davies, LL.D, Intellectual Arithmetic, or An Analysis of the Science of Numbers, with Special Reference to Mental Training and Development (New York: A.S. Barnes, 1856). 110 money.”64 This statement, although presented as a timeless arithmetic rule, stemmed from lending practices designed to mediate the risk of lost value in circulating paper, as it moved ever farther from its origin.65 But arithmetic textbooks’ overwhelming fixation on commercial calculations made a corporate practice into an arithmetic law of currency. In these ways, fights over rules and reason in arithmetic education muddied the distinction between economic and mathematical knowledge in antebellum America. Advocates of mental arithmetic wanted students to intuit arithmetic calculations—and therefore, by the logic of the time, business dealings. This argument encouraged, even necessitated, the breakdown of any distinction between what was a mathematical rule, like proportion, and an economic rule, like fellowship (i.e., profit-sharing within corporations). Critics of mental arithmetic shared the overriding concern that all arithmetic be practical, and although they wanted all arithmetic rules to be taught explicitly, distinguishing between arithmetic and commerce did not serve their purpose either. If arithmetic was to hold everyone to the same commercial expectations, there could be no useful distinction between a commercial rule and a mathematical one. Thus, the messy consensus around commercial arithmetic, in which individual actors could command both self-ownership of their own business calculations, and simultaneously expect that everyone would play by the rules, allowed economic concepts like annuities and discount to be learned as mathematical rules. 64 Elijah Hinsdale Burritt, Burritt’s Universal Multipliers for Computing Interest, Simple and Compound; Adapted to the Various rates in the United States on a New Plan (New York: Henry C. Sleight, 1830). 65 Scott Reynolds Nelson, A Nation of Deadbeats: An Uncommon History of America’s Financial Disasters (Alfred Knopf: New York, 2012), pp. 14-15; Jessica M. Lepler, The Many Panics of 1837: People, Politics, and the Creation of a Transatlantic Financial Crisis (Cambridge: Cambridge University Press, 2013), p. 10. 111 But it is also too simplistic to say that arithmetic textbooks duped Americans into accepting nascent neoliberalism, when they were so widely embraced and used. In combining self-ownership and communal rules, arithmetic promised Americans a specific kind of commerce, one based in static exchange. Fixed laws of interest (often literal ones), unchanging prices, exact proportions, and, most importantly, calculations in concrete numbers—never variables—that paralleled many Americans’ instinctive preference for hard money: these principles stemmed from an arithmetic economy. Ultimately, arithmetic commerce seemed to many people to be an inherently democratic form of doing business. Teachers and commentators still referred to arithmetic as “common” and “vulgar,” but they meant those pejoratives to be virtues. They took pride in arithmetic’s simplicity and concreteness, and based their understanding of understand economic practice in it, not because it was easy, but because it appeared natural, accessible, and fair. “We will set him a sum!” In December of 1836, the New York Commercial Advertiser, a Whig paper, published an article on the recent election results. In response to the article from the Albany Argus, the state’s leading Democratic paper, detailing the votes in the recent presidential election, the Advertiser insisted that the Democrats’ supposed triumph was instead a “great loss.” It did not dispute that the Democratic candidate Martin Van Buren had won 166,815 votes to Whig William Harrison’s 138,453, nor that Van Buren had won 28,272 more votes than Harrison. But, it loudly observed that Van Buren’s 166,815 votes was actually 2,154 fewer than William H. Seward had received when he was the Whig candidate for governor in 1834, and 15,090 votes fewer than William L. Macy, the incumbent Democratic governor, had won in the same contest. This meant, according to the Advertiser, that the Democratic Party had in fact lost votes when the whole electorate was 112 considered. “This may be called a gain by the Albany Regency arithmetic,” the paper scoffed, “but it looks to us very like a loss of more than fifteen thousand.”66 The utility of arithmetic in establishing a fair and transparent culture of business, and its apparent powers of repelling deceitfulness and fraud, made it as attractive in political discourse as in commercial exchange. In his travels through the antebellum United States, the visiting Alexis de Tocqueville observed that the “passions which agitate the Americans most deeply are not their political but their commercial passions.” He elaborated further that his evidence for this was the ways in which he saw Americans “introduce the habits they contract in business into their political life.” Tocqueville observed that what Americans valued about commerce, and what they wanted to see in their politics, were the ways it promised “order” and “regular conduct” as foundational to success. He claimed that “general ideas alarm [American] minds, which are accustomed to positive calculations, and they hold practice in more honor than theory.”67 To Tocqueville, arithmetic was key to American democracy: just as it provided a stable foundation for business transactions, so too it could describe political life with the same exactitude and transparency. Most Americans did not have a great deal of time for political economic theory, and they doubted that “political arithmetic” could really be “fully relied upon” in making important political decisions. Nevertheless, the idea that numerical data could be used seemed better. Numbers could “furnish the nearest approximation for truth, as data for reasoning”—and they were easy to attain.68 As other historians have shown, many antebellum Americans became enamored of quantification, 66 “Election Returns” Connecticut Courant, December 3, 1836, p. 2 (originally printed in the New York Daily Advertiser). 67 Alexis de Tocqueville, Democracy in America, Volume I, 3d American edition (New York: G. Adlard, 1839), 296. 68 “Untitled” Richmond Enquirer, May 12, 1837, p. 2. 113 applying it in new and inventive capacities.69 In everything from credit reporting to anti-slavery politics, nineteenth century Americans made use of quantification to pursue political and economic goals. Numerical data and basic calculations meant honesty in business, or so they had learned, and would therefore mean honesty in politics and policy as well. Antebellum newspapers regularly used numbers to make their arguments, in everything from elections to financial panics, evidently confident that their readers would be able to follow their calculative rhetoric. The very notion of adding up votes seemed to tie democratic practices to arithmetic truth. Widespread fixation on its utility encouraged a cultural discourse around arithmetic that emphasized its democratic potential. Textbooks, school systems, and commentators emphasized the democratic nature of arithmetic. The science of figures had a particularly American appeal: its practical utility was unimpeachable, but its connection to mathematical reasoning provided it an aura of enlightened perfection as well. It seemed to link the royal road and the common road in the pursuit of perfect truth, in a way that would be accessible to all its citizens—and assist national prosperity along the way. The “simple rules of Arithmetic” appeared able to provide all the answers to the nation’s most vexing political questions.70 Here again, the tension between the two styles of mathematical reasoning—rules on the one hand, intuition on the other—shaped ideas about how people would participate in public life. Arithmetic seemed to advocate both trust in the self above all other, and, simultaneously, a set of rules to hold the community accountable. 69 On numbers in antebellum America, see Cohen, A Calculating People (1982); on credit reporting, see Sandage, Born Losers (2006); on commodity markets, see William Cronon, Nature’s Metropolis: Chicago and the Great West (New York: Norton, 1991); on bookkeeping, see footnote no. 4 of this chapter. For numbers in antislavery politics, see Hinton Helper, The Impending Crisis of the South: How to Meet It (New York, 1857). 70 “The Sub-Treasury Bill” Richmond Enquirer, June 5, 1838: p. 3. 114 New pedagogical rejection of rules harmonized with arithmetic’s democratic credibility. Some educators rejected arithmetic based in rules and explanations as authoritarian. “The modes of operation or rules, ought to spring from the child’s own resources after his ideas have been rightly directed to self-evident principles,” one educator asserted in 1839. “Let him take nothing for granted because wiser heads than his have discovered it.”71 Not only would these rules give students the wrong idea about where authority and knowledge should come from, a rule-based education also threatened students’ future self-ownership in the market. Without the faculties to look at the information presented and quickly perform the correct calculations, a person would be in danger of having to accept a “merchant’s account without sufficient knowledge to examine it.”72 Even if the merchant were an honest man, this kind of ignorance worried Americans. They had long believed that the republic could not be secured if the common people became reliant on others’ reasoning to make decisions. If a numerically incompetent man had no choice but to take a merchant at his word, how could he be entrusted to vote in an election? That arithmetic principles should extend to the larger economic structures of the country, many Americans had no doubt. In his rejection of British currency, Erastus Root condemned it as undemocratic in both form and practice. The calculative complexities of sterling currency, he said, stemmed naturally from the nation’s tyrannical governance. Theirs was “the policy of tyrants, to keep their accounts in as intricate, and perplexing a method as possible”; that way, only a small, favored set would be able “to estimate their enormous impositions and exactions.” 73 By contrast, 71 Justitia, “On Teaching Arithmetic” Common School Assistant (Jul 1839), p. 54. 72 “Study of Arithmetic, No. IV” Common School Assistant (Dec 1836), p 89. 73 Root, An Introduction to Arithmetic for the Use of Common Schools (1796). 115 the decimal system of currency would exist in harmony with the United States’ republican ethos: every man would be able to understand it, and their vigilant calculations would keep track of the activities of the government and its officials. Arithmetic would do more than keep businessmen honest; it would allow the people to hold their rulers accountable. But accountability meant more than presenting the numbers, although that was crucial. It also meant that government officials and private companies, like individual businessmen, should be bound to the rules of arithmetical in their dealings.74 In the wake of the 1819 financial collapse, a citizen of Georgia wrote an open letter “to the next president,” in which he criticized the current Treasury Secretary, William Crawford. While he did not count himself a friend of Crawford’s, he also professed disbelief “that [Crawford] is so grossly ignorant as to be unable to make a common calculation.” After all, Crawford had once been a schoolmaster, so he must have developed “some proficiency in the fundamental rules of arithmetic” that had “not yet been entirely blotted from his memory.” And yet, the report that the Secretary had delivered to Congress on the nation’s financial situation had erred by more than seven million dollars. Unwilling to accept that Crawford could not follow the rules that he had once taught, the writer accused the Secretary of “represent[ing] the state of the finances to be worse than it really was” for partisan reasons.75 In this accusation, the writer put forth his personal calculations, but in the context of external rules. 74 The idea that accounting practices should be used in service of a larger accountability, commercial or otherwise, did not originate in the United States, although here as elsewhere, many Americans took pride in their supposed exceptionalism. On the long history of accountability through accounting, see Jacob Soll, The Reckoning: Financial Accountability and the Rise and Fall of Nations, 1st ed. (New York: Basic Books, 2014); Bruce G. Carruthers and Wendy Nelson Espeland. “Accounting for Rationality: Double-Entry Bookkeeping and the Rhetoric of Economic Rationality” American Journal of Sociology, Vol. 97, No. 1 (Jul., 1991): 31-69. 75 “To the Next President” Augusta Chronicle and Georgia Advertiser, November 26, 1822, p. 2 116 If state officials who dealt with public money held fast the rules of arithmetic that every schoolchild faithfully learned, the government would be virtuous and fair. “Economy in private life, is still, thank heaven, esteemed a virtue among the farmers and mechanics,” a delegate at the Massachusetts Democratic State Convention declared in 1839. But, he demanded, should it not also be the practice of “those who manage the finances of the State?” Governor Edward Everett, he claimed, had “concealed from the people in his Messages for two preceding years”—but he had enough data to conclude that the state had spent more than $72,353. “This is the ‘economy’ the people are to expect from their present chief magistrate and his advisers,” he raged. “Verily, if his excellency has not got beyond the rule of addition in his financial arithmetic, after three years hard study, how long will it take him to do a sum in simple reduction?” Furthermore, the Convention’s published address laid out the numbers for Massachusetts’ finances in the familiar form of textbooks and individual calculations: All receipts for income in 1837, $464,022 Current expenses of the year, 510, 460 Showing a dead debt by direct expenditures _______ over receipts and all resources, of $46,43876 Vertically presenting the public expenditures was a standard feature in many nineteenth century official reports and newspapers. The fact of the numbers themselves was usually taken for 76 “Address of the Massachusetts Democratic State Convention to their Fellow-Citizens” (1839). Readers may note that the paper presented the figures in an order that would have produced a negative number should the subtraction actually be calculated, but the result is shown as an absolute difference defined as a debt. The appropriateness of using negative numbers in arithmetic was not entirely settled in the Anglo-American mathematical world of the early nineteenth century. See Joan Richards, “Augustus De Morgan, the History of Mathematics, and the Foundations of Algebra” Isis, Vol. 78, No. 1 (Mar., 1987), pp. 6-30. 117 granted, although their sources could be challenged (or their omission criticized).77 But it was the act of calculation, the reasoning behind understanding the numbers, that ostensibly gave citizens the power to fully comprehend—and challenge—their government. As panic spread in May of 1837, American newspapers were well prepared to accuse the banks of failed or faulty arithmetic to account for the downturn. In the early days of the crisis, the Rhode Island Republican published a lengthy article under the heading “Rhode Island Banks and Banking” in which it argued that the banks’ “evil tendencies” had in essence stolen money from “the people” and given nothing beneficial in return. The Republican admitted that, unfortunately, “business is so interwoven with the banks, that a separation now would be attended with great additional evil,” and concluded that until the crisis had passed, only strict regulation could make them the “least obnoxious to the community.” To prove that the banks had lost “the people” their money, the Republican turned to arithmetic. The paper took on the very idea that money in banks “goes a great deal farther in sustaining trade and manufactures than before it was so invested” by showing that the banks took in more than they spent.78 For the years 1829, 1833, 1834, and 1835, the Republican explained in the vertical form of a schoolbook how much Rhode Islanders had put into the banks, how much they borrowed, and calculated the difference. And in each year, the Republican calculated that more had been put into 77 And, as historians have noted, that these numbers would actually be correct was not at all guaranteed at this time. Some newspapers intentionally tweaked numbers, but many others were simply careless, hasty, or got incorrect information from someone else. See, for example, Jessica M. Lepler, The Many Panics of 1837: People, Politics, and the Creation of a Transatlantic Financial Crisis (Cambridge: Cambridge University Press, 2013), pp. 49-50. 78 “Rhode Island Banks & Banking No. 1” The Rhode Island Republican, May 31, 1837, p. 2. Americans did not merely write about their animosity toward banks in this period, of course; the anger reflected by numerical diatribes like these sometimes played out much more forcefully in the streets. See Robert E. Shalhope, The Baltimore Bank Riot: Political Upheaval in Antebellum Maryland (Champaign, IL: University of Illinois Press, 2009). 118 banks than had been taken out at interest. Even in 1834, which the paper called “the great panic year,” it found that “the people used less than they put in by $976,733.” Comparing this difficult year with the one of relative prosperity that followed, it found that the bank took in $1,295,831 more dollars than it loaned out. This “sum would have average $13 each to every man woman and child in the state!!” the Republican exclaimed. “Is this not enough to account for the plenty of the one—and the barrenness of the other period?” It concluded its “remarks and calculations” by reiterating that during these four years, the people of Rhode Island had lost more than $190,000— and accused bankers of having hidden the returns after 1835, presumably to keep the people from doing the figures themselves with their common arithmetic education. When the one of the state’s Whig papers, the Newport Herald of the Times, responded to the Republican’s calculations under the pseudonym “Mr. Unit,” the paper published its “Banks and Banking No. 2” in June, 1837. Affronted by Mr. Unit’s questioning of their calculations, the paper challenged him to produce his own. “Mr. Unit has figured our sums over again, and differs from us in his results! This is in no way strange, for he left out some very important figures, and put in others which he did not find there!!” it insisted. It then launched into a scathing attack of Mr. Unit’s supposed inability to perform basic arithmetic: Since Mr. Unit is so apt at arithmetic, we will set him a sum. If the banks on a capital of $8,310,781, in the year 1834, let out $9,607,285, what would the capital in 1835, say $9,069,518 be able to let out provided it let out in the same proportion? There’s a sum for you, Mr. Unit, in the golden rule of three. In our very vulgar way of figuring we make the answer $10,484,387. But the banks did actually let out $11,085,543, being $601,156 over the proportion of 1834!79 79 $5,478,!9: As a textbook problem in proportions, this would be: = 1.156, and 1.156 x $9,069,518 = $10,484,387. $9,"#7,89# 119 According to these calculations, the state banks’ returns showed a different proportion of lending to borrowing in the panic year of 1834 and the prosperous year of 1835 than the “golden rule” would. As far as the Republican was concerned, this discrepancy was evidence enough of fraudulent practices. The idea that “panic about money destroys both reason and memory with some people” was a frequent lament among anti-bank commentators. Even “the plain rules of arithmetic… become humbugs,” one complained in the Richmond Enquirer. In such a crisis, he insisted, anyone who tried to deal in “matters of fact” and took his “lessons from experience” was “denounced as a visionary theorist” by bank supporters.80 But of course, the anti-bank argument went, nothing could be further from the truth. The Republican, speaking for the public good of Rhode Island, presented itself the direct opposite of a “visionary theorist.” It sought economic truth in arithmetic, the rule of three, and the “very vulgar way of figuring” learned by every schoolboy. The “real quacks” or “visionaries” were those trading “fictitious capital.” Arithmetic, more than promising disciplined calculations or business acumen, had the potential to stave off these visionaries, and the protect the real money, prosperity, and dignity of “the people.” Its appeal lay in its apparent ability to hold governments and corporations accountable. And yet, the Republican criticized the bank for the same reason Robert Patterson’s correspondent had taken issue with his tuition payment a decade earlier—a failure to follow the rules, as the aggrieved party saw them. For all the emphasis that arithmetic’s advocates placed in trusting one’s own, intuitive calculations, they could not shake the rules entirely. Some external authority seemed perpetually necessary to make the economy fair. 80 “For the Enquirer. ‘I Told You So’” The Richmond Enquirer, 23 May 1837, p 3. 120 The American Science “Perhaps the importance of no other Common School study can be made more obvious and palpable to all pupils than that of arithmetic,” stated the Massachusetts Board of Education in their Annual Report of November 1842: Almost every week, if not every day, the young arithmetician, in solving his imaginary questions, disposes of such quantities of goods as would make or ruin the fortune of a wholesale dealer; he makes calculations respecting such sums of money as but few capitalists have the disposal of; and he balances such heavy accounts between supposed merchants, as would decide the fortune of any actual merchant in Boston or New York, were the sums and quantities dealt with real, instead of being fictitious. 81 The “beauty of the process,” said the report, was that students could practice “in the actual business of life,” without accruing any “pecuniary loss.” It assured readers that the practicality of arithmetic kept pupils’ attention; should the class be devoted solely to “finding certain answers corresponding to those in the key,” the subject would be “worthless.” Instead, learning arithmetic should lead pupils “to imagine the schoolhouse to be like a warehouse, an exchange, or a market- place… and themselves the agents or owners by whom the business was transacted.” With this “sense of reality and responsibility” so firmly attached to the content of the lesson, the Board of Education felt confident that students would listen and learn, without “resorting to the pernicious stimulus of emulation, or rivalry with classmates.” In the symbolic marketplace of the classroom, engaged through the practical pursuit of arithmetic, American schoolchildren imagined themselves as agents and owners, individual masters of their commercial fates. “For the Enquirer. ‘I Told You So’” Richmond Enquirer, May 23, 1837: p. 3. 121 The changes wrought in arithmetic education during the second quarter of the nineteenth century illuminated the multifaceted ideas and contests surrounding Americans relationship to both mathematics and economic life. In each, arithmetic was lauded as the perfect democratic science. It meshed practical experience with conceptual reasoning, giving students the skills they would need in their idealized business life while also encouraging them to trust their own reasoning over that of authority figures. American educators elevated arithmetic’s scientific reputation by making its principles the basis for their growing national system. They viewed calculation as a crucial skill for preserving democracy, self-ownership, and economic prosperity. But they struggled to balance the anti-authoritarian goals of mental arithmetic with the persistent worry about who to trust in the marketplace, and the necessity of rules to hold untrustworthy people accountable. These two styles of arithmetic reasoning—one internal, one external—necessarily pulled in different directions. In many cases, Americans tried to balance the difference, or ignored it altogether. Nevertheless, the core of the calculating people’s education remained fundamentally unstable. Arithmetic’s political economy still depended on the external authority of mathematical laws. Arithmetic constituted the cornerstone of antebellum American efforts to make practical, useful, commercial calculation the foundation of mathematical education. Teaching children how to calculate became a central debate among educators and reformers. They established a pedagogy that emphasized the interdependence of arithmetic and commercial concepts, which naturalized the market in the minds of the many people, of all ages, who encountered the many arithmetic texts published in this period. But just as the useful knowledge economy had been unable to resolve the question of who would make mathematical knowledge and who would follow it, the concurrent invention of arithmetic commerce could not decide who made the rules. Debates over how to teach 122 arithmetic revealed a fundamental tension over where to locate economic authority in a democratic nation: in the self, or in the community? Even a near-universal effort to teach American children to be rational commercial actors through calculation could not escape the tension in mathematics between democratic self-ownership and external authority. Arithmetic naturalized the “calculating people,” but it could not eliminate the need for outside expertise. As a result, it opened the door for others to establish the rules of mathematical commerce. 123 Chapter 3: Men of Science In the late 1830s, Charles Ellet Jr. found himself annoyed with his superiors. A military man by training and now a civil engineer, he had traveled the length of the James River in Virginia, planning, surveying, and overseeing the construction of a major canal project. But most nights he would find a local tavern somewhere along the proposed 300-mile route, and try to work out how much the canal toll should be. Eventually, he compiled these thoughts and sent them to the board of directors of the James River and Kanawah Improvement Company, his employers, in a 250- plus page document. In his treatise, he told the directors that with the canal nearing completion, it would be imperative to charge properly for its use, “so that it may be rendered most profitable to the stockholders, and most beneficial to the community.”1 But Ellet had seen too many other projects undone by a careless imposition of tolls. Such charges, he warned, “are not optional with the board, but must be governed by certain fixed and palpable principles.” The principles Ellet identified were the elements of the project he knew intimately: the cost of construction, the length of the canal, how much traders would use it rather than (or along with) nearby roads, the commodities being transported and what price they commanded at the terminus, and the location of competing projects. But not only did Ellet feel he could best assess how much value this canal would be to the people who would be using it, and therefore what operators should set as the toll, he also claimed that his Essay could tell any board of directors of any infrastructure project what they should charge for their line. To do so, he produced both text and mathematical 1 Charles Ellet, Jr., An Essay on the Laws of Trade, in Reference to the Works of Internal Improvement in the United States (New York: Augustus M. Kelley, 1966), vi-vii. 124 formulae that, according to him, could be used in Georgia, New York, or Ohio as effectively and easily as in Virginia. The universality of these principles led Ellet to deem them “laws of trade.” But unlike other generalizations about commerce in this period, such as those advanced by political economists, Ellet’s laws were explicitly mathematical. They would, he hoped, guide not only the management of the James River canal, but all American commerce. Charles Ellet, Jr. was not a political economist, or a statesman, nor did he own a business or other commercial venture. He was, as he noted proudly in his own text, a civil engineer. He had been hired by the James River and Kanawah Improvement Company to survey land, design the canal, oversee the work, and move onto a new project. In this, he was perfectly representative of civil engineering in the antebellum decades. With infrastructure boosters in the state and federal legislatures pushing for new roads, bridges, canals, and railways, civil engineers became a crucial resource in the expansion of American commerce by providing the technical knowledge needed to facilitate internal trade. But Ellet went further. With his “laws of trade,” he envisioned a national system of trade that could be modeled geometrically. His Essay depicted a rationalized system of commercial activity that could be predicted and shaped through the central mathematics of a civil engineers’ education. Though antebellum engineers had originally learned geometry for surveying, hydraulics, and construction, it also shaped their economic knowledge. While managerial engineers have absorbed a great deal of historians’ attention, antebellum civil engineers developed economic expertise, and a political economic vision, well before the rise of the postbellum corporation.2 By the 1840s American civil engineers had claimed mathematical 2 This is in part the result of the attention given to postbellum managerial engineers in Alfred D. Chandler’s The Visible Hand: The Managerial Revolution in America (Knopf: New York, 1977), whose acolytes and critics alike 125 economic authority by presenting themselves as apolitical scientific experts. For Ellet and his social and professional peers, the civil engineer was a public economic authority. Ellet’s conviction that he held the economic authority to advise his employers about questions of tolls stemmed from the influence over public economic matters that engineers had gained during the previous four decades. Moreover, as his Essay makes clear, Ellet grounded his authority in these matters in his mathematical education and its application in the everyday technical matters of his job, specifically the spatially-balanced, reasoned discipline of geometry. As a practical mathematician in the age of useful knowledge, Ellet argued that the civil engineer should not be confined to construction. Rather, he should also be consulted on economic matters: how a project should be financed, how much it should cost, how many people would use it, and more. The early American consensus that mathematics should be used in the practical pursuit of national prosperity allowed those with explicit training in practical mathematics to begin to bring mathematical ideas into larger economic structures. In their daily work, civil engineers like Charles Ellet, Jr. helped collapse the distinction between calculating the slope of an embankment and the interest on a loan. They arrived at that economic expertise by using the mathematical knowledge garnered in their technical education to project apolitical, objective authority in political debates: first in matters of construction, and soon after in matters of cost. In doing so, they professed to represent the public interest by way of accessible, objective numbers. Their disciplined knowledge focused on the role of engineers in cost-accounting, scientific management, and corporate expertise. See also David F. Noble, America By Design: Science, Technology, and the Rise of Corporate Capitalism (New York: Knopf, 1977); JoAnne Yates, Control Through Communication: The Rise of System in American Management (Baltimore: Johns Hopkins University Press, 1989); Daniel Nelson, Frederick W. Taylor and the Rise of Scientific Management (Madison: University of Wisconsin Press, 1980). 126 of mathematics, acquired at West Point and the technical schools that based their curricula on the military academy, gave civil engineers a powerful claim to scientific disinterestedness against both government overreach and corporate rapaciousness. As practical men of science in the era of useful knowledge, they presented their mathematical knowledge as beneficial to the nation: legible both to the useful knowledge economy and the arithmetic strictures of the market. However, in applying mathematics to the transportation revolution, engineers like Charles Ellet exceeded the arithmetic principles that defined these antebellum conceptions of mathematical commerce. Instead, they used their practical scientific educations to advance their personal, expert judgment—combining rules with reason. Although they achieved their economic influence largely by promising to make states and corporations follow the rules in building public works projects, antebellum civil engineers became increasingly protective over their own right to say what those rules were. As a result, while civil engineers gained authority as disinterested experts protecting the public good with numerical objectivity, they simultaneously invented their own commercial authority. As some of the United States’ first numerate elites, engineers mathematized the nation’s infrastructure boom. They turned mathematical ideas into a rationalized political economic vision, and from there, built that vision into a material economic system. As a result, antebellum engineers turned some of the most fraught political contests of their day into mathematical problems, ones to be solved by expert reasoning rather than democratic politics. “The quantum of public good” “Providence,” declared English-born Virginian William Tatham in 1794, “hath furnished America with abundant internal resources, and an endless stock of raw materials.” All it needed was “the convenience of canals to facilitate their conveyance at lower rates, than the expense of 127 animal labour will afford” to raise the United States to a glory unimagined by any nation of the past or future. His enthusiasm hardly belonged to him alone. In early days of its nation-building project, the United States had many supporters of infrastructure who claimed it would be an unadulterated public good: it would distribute the United States’ many resources among its wide- spread population, thereby increasing the wealth and happiness of all its citizens. Now that the republic was a political reality, the time had come to make it a commercial one as well: to bring together distant towns and peoples into an integrated system of roads, canals, and railways—what Henry Clay would eventually call “The American System.” New technology meant that merchants no longer had to depend on old difficult roads to get to urban ports, but could look forward to the kinds of infrastructure, especially canals, then being built in Europe.3 The transportation revolution in the antebellum decades has been well documented in the annals of American history. New technologies of construction and communication, the westward expansion of people and goods, growing industrial needs, and rapidly increasing domestic and foreign trade (for cotton especially) necessitated that the United States find a way to facilitate the movement of people and goods. Boosters looked for friendly city and state governments, federal 3 The literature on internal improvements in antebellum America is enormous. Some useful context for this paper are: John Lauritz Lawson, Internal Improvement: National Public Works and the Promise of Popular Government in the Early United States (Chapel Hill: UNC Press, 2001); Morton J. Horwitz, The Transformation of American Law, 1780-1860 (Harvard University Press, 1977); Peter Way, Common Labor: Workers and the Digging of North American Canals, 1780-1860 (Baltimore: Johns Hopkins University Press, 1997); William G. Roy, Socializing Capital: The Rise of the Large Industrial Corporation in America (Princeton: Princeton University Press, 1997); L. Ray Gunn, The Decline of Authority: Public Economic Policy and Political Development in New York, 1800-1860 (Ithaca: Cornell University Press, 1988); Carter Goodrich, “Internal Improvements Reconsidered,” Journal of Economic History, 30 (June 1970), 289-311; Ryan A. Quintana, “Planners, Planters, and Slaves: Producing the State in Early National South Carolina” Journal of Southern History 81 (February 2015): 79–116. On early American engineers, see especially Ann Johnson, “Material Experiments: Environment and Engineering Institutions in the Early American Republic” Osiris, Vol. 24, No. 1, Science and National Identity (2009), pp. 53-74 and Terry S. Reynolds, “Overview” in The Engineer in America: A Historical Anthology from Technology and Culture (Chicago: University of Chicago Press, 1991). 128 legislators, and ambitious corporations to, whether independently or in conjunction, take on the material and financial task of constructing these projects in the first decades of the nineteenth century. Many were built through hybrid public-private corporations that combined state funds with private capital, and often charged for use of the canal or bridge to hopefully secure a return on investment. Through this practice, the government could subsidize the expansion of internal American trade without taking on the direct responsibilities for the construction and operation of the line, which many Americans understood as monopolistic.4 That said, the rights and responsibilities of private and public entities to the taxpayers and the users of infrastructure remained up for debate. Not all Americans supported the building of these projects, some complaining of uncompetitive monopoly, and others of having their land taken and unjustly compensated, although they were increasingly forced to accept the will of the courts as “just compensation” in eminent domain cases overrode objections of landowners.5 And many who did support the building of infrastructure in theory still sometimes pushed back on their city or state governments if they felt the cost was too high, or the project was being built in the wrong place, or otherwise objected to specifics. Even local projects posed a thorny set of problems: they had to be paid for by someone, they were bound to be disruptive to anyone whose property they crossed, and they were likely to profit someone at the expense of others, without anyone being sure, with any precision, what the good of such a project would be.6 Boosters argued that such 4 Brian Balogh, A Government Out of Sight (2009), p. 380-1. 5 Morton J. Horwitz, The Transformation of American Law, 1780-1860 (Cambridge: Harvard University Press, 1977), pp. 63-66. 6 The literature on the political and legal dimensions of the “public good” in antebellum American politics is extensive. See, for example: Horwitz, Transformation of American Law (1977); William J. Novak, The People’s Welfare: Law and Regulation in Nineteenth-century America (Chapel Hill: UNC Press, 1996); Mary P. Ryan, Civic 129 projects would provide greater benefit than cost, and thus be worthy of government funding and legal support. But how could such unlike things be compared? When Thomas Leiper, a quarryman in Delaware County, petitioned the state legislature of Pennsylvania for the rights to build a canal in 1791, to more easily transport his stones into the city, the legislature argued for days. Leiper was asking for rights to land along Crum Creek that was already owned, and not by him. He promised the legislature that the canal would be a great improvement to the area, and that “every other owner of property upon the Creek will eventually be a gainer” from the canal.7 He also produced reports by James Brindley, an English engineer, and David Rittenhouse, one of Philadelphia’s most eminent scientists, both of whom asserted that the plans for the canal were sound and would be of great value.8 And many in the legislature agreed that the canal would be good for public welfare, and noted that the state’s “best judges” had determined that the project would not be nearly so injurious to the counter-petitioners as they claimed, as long as Leiper assumed all responsibility and potential risk.9 Wars: Democracy and Public Life in the American City during the Nineteenth Century (Berkeley: University of California Press, 1997); Harry L. Watson, Liberty and Power: The Politics of Jacksonian America (New York: Hill and Wang, 1990); Laura Edwards, The People and Their Peace: Legal Culture and the Transformation of Inequality in the Post-Revolutionary South (Chapel Hill: UNC Press, 2009); Johann N. Neem, Creating a Nation of Joiners: Democracy and Civil Society in Early National Massachusetts (Cambridge: Harvard University Press, 2008); Kyle Volk, “The Perils of ‘Pure Democracy’: Minority Rights, Liquor Politics, and Popular Sovereignty in Antebellum America” Journal of the Early Republic Vol. 29, No. 4 (Winter, 2009), pp. 641-679. 7 “To the Honorable the House of Representatives of the General Assembly of the Commonwealth of Pennsylvania, The Humble Petition of Thomas Leiper, of the City of Philadelphia” [1791]. Robert Patterson Papers, Series 1, Box 1 (1776-1810). American Philosophical Society, Philadelphia PA. 8 James Brindley, “Calculations of the water level for Leiper’s and Wall’s proposed canal” and David Rittenhouse “Certification of the value of Leiper’s canal” (1791) Robert Patterson Papers: Series 1, Box 1 (1776-1810). American Philosophical Society, Philadelphia, PA. 9 Pennsylvania House of Representatives, minutes of debate over Leiper’s Canal, January 27, 1792. Robert Patterson Papers: Series 1, Box 1 (1776-1810). American Philosophical Society, Philadelphia, PA. 130 But not everyone was convinced. Mr. Fisher, a representative, reminded the assembly that “private property should not be violated, unless to promote the public good,” and demanded further proof from Leiper that his project would truly “be of public utility” and that “no private property would be injured.” Fisher and others distrusted Leiper’s financial interest in the project, insisting that any injury resulting from the canal must “be made to bear altogether upon Leiper’s interest in said mills.” It could not be denied that the canal “would, independent of its public utility, be of some benefit to the petitioner.” Others noted that, while some Philadelphians—“no inconsiderate portion of the citizens of the state,” to be sure—would benefit from the new canal, many others would get nothing out of it at all, and they wondered if the benefit could thus really be called a “public” good.10 Yes, there would be some benefit to people other than Leiper, but would “the quantum of public good,” as one legislator called it, produced by the canal really “be sufficient to warrant doing a small injury to a private individual”? An act to support and fund Leiper’s Canal was put forth, but ultimately defeated. Thomas would never see his canal built, as he had died by the time his son George convinced the state to allow him to build it in 1829. But Leiper’s ordeal might be productively contrasted with the fate of Massachusetts’s Middlesex Canal, one of the United States’ first major canal projects, begun in the 1790s and in construction for nearly twenty years. Before beginning, the Middlesex Canal Company hired American military engineer Loammi Baldwin. Taking their cues from European, especially French, projects, the Company wanted Baldwin to design and oversee the construction of the canal, to manage the workforce, communicate with the board and the legislature, and be 10 Debate over Leiper’s Canal, 1792. 131 available to answer, at almost any moment, any technical questions that any invested parties had about the progress of their project. They would use Baldwin as a kind of conduit through which to objectify these highly political questions of public and private good. If Leiper’s problem had been that of “interest,” someone who lacked it—a “disinterested” consultant, as it were—would be the ideal person for a legislature to entrust with sensitive decision-making.11 Baldwin was initially surprised by the magnitude of his duties. When approached in 1794 about the prospect of becoming superintendent, he hesitated; the most important thing, he told the board, “is the ability to execute the design in a proper manner,” and “in this, I certainly have nothing to boast, having had no experience at all.” It was true, he conceded, that he had “studied the theory for many years” and “been at considerable pains” to learn “the principles of canaling,” but he had to admit that he had “never seen one foot of a canal which had been completed in a proper and most approved manner.” But, promised the help of William Weston, an English-born and educated engineer then living in Massachusetts, Baldwin agreed to take the position.12 His role was not only to apply his technical knowledge, although that was important. He also fulfilled a key social role for the Middlesex Canal Company, and as a veteran of the Continental Army and a well-regarded engineer, he possessed the rare ability to fill both roles. Unlike Leiper’s small project, the massive Middlesex Canal project received approbation from the Massachusetts legislature. Political opposition came instead from aggrieved private land- 11 Paul Lucier, “Commercial Interests and Scientific Disinterestedness: Consulting Geologists in Antebellum America,” Isis (1995): 245-267 and Lucier, “The Professional and the Scientist in Nineteenth-Century America,” Isis (2009): 699-732. On the longer history of objectivity and disinterestedness, see Peter Dear, “From Truth to Disinterestedness in the Seventeenth Century” Social Studies of Science, Vol. 22, No. 4 (Nov., 1992): 619-631. 12 Folder 1: Middlesex Canal, Letters by Loammi Baldwin 1794–1795. Box 1, Part I: Letters by Loammi Baldwin. Baldwin Family Business Papers. Baker Library at Harvard Business School (Boston, MA). 132 owners; Baldwin complained to the board that many residents in Stoneham and Reading “utterly refuse to sell us their land, at any price,” and had petitioned the state General Assembly to protect them.13 The state supported the canal company, but difficulties persisted. In 1802, Governor James Sullivan complained to Baldwin about an irate constituent who accused him “of taking his land by unfair means… for the individual profit of important gentlemen,” a claim Sullivan groused was “ungenerous” with “no kind of foundation.”14 Still, the practice of just compensation for eminent domain prevailed: the value of the public good merely needed to pass muster with state surveyors (many of whom had also been trained as engineers) who determined how much landowners needed to be compensated in exchange for using their property for the canal. From there, Baldwin and his team could make use of the land however they saw fit. From the Middlesex Canal onward, a superintending civil engineer became a necessity to oversee the planning and construction of American infrastructure construction. Corporations and states alike needed a superintendent who could survey land, conceptualize the different elements that would go into the project, and oversee the correct construction of them. The larger the newly envisioned projects were, the more its financiers wanted a civil engineer. They recognized the value in having someone with both social standing and technical knowledge as the face of their project: not Thomas Leiper, who stood to gain personally from the project, and not the governor or legislature, who were subject to the tides of political popularity and ideology. Civil engineers 13 Loammi Baldwin, 1794?. Box 1, Folder 1: Middlesex Canal, Letters by Loammi Baldwin 1794–1795. Baldwin Family Business Papers. Baker Library at Harvard Business School, Boston, MA. 14 Sullivan to Baldwin, June 1, 1802. Box 1, Folder 13: Middlesex Canal — Incoming Letters, May-July 1802. Baldwin Family Business Papers. Baker Library at Harvard Business School, Boston, MA. Horwitz notes that Massachusetts was among the first states to insist on just compensation if private lands were taken by the state for public use. 133 did not only provide technical knowledge; they also appeared to remove questions of political or pecuniary gain from decision-making that would affect the whole community. Over time, people like Baldwin would become a political necessity in the transportation revolution. As a result, the early decades of the nineteenth century witnessed massive demand for civil engineers. The supply, however, remained small—especially for domestically trained engineers. Foreign engineers like William Weston provided a critical stopgap to widening demand, but could not fill the new nation’s infrastructure needs. The Continental Army had trained some adept young men, such as Loammi Baldwin, to survey new territory and oversee the construction of makeshift armaments, so the nation had a small cadre of military engineers already. And, as time went on, the massive expansion of infrastructure construction created new possibilities for young men to learn on the job; on the Erie Canal, for example, such as massive geographical and work-intensive undertaking required that some young men be pulled out of mechanical work and elevated to the position of engineer, which usually meant a promotion to management. For each of these, especially the latter two, the technical knowledge involved was piecemeal or adapted from another, different context. By 1820, the United States had too many Middlesex Canals and not nearly enough Loammi Baldwins. Furthermore, it was not entirely clear to anyone exactly what a superintending engineer needed to know to succeed, as there were no professional organizations or standardized curricula from which to develop a coherent practice. For most of the early republic and antebellum periods, little to no professional accreditation process existed for any of America’s various types of engineers. Military engineers like Loammi Baldwin achieved their rank by way of their experience and training in the army, but many others during this period claimed the title of “engineer” for themselves. By the 1830s, however, the rise 134 of advanced education for engineers led to a widespread understanding that the term represented greater education and expertise than other terms that described related work, such as mechanic or surveyor. One popular children’s story from 1839 had a father to explain to his son the value of knowledge by pointing to the fact that engineers, who “must have studied mathematics, so as to know how to calculate,” were paid more for doing less strenuous work than the chain-man or the laborer employed on the same job.15 Professionalization reinforced shifts in engineers’ education and cultural standing. Professional associations formed between the 1850s and 1880s, in an order that reflected the social prominence of their members. The first of these associations, the American Society of Civil Engineers, was officially founded in 1852.16 The early republic infrastructure boom created a social and professional gap. Corporations and states needed someone who could manage labor and materials, ensure that projects be built correctly and efficiently, and earn the trust of capitalists, politicians, and citizens alike. He would need to move private and public projects without political bias or disruption, and somehow deal with the question of what it meant to understand the value of public good and private rights. This growing need in the first decades of the nineteenth century directed the course of homegrown American engineering, and nowhere more so than at the United States Military Academy, where mathematics promised a potential solution to all these problems. But even there, familiar questions about mathematical pedagogy emerged. How much should an engineer trust mathematical rules, 15 Joseph Abbott, Rollo’s Vacation (Boston: Weeks, Jordan, & Co., 1839). 16 David F. Noble, America By Design: Science, Technology, and the Rise of Corporate Capitalism (New York: Knopf, 1977), p. 35. 135 and how much his own judgment? The answers, both in the curricula and in engineers’ professional lives, would have significant consequences for American commerce. Military Mathematicians During the first half of the nineteenth century, the United States Military Academy in West Point, New York became the premiere institution for mathematical education in the nation. Under the direction of the Army Corps of Engineers, West Point emphasized both practical and abstract mathematics, and developed a curriculum for cadets that established the school as the United States’ first technical school. The academy would soon become one of the primary places from which demand for civil engineers could be met. But even more than simply producing men well versed in surveying, hydraulics, mechanics, conics, and the calculus, West Point established the expectation that an American engineer, like the French engineers who constituted much of its early faculty, would possess extensive knowledge of the mathematics behind their work. The Military Academy tied the social prestige of the institution to the advanced mathematical curriculum that it required of its students. And, it trained engineers with the understanding that their authority lay in the disciplined applications of mathematical rules, not unlike military service itself. Discipline, the faculty believed, would lead cadets to mathematical right-reasoning.17 17 On the educational history of West Point, see: Todd Shallat, Structures in the Stream: Water, Science, and the Rise of the U.S. Army Corps of Engineers (University of Texas Press, 1994); James Lunsford Morrison, Jr., “The United States Military Academy, 1833-1866: Years of Progress and Turmoil” PhD Dissertation (Department of Political Science, Columbia University, 1970). On mathematical discipline in the West Point curriculum, see: Christopher J. Phillips, “An Officer and a Scholar: West Point and the Invention of the Blackboard,” History of Education Quarterly 55 (Feb. 2015): 82-108. 136 Mathematics formed the heart of the West Point curriculum, which aimed to turn cadets into officers. Every subject, from drawing to artillery, had a mathematical component or rationale; French, for example, was necessary to translate additional mathematics and engineering textbooks coming out of French technical schools. Although the military academy would lose its monopoly over technical education in the 1820s and 1830s, it nevertheless set American expectations for an education in both civil and military engineering, and its prestige as an institution of mathematical pedagogy and research in the United States lasted much longer.18 The mathematics curriculum at West Point emphasized practicality, discipline, and accuracy. The French instructors of the 1810s saw mathematics as key to forming a complete officer: someone who could rationally envision the landscape and make rapid, coherent decisions. Through applications in other courses, especially drawing, mathematics taught West Point cadets to command both mind and body.19 As elsewhere in the useful knowledge economy, mathematics education at West Point emphasized both orderly rules and individual reasoning. It taught cadets to rationalize the world, originally from a military perspective, but in ways that would lend themselves to more general applications. In 1801, George Baron, a local Hudson Valley teacher, was hired to teach a class in basic mathematics to a group of cadets at the fort in West Point. But Baron did not last long in the position; when the Military Academy was legally instituted by an act of Congress in March of 1802, he was replaced by Captain Jared Mansfield, who was soon joined by Captain W.A. Barron, 18 Karen Hungar Parshall and David E. Rowe, The Emergence of the American Mathematical Research Community, 1876-1900 (Providence, R.I.: American Mathematical Society, 1994), 17-21. 19 Phillips, “An Officer and a Scholar” (2015); on drawing, see Elizabeth Bacon Eager, Drawing Machines: The Mechanics of Art in the Early Republic, PhD Dissertation, Harvard University (2017). 137 who took over teaching geometry so Mansfield could focus on algebra.20 In 1812, as part of a wartime provisioning act, Congress provided funds for “a professorship of mathematics” at West Point, and in 1813, Major Andrew Ellicott assumed the role.21 Ellicott, who had primarily worked as a government surveyor and city planner since the Revolutionary War, was not pleased with what he found at the Academy. He complained of “improper and injudicious appointments from among the Cadets” based on their mathematical learning, noting with horror that some cadets had received appointments in the corps of engineers “who were unacquainted with the principles of plane trigonometry!!!” As a military man and a practical surveyor, Ellicott envisioned a more rigorous pedagogical future for the Academy. “The corps of engineers,” he stated, “ought to consist of the first mathematical and scientific characters in the nation.”22 Ellicott would not live to see it, as he died in 1820, but as a result of his efforts, West Point developed the most prestigious mathematics department in the country. Initially, cadets had relied on the mathematical texts used by Britain’s Royal Military Academy, specifically Charles Hutton’s Compendium of Mathematics. But the arrival of European engineers, as well as new curricula at other colleges, changed the landscape at West Point. Claudius Crozet and Ferdinand Hassler, both European military engineers, came to West Point in the 1810s, at the invitation of Superintendent General Joseph Gardner Swift. By 1825, cadets no longer read Hutton. Instead, they primarily 20 Mansfield would later be appointed to the Land Office by Jefferson, as part of the larger process of mathematicians being called to practical scientific work to serve the national project in the early republic and antebellum periods. Charlotte W. Dudley, “Jared Mansfield: United States Surveyor General” Ohio History, 85 (1998): 231–246. 21 The Centennial of the United States Military Academy at West Point, New York, 1802-1902: Volume I, Addresses and Histories (Washington: Government Printing Office, 1904), pp. 241-242. 22 Andrew Ellicott to William Simmons, December 25th, 1815. United States Military Academy (West Point, NY). 138 worked with translations of the most up-to-date French works, including Harvard professor John Farrar’s translation of LaCroix’s Algebra.23 At least until the rise of modern research institutions in the postbellum period, the Military Academy at West Point was the focal point for mathematical learning in the United States. No longer would anyone complain that cadets did not know plane geometry. On the contrary, the Academy became the United States’ premiere institution at which to learn it, exemplifying the prestige of practical mathematics.24 Mathematics soon became the cornerstone of a West Point education. Unlike John Farrar, Ellicott and his new faculty, especially Crozet and Charles Davies, had little doubt that French mathematics were crucial to establishing West Point’s credentials. Envisioning an American École Polytechnique, Ellicott immediately introduced algebra, geometry, logarithms, conics, surveying, and, of course, trigonometry into the curriculum. From there, he began to introduce more abstract subjects, including analytical trigonometry and differential calculus. When the famed Sylvanus Thayer became superintendent in 1817, he continued the expansion of West Point’s mathematical curriculum, introducing more of the French engineering that he himself had learned in his two years at the École.25 Standards were high; in 1832, of the twelve cadets in the Fourth Class deemed “deficient,” ten had failed mathematics.26 But unlike other educational institutions in the United States, interest in mental or intuitive mathematical pedagogy did not appear to breach the walls at 23 The Centennial of the United States Military Academy at West Point, New York, 1802-1902: Volume I, Addresses and Histories (Washington: Government Printing Office, 1904). 24 Ellicott also turned West Point into a credible school at a time when Jeffersonians were quick to criticize it as intending to create an aristocratic standing army. In particular, his rigorous exams and the appointment of new faculty bolstered the school’s prestige and helped ward off some—though hardly all—of the criticism. Silvio A. Bedini, Thinkers and Tinkers: Early American Men of Science (New York: Scribner’s Sons, 1975), p. 365. 25 Bedini, Thinkers and Tinkers (1975) p. 365. 26 “Regulations of the U.S. Military Academy at West Point” (J&J Harper: New York, 1832). 139 West Point. On the contrary, the school faculty of military men emphasized the central importance of discipline in the Military Academy’s mathematical coursework. Certainly, Ellicott and his successors believed that army officers needed mathematics for practical reasons, whether in wartime or as the federal government’s primary source of scientific expertise. But more than practicality, the Military Academy saw mathematics as the path to reason by way of discipline. In 1843, the Academic Board stated that the school’s primary purpose should be “to subject each Cadet… to a thorough course of mental as well as military discipline, to teach him to reason accurately” in “cases of daily occurrence in the life of a soldier.” The Board believed that “a strict course” of mathematics, taught in conjunction with its applications in military science, would be “by far the best calculated to bring about this end.” West Point’s administrators believed trigonometry and calculus were practical skills for students: to visualize battlefields, predict military maneuvers, aim cannons, and construct barricades. But they also still maintained that a successful mathematics course, “exercised and disciplined” the “reasoning faculties,” delivering “a system and habit of thought” which could be used in any profession.27 Indeed, thanks to the infrastructure boom, civilian pursuits awaited West Point graduates throughout the nation. After the War of 1812 ended, some graduates returned to their home state to lead state boards of public works. Others, as Loammi Baldwin Sr. had after the Revolutionary War, took superintendent positions with corporations to oversee private projects. Prominent West Point graduates such as Joseph Swift, Benjamin Latrobe, George Whistler, E.S. Chesbrough, and William Gibbs McNeill all worked at one time or another for prominent infrastructure projects 27 Centennial of the United States Military Academy (1904), p. 245. 140 throughout the United States, in places as diverse as Boston, Cincinnati, Albany, Chicago, and Charleston, as well as many rural areas in between.28 And while those men went on to particularly prominent non-military careers, many less eminent West Point graduates found civilian jobs in engineering too. According to the Registry of Graduates, of 374 graduates between 1833 and 1866 who went into civilian careers, ninety worked as civil, mining, or railway engineers, more than any other non-farming civilian occupation.29 As a result, military mathematics moved into civilian economic life at a national scale, not as the result of directed policy, but because of the central role that West Point played in meeting the national demand for engineers. Mathematics remained essential to the civil engineering profession as it moved beyond its military origins. Large scale infrastructure projects could serve as mathematical training ground for numerically adept boys who were unable to attend high school and thereby learn algebra and geometry; before the rise of West Point, many American engineers trained on the job.30 But, due to Ellicott’s efforts, expectations for engineers’ mathematical abilities were rising. Without time to study calculus, projective geometry, and mathematically-informed drawing —whether in school or at home—boys stood relatively little chance of growing up into engineers. While overseeing a 28 “Biographical Sketches of Eminent Engineers (With Portraits), No. VII., George W. Whistler, C.E.” in the American Engineer, Vol. I No. 7 (Chicago: July, 1880); “Biographical Sketches of Eminent Engineers: E.S. Chesbrough” American Engineer, Vol. I No. 3 (Chicago: March, 1880). United States Military Academy (West Point, NY). 29 James Lunsford Morrison, Jr., “The United States Military Academy, 1833-1866: Years of Progress and Turmoil” PhD Dissertation, Department of Political Science, Columbia University (1970). The 374 civilian graduates composed about a quarter of the 1449 total graduates in the period. The figure of 90 also does not include graduates who became teachers or professors, as their teaching subjects were not recorded, but of the 43 professors (as well as 15 college presidents and 8 school principals), many are sure to have taught mathematics or engineering. 30 Bedini, Thinkers and Tinkers, p. 366. The professionalization of engineering was two-fold: one, with the rise of West Point and other technical schools, the massive gap between supply and demand in engineering began to close; and two, the expanded mathematical curriculum at these schools set a much higher bar for entry than had previously existed. 141 team developing a system of locks and canals for the Merrimack River Valley in Massachusetts, George Whistler received a letter about a young man who had worked with Whistler the previous fall, but whose father had called him home, “desirous of having him pay more attention to his mathematical theory than he had done” already. Months later, he felt that his son had satisfactorily “laid the foundation so that he can continue,” and asked Whistler if he might again “have him under your care.”31 Without an adequate ‘foundation’ in the mathematics of a college curriculum, engineering would remain an unrealized aspiration for many young men. Civil engineering may have also appealed to West Point graduates because it provided an escape from the political criticism that the Military Academy was never quite able to shake. Even if they had been educated at West Point, engineers who worked on commercial projects were not called, as members of the Army Corps of Engineers often were, “military dandies”; “effete”; or “delicate.” Jeffersonian attacks on the idea of a standing army transitioned, during the antebellum period, into a criticism of the Army Corps as an aristocracy, a critique that was certainly bolstered by the Corps’ obvious emulation of French engineering.32 Even civil engineers who had trained in France were often warned to play down that element of their education: Loammi Baldwin Jr. warned his colleague Charles Storrow, who had studied in France, to emphasize his “practical knowledge” and “learning by observation” instead of mentioning his foreign training.33 While mathematics courses at West Point and other technical schools remained critical to their prestige, 31 George [Danwald] to George W. Whistler, March 1, 1836. Vol. XXIII, A-24, Proprietors of the Locks and Canals on Merrimack River Records, 1792-1947. Baker Library, Harvard Business School (Boston, MA). 32 Shallat, Structures in the Stream, p. 172. 33 Ibid., p. 105. 142 the application of these skills to commercial projects also helped ward off the whiff of luxury, aristocracy, and femininity that still clung to mathematics. Nevertheless, West Point graduates themselves did not fear that their extensive education in geometry, conics, calculus, and analytics threatened their masculinity at all. On the contrary, the combination of military discipline, applied mathematics, and the eventual careers that alumni held, whether in the military or in civilian occupations, convinced many engineers that they embodied the apex of the useful knowledge economy’s productive working man. In 1835, a commentator observed of West Point that, while “it has educated officers who have done much to preserve and defend our country from the ravages of war, we are especially indebted to it for the engineers who survey our coasts, and examine our harbors and our rivers, who have planned and executed many of the improvements, rail roads, canals, &c., which are so rapidly promoting the prosperity of our country, and the strength of our union.34 As institutions like Rensselaer and other technical schools and colleges were founded in the 1820s and 1830s to meet the growing demand for people to supervise and execute infrastructure projects, West Point gradually ceased to be the primary source of America’s civil engineers. But during the first half of the nineteenth century, most of the nation’s preeminent civil engineers had some connection to either West Point or the Army. Amidst the growing enthusiasm to connect Americans to one another, whether by road, canal, or rail, the importance of surveying, planning, construction, and infrastructure design continued to expand in the United States. As a result, the importance of engineers’ mathematical training became essential to their public personas. Whereas 34 “The Military Academy at West Point: Report of the Board of Visitors, invited by the Secretary of War to attend the General Examination of the Cadets of the United States Military Academy” American Annals of Education (Aug 1835), p. 1. 143 civil engineering had hardly constituted a recognizable occupation at the start of the nineteenth century, by 1850, industry and state alike relied almost solely on engineers to oversee and evaluate infrastructure, the backbone of an expanding and growing American nation. They would bring the mathematics of military discipline to the political world of public works. “Scientific employment” In February of 1835, Henry A. Dearborn, a former Massachusetts congressman and lawyer, complained to Loammi Baldwin Jr., son of the former superintendent of the Middlesex Canal, that the United States suffered from a “plentiful lack of scientific knowledge” and artistic taste.35 The conservative Dearborn condemned the widespread public preference for the new and profitable at the expense of those “intellectual luxuries” that might be beneficially, but privately, studied. “If now and then [science and art] command attention,” Dearborn lamented, “it is only when they do something that administers to the accumulation of wealth.”36 Baldwin, in his reply, agreed with Dearborn’s assessment, apparently unconcerned that he was, at the time, receiving a healthy salary from profit-seeking corporations in exchange for his scientific expertise. Nor did Dearborn appear to see any irony in complaining to the engineer about the very cultural, economic, and intellectual structures that undergirded his livelihood. On the contrary, both seemed to believe that Baldwin and his work were “superior to all these discouraging hindrances.” 35 The younger Baldwin had initially attended Harvard to study law, but grew tired of working as an attorney soon after graduating, and traveled to Europe to study with French and British engineers. 36 Henry A.S. Dearborn to Loammi Baldwin, February 26, 1835. Box 9, Folder 1: Boston Water Works—Letters, Loammi Baldwin, 1835. Baldwin Family Business Papers. Baker Library, Harvard Business School (Boston MA). 144 It would be rather unfair to accuse either man of hypocrisy at a time when the line between American science and commerce was so easily traversed. Both the federal government and private corporations funded scientific activity in commercially “useful” fields: engineering, astronomy, chemistry, geology, and more. Indeed, when engineers sought to describe what they did, they often called their work “scientific employment,” an apt description of the practices that constituted their professional lives.37 Meanwhile, the shape of the American corporation was changing. Beginning in the 1810s, courts increasingly began to distinguish between public and private actions and rights for corporations. Private corporations built roads, canals, and other public services for which they could charge whatever price they deemed appropriate, while “public corporations”—cities and states—could undertake projects of their own, with taxpayer money. Both forms, but especially the latter, pressured infrastructure builders to be accountable to the public.38 Here, the rigorous and disciplinary mathematics that most engineers had learned intersected with public expectations that everyone in economic life should adhere to mathematical rules. Because of these intersecting ideas and practices, civil engineers like Baldwin emerged as a new group of experts who many viewed as able to hold corporations and politicians accountable, particularly in the political minefield of public works. From a mathematical standpoint, this work very likely could have been carried out by people with less education than the Baldwins. Indeed, before the establishment of technical schools in the 1820s onward, many books held in the libraries 37 Samuel A. Eliot to the Boston Waterworks Commission (Treadwell, Baldwin, and Lowell), March 22, 1837. Box 9, Folder 2: Boston Water Works Correspondence, 1832-1846. Baldwin Family Business Papers, 1694-1887. Baker Library, Harvard Business School (Boston, MA). 38 On the end of corporations’ legal obligation to the public, see: Brian Balogh, A Government Out of Sight: The Mystery of National Authority in Nineteenth Century America (Cambridge: Cambridge University Press, 2009); Horwitz, Transformation of American Law (1977); Roy, Socializing Capital (1999). 145 of useful knowledge societies included surveying among the types of scientific knowledge they promised to teach the layman. But the curriculum at West Point and other technical schools was more than practical. A mathematical education made engineers into men of science, people who appreciated those “intellectual luxuries” that Dearborn longed for, while still employing them in the service of the useful knowledge economy. A formal mathematical education meant that civil engineers were endowed with a clear understanding of mathematical rules, which made them seem like disinterested experts who could untangle the politics of these projects. But when engineers like Loammi Baldwin embarked on their civilian careers, they found that they wanted to be more than calculative police. Formal education tied abstract mathematics to the social prestige of possessing sufficient technical expertise and personal responsibility to be trusted with the management of enormous and complex projects. Baldwin had studied engineering with his father, a military man, as well as with primarily military engineers in Britain and France. He had undoubtedly imbibed the disciplinary mathematical tradition that defined education in the trade during this period. But when he and other civil engineers faced the political realities of public works projects, they did not only insist on the relevance of their technical expertise. Rather, they rapidly came to see their real authority as stemming from their expert judgment. They knew the geometrical, trigonometrical, and analytical rules of construction—but more than that, they also knew best when to apply which one to what situation. In their scientific employments, antebellum civil engineers did not only follow the rules; they also learned to make them. Initially, engineers came to public works projects for the same reason that the Middlesex Canal Company hired Loammi Baldwin Sr.: to oversee the actual construction of the work. This work involved a high level of mathematical proficiency; the plane trigonometry that Andrew 146 Ellicott had insisted on for graduation from West Point would be among the least of their needs. Engineers needed to plan the work: survey the land that it would cover, establish where the best place to build would be, and plan for any particularly difficult topographical obstacles. They had to master a variety of instruments for observation and measurement, carefully record distances, map out the area as best they could, and then make the trigonometrical calculations to establish the spatial parameters of the work, often on site. Surveys were crucially important for engineers; without accurate information from which to plan, none of the remaining calculations would be of any practical use. Many large projects involved multiple surveys, including large teams led by an engineer that would collect as many measurements as possible.39 Engineers’ mathematical work did not end with the survey, however. Depending on the type of construction, they might need to then rely on various physical mathematical laws. For a canal, hydraulics was essential: how fast the water in the canal would move given a slope or how narrow the banks were, how much water was needed for the expected tonnage, and how to ensure that the locks operated properly. Roads and bridges required knowledge of friction and gravity, and railways required advanced knowledge of engine mechanics.40 Even simple tunnels required some knowledge of conic sections, as ellipses and parabolas were able to “sustain the greatest superincumbent weight” and would best prevent collapse.41 These scientific problems composed the bulk of engineers’ mathematical responsibilities when it came to infrastructure, and required 39 Shallat, Structures in the Stream (1994), pp. 38-39. 40 Vol. B157: Letter books—Engineering Department, March 18, 1836 – August 10, 1837. Boston and Albany Railroad Co. Boston and Albany Railroad Co. Records, 1829-1916. Baker Library, Harvard Business School (Boston, MA). 41 William Strickland, “Reports on Canals, Railways, Roads, and Other Subjects, Made to ‘The Pennsylvania Society for the Promotion of Internal Improvement’” (Philadelphia: H.C. Carey & I. Lea, 1826). 147 experience as well as learnedness. By the 1830s, state commissioners or boards of directors trusted that when they hired a new civil engineer, he would be familiar with applying these principles, and ready for the responsibilities of planning a new infrastructure project. The West Pointers were particularly convinced of their own scientific disinterestedness. In 1808, before the school’s revival during the War of 1812, Joseph Gardner Swift complained that at the Academy, professors were too influenced by their pupils’ “wealthy connections and college friends.” But, twenty years later, he must have been happy to hear from Whistler, his friend and cousin by marriage, when the latter wrote Gardner from Liverpool in 1829. Whistler complained that he would never be an engineer in England, because there, “the profession does not, nor can it, stand upon so respected a footing as in our Country.” He told Swift that engineers in England were no more than “pettifogging attornies” who could “be made to have any opinion as engineers for money.” This he contrasted with American engineers like himself, who would “give a professional opinion as disinterested persons.”42 Swift and Whistler were both West Point graduates who had made their careers working for corporate entities on largely private projects. The notion that they were disinterested experts no doubt helped assuage any worry among these former military officers that they might have abandoned a noble profession in pursuit of filthy lucre. Engineers also increasingly saw their role as not merely beneficial to public works, but also necessary. Without them, they quickly came to believe, any such endeavor would certainly fail. In 1826, Loammi Baldwin Jr. told Dearborn that he had been in talks with the state of Pennsylvania to survey and plan a canal project to connect Philadelphia and Pittsburgh, a distance of nearly 400 42 George W. Whistler to Joseph G. Swift, February 10th, 1829. Joseph G. Swift correspondence 1809-1862 [MssCol 2935]. New York Public Library (New York, NY). 148 miles. The state commissioners, however, had been unable to choose a superintending engineer, with one voting for Baldwin, another for Strickland, and the third for another engineer altogether. The split ticket evidently hurt Baldwin’s feelings, and it seems likely to have offended the other engineers as well, because the state went on “without an Engineer,” instead “pushing up common surveyors here and there as they could.” This compromise, Baldwin scoffed, resulted in “one of the most puerile and… inconsequent reports imaginable.”43 Whether his contempt was warranted is hard to know, but no canal between Philadelphia and Pittsburgh was ever built. Incidents like this reinforced politicians’ sense that public works required trained engineers, discouraging efforts to train engineers on the job, or hire those without formal education. When Baldwin sneered at “puerile” reports written by legislators, he compared democratic politics to squabbling children with himself and his peers as the adults in the room. The more engineers were thrust into the public eye, the more their desire for autonomy and authority grew. To preserve this tenuous position, they insisted that their mathematical expertise and their practical experience went hand in hand, that they solved problems through intuition born of experience, not mere rules. Although zealously committed to accurate reports, engineers also looked down on the fetishizing of rules alone, because the absolutism implied by relying only on mathematics in these projects threatened to undermine their judgment, and therefore their authority. They insisted that they possessed a unique combination of education and experience that suited them to their tasks. Engineers’ abiding faith in their own disinterestedness convinced them that they were a class apart: 43 Loammi Baldwin to Henry A.S. Dearborn, May 12, 1826. Miscellaneous Manuscripts Collection, 1668-1983. American Philosophical Society (Philadelphia, PA). 149 not public officials who, without them, produced useless reports, but also not greedy, stock-jobbing capitalists who sought to turn engineers into “pettifogging attornies.” Engineers believed themselves uniquely qualified to manage infrastructure, this crucial facet of American prosperity, and whatever commitment they had to public accountability ended when it threatened their expert judgment. When he was challenged on the implementation of a mathematical rule by Congressman W. W. Ellsworth from Connecticut, Baldwin sniffed that while the Congressman had clearly read “several eminent writers on the subject,” any engineer worth his salt knew that “a philosophical investigation must often be modified by a judicious practitioner.”44 Years later, his brother George echoed this sentiment, cautioning legislators who had made damage claims on the Boston Water Works that certain questions “cannot be wholly settled by theory” and required certain experience to determine. Even if “direct experiments” did not “altogether accord with any general theory of falling fluids,” that would not invalidate an engineer’s conclusions. Even the “most accurate experiments” contained error, and it would be a mistake to “confine this complex subject strictly to fixed rules.”45 Mathematics had authority, but it meshed imperfectly with the material world. For engineers, their judgment trumped rules. Experience had long played an essential role in American mechanical knowledge. Even in this period, certain aspects of engineering and engineering-adjacent craftsmanship retained older ideas about experiential, tactile expertise.46 But for those who had been educated in the United 44 Loammi Baldwin Jr. to W.W. Ellsworth, August 19, 1833. Box 16, Folder 5: Loammi Baldwin II, Misc. Letters re: Engineering, 1816-1835. Baldwin Family Business Papers, 1694-1887. Baker Library, HBS (Boston, MA). 45 Deposition of George Baldwin, Massachusetts Supreme Judicial Court, c. 1849. Box 10, Folder 5: Boston Water Works, Damage Claims, 1849. Baldwin Family Business Papers, 1694-1887. Baker Library, HBS (Boston, MA). 46 See Chapter 3 in William Thiesen, Industrializing American Shipbuilding: The Transformation of Ship Design and Construction, 1820-1920 (University Press of Florida: 2006). 150 States or Europe through an advanced curriculum in mathematics, and who assumed positions as superintendents of large infrastructure projects, the appeal of mathematics was two-fold. It gave engineers a claim to expertise in technical management, which they used to authoritatively direct the construction and maintenance of a project. And, at the same time, it provided them a language with which to justify their social position. American civil engineers thus began to use both rule- based standards of mathematics to gain public trust, while also maintaining that they possessed the expert judgment of a theoretical mathematician. They tied their education in geometry and calculus to their social roles as men of science who stood apart from political controversy. From there, they began claiming the ability to solve problems beyond the technical. “Arithmetical precision” In 1808 Albert Gallatin, then Secretary of the Treasury, briefed Congress on the state of American infrastructure. Echoing William Tatham before him, he argued that new roads and canals would not only bolster national unity and make trade easier for merchants, but would potentially also bring more traders into the market, raise the price of land, and otherwise contribute “social benefits” to the people and communities that bordered these projects, whether they made use of them or not. A national, federally-funded system of roads and canals, Gallatin argued, might “be calculated to diffuse and encrease [sic] the national wealth in a very general way.” But Gallatin admitted that accurately predicting these benefits was impossible. “Arithmetical precision cannot indeed be obtained in objects of that kind,” he confessed, “nor would an apportionment of the monies applied, according to [population], be either just or practicable,” because benefit might not 151 accrue evenly.47 How could the value of infrastructure be calculated? What degree of “arithmetical precision” could reasonably be achieved, and what should be done with the results? Gallatin’s desire for numerical precision in public works would be made real by the rising availability of mathematically-trained engineers in subsequent decades. The result was widespread embrace of precise calculation as a crucial component of public works projects. The rapid spread of arithmetic education during this period encouraged politicians and corporations alike to seek objective accountability in addition to safe and reliable infrastructure. Both found a solution in civil engineers. And in turn, engineers assumed a new role: that of the economic expert, who held states and infrastructure corporations accountable with precise calculations backed by their formal educations, thereby turning mathematical expertise into commercial authority. This authority gave engineers not only new professional influence and, in some cases, personal wealth; it also allowed them to directly shape internal trade during the antebellum decades. Increasingly, many believed that only engineers should be able to wield this power, not only to oversee infrastructure projects, but also to use their expert judgment in issues of cost. The performance of “arithmetical precision” became a crucial tool in establishing engineers’ commercial authority. For antebellum civil engineers, cost estimates became just as essential as the calculations pertaining to construction. Whereas reports from the 1790s, such as that for Leiper’s Canal, said nothing about the cost of materials, wages, or maintenance, the expanding importance of public works projects in later years elevated engineers’ role to manager and sometimes to public face. Their evident competence with figures and calculation transitioned easily to accounting for the 47 Albert Gallatin, “Report of the Secretary of the Treasury, on the subject of public roads and canals; made in pursuance of a resolution of the Senate, of March 2, 1807” (Washington: R.C. Weightman, 1808), 68-9. 152 project. As engineers decided what and where to build, they kept careful track of everything they needed and the price per item or laborer. The account books and diaries kept by superintending engineers on infrastructure projects illustrate that they were always ready to answer to the board. Which route would be cheaper, and would the cheaper route still be as effective? How many men were working on the line, and what were they being paid? How long would the current design last, and how much was any future maintenance likely to cost? Materials, time, and men all became inextricable parts of civil engineering reports in the 1830s and 40s. These reports became a necessity not only for the engineers to keep track of the financial responsibilities of the project, but to answer both to boards of directors and, when relevant, to the public at large, and their credibility rested in the presumed accuracy of engineers’ calculations. Given their advanced mathematical backgrounds, engineers’ adoption of accounting as central to their responsibilities happened smoothly. They had already calculated, for example, the number of engines required to get a train up a hill of a certain grade, using both experiential knowledge and the mathematics of gravity and friction. From there, it was only a short step to add that the cost of each engine would be approximately $900, totaling $8,100 overall.48 Even beyond the accounting of costs for individual aspects of materials and labor, engineers could extrapolate into further costs, such as maintenance or insurance. At the end of this accounting, an engineer could say definitively, to his employers and the public, that one plan would be cheaper or more economical than other, based on a host of mathematical factors that he had calculated for himself. 48 This example taken from a Report, to the President and Directors of the Worcester Railroad Corporation, September 30, 1836. Vol. B157: Letter books—Engineering Department, March 18, 1836 – August 10, 1837. Boston and Albany Railroad Co. Records, 1829-1916. Baker Library, Harvard Business School (Boston, MA). 153 But even more than that, engineers’ reports suggested a level of obsession with numerical precision that went beyond the genuinely useful into the nearly fetishistic. Some reports, often for projects that were particularly large or politically fraught, contained tables with cost estimates to two, even three decimal places, an impossible level of precision for what was necessarily only an estimate of what would be required for a long construction process, not to mention the costs of maintenance in the distant future. If engineers were skeptical of the precision of their numbers all the way to hundredths of cents, they remained mum. They kept strict internal accounts so that they would always be able to answer to a board or commission, and if they were somewhat laxer in their communications to one another, perhaps that was only to save time.49 The precision in both account books and published reports suggests that at the very least, engineers’ employers wanted to harness the rhetorical power of precision. The numbers, especially backed by highly-educated and disinterested engineers, carried the burden of accountability for them.50 The importance to engineers of accountability through precision is perhaps best reflected by the fact that their reports were widely published. Public works corporations frequently printed many copies of their engineers’ reports, which comprised tables and explanations of every facet of the work: the length of each segment, the cost of materials, the wages of the laborers, the weight of the bridges, and so on, often to two decimal places. The precision of these reports almost never matched reality; even small infrastructure projects usually went over budget, and the large ones 49 Vol. B118: Engineering Department—ledger—monthly accounts of Engineering Department, April 16, 1836 – June 30, 1840. Boston and Albany Railroad Co. Records, 1829-1916. Baker Library, Harvard Business School (Boston, MA). 50 On the rhetorical and ideological power of numerical precision, particularly in the nineteenth century, see M. Norton Wise (ed.), The Values of Precision (Princeton: Princeton University Press, 1995). 154 sometimes exceeded their budgets by hundreds of thousands, even millions, of dollars. But the fact of the printing assured taxpayers that the project would be well managed. Engineers could assure employers, as Lt. Col. James Gratiot did to the Dismal Swamp Canal Company in Virginia, “that the sum authorized… will be sufficient to finish according to said plan.”51 They persuaded states and corporations alike that they could appease the public “apprehensions of expense,” particularly where tax dollars were involved, with the “most accurate information.”52 While engineers themselves understood their authority as based in reasoned mathematical judgment, the arithmetic precision of published reports suggests much of their public authority lay instead in the idea that they were holding corporations and states accountable. More than any claim to technical knowledge, these reports portrayed engineers as public agents who made authorities play by the rules. State projects often emphasized the primary role of the engineer in keeping the accounts, to assure taxpayers that their money was being spent wisely. In 1854, the Pennsylvania legislature voted to have the state treasury department deliver to them a report of the cost, revenue, and expenditure of all public works projects in the state, and printed it publicly for widespread readership.53 American civil engineers crafted their authority by explicitly positioning themselves apart from both political and economic interest.54 They offered legislatures a way to depoliticize 51 “Eleventh Annual Report of the President and Directors of the Board of Public Works, to the General Assembly of Virginia, January 17th, 1827” Library Company of Philadelphia, Philadelphia PA. 52 William Strickland, “Reports on Canals, Railways, Roads, and Other Subjects, Made to ‘The Pennsylvania Society for the Promotion of Internal Improvement’” (Philadelphia: H.C. Carey & I. Lea, 1826), LCP. 53 “Public Works of Pennsylvania. Cost, Revenue and Expenditure, up to November 30, 1853. Printed by Order of the Legislature.” (Harrisburg: A Boyd Hamilton, State Printer, 1854). 54 Theodore M. Porter, “Objectivity and Authority: How French Engineers Reduced Public Utility to Numbers” Poetics Today, Vol. 12, No. 2, Disciplinarity (Summer, 1991), pp. 245-265. Porter’s argument about French engineers, that they succumbed to state pressure to clarify their formula and numbers, and wouldn’t have otherwise used strict quantification techniques, is related but not identical to the American case. Because American civil engineers (outside of the Army Corps) were not seen as state actors in the same way, corporations and state 155 infrastructure projects, and corporations a reprieve from accusations of profiteering or greed. They achieved this because so many antebellum Americans saw mathematics as public knowledge that allowed individuals to evaluate numerical arguments for themselves. The larger and more expensive projects became in this period, and the more stakeholders became involved, the more central engineers became to the question of accountability. When state- funded projects exceeded their budgets, usually the legislature or corporation received blame, not the engineers. In Boston’s quest to build a public aqueduct in the 1840s, discussed in more detail in the next section, many objected that New York’s Croton Aqueduct had gone nearly a million dollars over budget. And yet, when the final overview of the plans was needed to bring the project to fruition, the Massachusetts legislature called on John B. Jervis to do it, even though Jervis had superintended the colossally expensive Croton project. Here and elsewhere, engineers’ blend of social authority and scientific expertise protected both them and the cities or corporations they worked for; the fact of producing the reports at all seems to have been enough to assuage a great deal of public fear. With their theoretical and practical educations in hand, engineers possessed the social standing to remain disinterested experts in questions of public finance. The assumption of cost calculations as part of civil engineers’ responsibilities—indeed, as their primary responsibility—established them as the United States’ first mathematical economic experts. Engineering reports combined the mathematical knowledge required for surveying and construction with public enthusiasm for a political economy defined by arithmetic rules. Reports legislatures borrowed their powers of numerical accountability. Nevertheless, Porter’s larger argument about how numbers and quantification served as a “weapon of the weak” in state-sponsored infrastructure projects still essentially holds in the antebellum United States. 156 gave engineers the authority not only to say what to build and where, but also why a project should be built at all. They argued, through their daily work, that the construction of a road, canal, or rail- way was not a political question, but a mathematical one. And if that was the case, then the only people suited to decide where and how these conduits for domestic trade should be built, and how they should be managed, were engineers themselves. Only they possessed both the mathematical skill and sufficient distance from commercial interest to make reliable calculations. They knew the mathematical rules, and had no reason to break or ignore them, and therefore could be trusted with the professed central goal of infrastructure: the public good. The Engineer as Economist For all their claims to disinterestedness, civil engineers did not merely consult. Over time, their public economic influence shifted the terms of political debate over infrastructure to the field of numbers, rather than the issues of private and public right that had stymied Leiper. That shift did not mean that Americans did not argue about infrastructure any more—on the contrary, many public projects remained fraught and controversial as ever. But the debates increasingly centered on whose numbers were correct or could be trusted. It meant that both the calculation of costs, and the social authority to have those cost calculations believed, shaped the arguments over whether and how certain projects should be constructed. One exemplary, but far from unique, example is the decades-long debate in Boston over the construction of a public aqueduct to improve the city’s water supply, a loaded contest over who would define “public” good. 55 55 Between 1820 and 1850, Philadelphia, New York, Boston, and Chicago all built public water supply systems to supplement or replace private water providers. Each was overseen by a civil engineer, employed by the cities to oversee the construction and, crucially, keep watch over expenditure. Purely public projects put engineers in a 157 The debate in antebellum Boston over the construction of a public water system shows how influential civil engineers had become in the decades since Leiper’s failed canal bid, especially in defining the terms of “public good” as something that could be ascertained, or at least compared, through numbers, calculation, and—crucially—mathematical expertise. Combining the scientific expertise of the useful knowledge economy and the public accountability of the arithmetic market, civil engineers for themselves created a new, unassailable, apolitical expertise. They did not only begin to make the public good into something discussed primarily in terms of numbers, rather than in rights, although the history of cost benefit analysis has deep roots in civil engineering. Rather, the debate over Boston’s water shows that even as others attempted to bring the rhetorical power of numbers to bear on a political problem, civil engineers still had more power. They did not just have numbers; they also commanded mathematical reasoning. Engineers turned political debates into mathematical questions, but ones that only they had the ability to solve. In 1834, the city of Boston hired Loammi Baldwin Jr. to make a survey of nearby lakes and rivers and evaluate which would be the best source and route for a new, public water source to a common reservoir in the city. At the time, the Boston Aqueduct Company, chartered in 1791, constituted the city’s only form of clean water, which the company brought in from Jamaica Pond delicate position, as city officials relied on their established credibility while also pushing them to go beyond the logic of cost and return. On this story in particular, see Michael Rawson, “The Nature of Water: Reform and the Antebellum Crusade for Municipal Water in Boston” Environmental History, Vol. 9, No. 3 (Jul., 2004), pp. 411- 435. For a wider discussion of water in antebellum infrastructure, see Theodore Steinberg, Nature Incorporated: Industrialization and the Waters of New England (Amherst: University of Massachusetts Press, 1994); Carl Smith, City Water, City Life: Water and the Infrastructure of Ideas in Urbanizing Philadelphia, Boston, and Chicago (Chicago: University of Chicago Press, 2013); Maureen Ogle, “Water Supply, Waste Disposal, and the Culture of Privatism in the Mid-Nineteenth-Century American City” Journal of Urban History 1999 25: 321; Louis P. Cain, “Raising and Watering a City: Ellis Sylvester Chesbrough and Chicago's First Sanitation System” Technology and Culture, Vol. 13, No. 3 (Jul., 1972): 353-372. 158 at a steep price. Residents unable to afford this private water relied on wells and cisterns. In his overview, Baldwin concluded that the available water in Boston was nightmarish—dirty, hard, and unsuited for cleaning, drinking, or cooking. He undertook a relatively quick survey of nearby water sources from which the city could build an aqueduct, ultimately identifying the city’s own Charles River, Long Pond in Natick, and Spot Pond in Stoneham as possibilities. Of these options, he felt the Charles River was too dirty, and Spot Pond too small to be sustainable. Although Long Pond was the furthest from the city, Baldwin deemed it the largest and cleanest, and therefore the best choice.56 Having done this report, Baldwin returned to his work on the Charlestown Navy Yard, where he worked until his early death in 1838, at the age of fifty-eight. Given Baldwin’s reputation, this report likely could have been enough for city officials to begin work. But the legislature continued to stall on the project, issuing at least three referenda to evaluate whether sufficient public support existed. In the meantime, a group of wealthy Bostonians formed a corporation and purchased the rights to Spot Pond, and any water that came out of it, in 1843.57 They saw no issue with a private solution to a public problem; the only difficulty was that the existing aqueduct from Jamaica Pond did not provide a sufficient water supply. Thus, a second private aqueduct would solve the problem, and they offered to take upon themselves the cost and risk of building such a project. They argued that whereas a public system would grossly inflate the municipal debt and place an oppressive burden on taxpayers, some of whom already had water, 56 Loammi Baldwin Jr., “Report on the subject of introducing pure water into the City of Boston” (Boston: John H. Eastburn, 1834). Massachusetts Historical Society (Boston, MA). 57 Massachusetts General Court, “Act to Incorporate the Spot Pond Aqueduct Company” (Boston: 1843). Massachusetts Historical Society (Boston, MA). 159 private corporations understood profit and risk. They believed that this was the most effective way to calculate the value of the public good in infrastructure projects. But then-mayor Theodore Lyman resisted, as did his successor, Josiah Quincy Jr. Lyman admitted in a public address that building infrastructure was costly, especially if complications required additional payment. Nevertheless, he argued, supplying Boston with more and better water would immediately prove “a wise and salutary and eventually a profitable undertaking,” for the public, even if the project went over Baldwin’s estimated budget. Boston already spent plenty of money and, Lyman argued, with good reason. “We pay vast sums every year to build drains and sewers to conduct away the filth,” he reminded his listeners, and in doing so “annually improve the health of all. Yet this cannot be called money ill spent.” A “civilized and enlightened” society, he said, required public expense, whether it went to infrastructure, public schools, firefighters, or asylums.58 He expressed frustration with the argument that a public waterworks would produce no revenue, and should therefore not be built. To these critics, Lyman said, If in our own City we could calculate the time spent in pumping water from bad or frozen pumps, —in fetching it from a distance, —in carrying it up stairs, —using bad water in cooking or washing, —the expenses of repairing pumps and cisterns, —to say nothing of the discomfort of using bad water in some cases and in others not having enough to use, —If these matters, by and in themselves insignificant and little observed, could be reduced to a single sum in federal money, it would be found, I believe, to amount to a greater one than is required to pay the interest of the cost of ample and solid water works. In other words, they would finally be able to quantify the public good. Lyman did not suggest a methodology, but he articulated the exact contours of the problem. It would likely have 58 Theodore Lyman Jr., “Communication to the City Council, on the subject of introducing water into the City” (Boston: J. H. Eastburn Press, 1834), 22. Massachusetts Historical Society (Boston, MA). 160 been impossible to measure these “insignificant and little observed” events, and Lyman used them more as rhetoric than suggestion, but he nevertheless argued for the concept of public welfare as a “single sum in federal money.” Rather than argue on the basis of rights or community, his words reflected the supreme significance of calculation in infrastructure debates. If James Baldwin, who had taken on some of his brother’s outstanding projects after the latter’s death, was convinced by Lyman’s argument, he did not say so in his follow-up report in 1839. With the help of another engineer, Nathan Hale, and leading Boston industrialist Patrick T. Jackson, Baldwin delivered a detailed report that reiterated his brother’s claim that Long Pond would be worth the cost. Although its initial cost would be high, he argued that those costs would ultimately be justified by Long Pond’s various benefits. An aqueduct from Long Pond would “be more permanent, of more simple and convenient management, and much less liable to get out of order” than either of the other two options.” Though the Baldwins were appointed by the city, they did not weigh in on whether a public option would be preferable to a private. Like other civil engineers, they moved frequently between public and private projects, even as the two had become more distinct. Rather than argue about public or private, a question of politics, they emphasized their own mathematical reasoning in determining the best outcome. Even after James Baldwin’s new report, however, it alone would not be enough to convince the State of Massachusetts to sign off on the City’s proposed plan after more than a decade of intermittent efforts to begin the aqueduct project. Instead, the state legislature convened a Joint Commission in the winter of 1845 to hash out the problem. In that debate, the question of how much public good was worth, and the role of engineers in determining the numerical parameters of that debate, came explicitly to the fore. Decades of civil engineers’ prominence in conversations 161 about infrastructure and public good, combined with the widespread antebellum enthusiasm for arithmetic accountability in commerce and governance, paved the way for a public debate over the use and misuse of numbers. But the Commission’s trajectory suggests that although numbers were used as a rhetoric of democratic politics, a means for ordinary people to achieve legitimacy in view of the legislature on a question of public policy, the mathematization of the conversation conceded the ultimate authority of the mathematically expert city engineers. Representing the city, lawyer C.H. Warren argued that a new, public water supply would increase the public interest, not “personal wealth,” a dig at the Spot Pond Company, and a familiar refrain in such debates. He argued that the citizens of Boston had spoken in favor of a public supply from Long Pond in the various referenda that had been held in the previous decade. More abundant and accessible water, he claimed, would save the city more than $100,000 in fire insurance alone, calculations he based on New York’s Croton Aqueduct. Not having to expand the fire department would save $20,000 more, and the “greater security” water provided the city’s real estate would increase its value by ten percent—nearly one million dollars in Warren’s estimation. Though he insisted that none of the dollar values mattered as much as “the daily comfort of almost all the inhabitants of the city,” his rhetorical strategy suggested otherwise. Numbers were clearly crucial to establishing a legitimate argument on the matter of public works. Opponents to a public aqueduct from Long Pond attended the session as well. In addition to members of the Spot Pond Company, much of the naysaying hailed from aggrieved citizens of the neighboring towns. This opposition comprised a wide variety of different opinions, ranging from the practical to the ideological, personal to structural. One detractor argued that the city had no business providing its citizens with water, as it was just a necessity like food and clothing. Was 162 the city going to start providing those, too? A Framingham man claimed that a municipal water supply, paid for with taxes and debt, would be far too expensive, and injurious to the towns that it passed through. Others insisted that seizing rural land to provide Bostonians with water violated sacred principles of private property, and constituted a benefit to a privileged population at the expense of a larger, less affluent one which would not benefit at all. Notably, a few counter-petitioners produced their own calculations. Charles Cartwright, of the Manufacturers’ Insurance Company, challenged the claim that a larger water supply would “materially reduce insurance,” although he admitted under a barrage of Warren’s questions that that the City did not currently have an “ample supply” of water, and that this could mean that the city’s fire insurance would be lessened by a reservoir filled by way of the new aqueduct.59 Others estimated potential damages based on the dimensions of their property, or personal expertise; one Common Councilman produced custom house numbers about the number of ships, barques, brigs, schooners, and sloops to enter Boston in 1844, supposing “the cost of water for each to be at the rate of $5 a vessel.” Another estimated, based on the turning of a water wheel, that Spot Pond could easily produce “28,066,500 gallons every day of 10 hours.” The Spot Pond Company also brought fourth their own engineer, R.H. Eddy, who held up a table of data on water levels to show that Spot Pond would be cheaper and still supply sufficient water. Amidst all these arguments, however, none of the engineers hired by the city to survey the land and produce the reports attended the committee meetings. James Baldwin’s most recent report had again surveyed the options and once again recommended the long aqueduct to Long Pond. 59 “Proceedings,” 22. 163 When Caleb Eddy of the Middlesex Canal Company came to the stand to advocate for an additional privately-owned aqueduct, a fight broke out over the exactitude of the estimated expenses in Baldwin’s report. Eddy challenged the reported numbers, and Warren leapt in to claim that this was not an acceptable line of argument. He urged that even if the numbers were a little low, those who had gathered there today “were not to act as Board of Engineers for the city.” Eddy protested, as challenging the accuracy of these calculations was foundational to his argument. A fellow Spot Pond partisan chimed in, insisting that opponents to the Long Pond project planned “to show a very different state of facts from that reported by the Commissioners,” but the argument rapidly devolved into one about the nature of governmental power. Eventually Warren regained the upper hand, and insisted that the original numbers were not grounds for debate. “The city,” he insisted, did “not fear these inquiries about the price of brick, &c.,” but “every step of this examination” pulled the assembly further “from the true objects of the legislative inquiry.”60 Then, when Eddy refused to surrender his claim that the engineer’s report was careless and that the numbers pertaining to structure, expense, and supply were simply not to be trusted, the Chairman finally weighed in. The reports, he stated, had been produced by members of the state’s most eminent engineering family. Whatever they had found was sufficient to carry on the conversation. The numbers about expense and supply from the most recent report would not be grounds for further debate. Whether the city decided on a public or private option, the end project would be developed by engineers and their mathematical knowledge. The public 60 “Proceedings,” 24. 164 would not debate the feasibility of this method. If the public could not trust the numbers produced by engineers in 1845, the very idea of accountability began to look like a myth. This judgment was an enormous blow to the Spot Pond advocates, who in addition to Eddy had lined up Lemuel Shattuck, an amateur statistician, to show that New York’s Croton Aqueduct had outrageously exceeded its budget, and prove that a city-funded aqueduct would substantially raise property taxes in Boston.61 But the Baldwins’ numbers maintained supremacy, because no amount of additional numbers could pose a real alternative to the mathematical expertise that their professional colleagues had developed during the past four decades. In the end, Boston relied on Long Pond (quickly rechristened “Lake Cochituate” to emphasize its significance) for public water for the next century. It did not do so because the advocates of public water won the moral debate about the rights of people to public water regardless of their ability to pay, but on the grounds of cost, efficiency, and reliability as produced by expert civil engineers. Thanks to a range of economic and political processes, antebellum engineers had developed expert authority, and they learned to guard it carefully. Their effort paid off in situations like the Boston water debate. Despite widespread awareness that similar aqueducts had exceeded their public budgets by millions of dollars, the engineers’ estimates—not just the geometry of surveying and construction, but also the project’s material expense and economic consequences—remained sacrosanct. From the price of brick to the construction of the line, engineers held ultimate authority in setting the terms of public debate. As a result, formerly political and legal debates over the rights and privileges of individuals, their property, and their representation in the legislature became ones 61 “Proceedings,” 33. See also: John B. Blake, “Lemuel Shattuck and the Boston Water Supply” Bulletin of the History of Medicine, Vo. XXIX, No 6., Nov-Dec 1955. 165 about numbers and calculations, where mathematical expertise reigned supreme. Antebellum civil engineers, however, did not possess a generic mathematical reasoning. At West Point and its heirs, the foundation of an engineers’ education was geometry, and it was that mathematical discipline that shaped the way engineers applied their economic authority. Charles Ellet and the Geometrical Economy This idea, finally, brings us back to Charles Ellet, Jr. While most civil engineers of his day did not spend so much time and effort applying mathematical formulae to questions of tolls and trade, Ellet’s key claims stemmed from assumptions about economic knowledge that engineers developed out of their mathematical authority. The Essay is unusual, but it nevertheless provides a sense of the very real influence that engineers had over the literal construction of the domestic American economy, and a reflection of how many viewed their expertise. Moreover, the fact that he so explicitly used geometry to model internal trade, while mirroring many of the same values and conclusions that other civil engineers espoused, demonstrates how much of an influence, even unconsciously, that geometry had on other engineers’ ideas about economic life. Crucially, geometry led engineers to see economic activity occurring across rational space, over measurable distance, between fixed points. Rather than focus on an individual farm or firm, they portrayed the relationships between every farmer and every businessman in a defined space. This vision stemmed reflected an American economy literally shaped by engineers. By the onset of the Civil War, engineers’ mathematical training and professional disinterestedness had elevated them to a unique level of scientific and economic expertise in the United States. The geometrically balanced system of roads, canals, and railways was not necessarily the result of conscious effort on the part of engineers to reshape the internal trade of the country, although Ellet suggests that 166 some were considering it. Instead, civil engineers best illustrated the next stage of the mathematical economy. They combined the marriage of the theoretical mind and the skillful hand with the rigid accountability of commercial arithmetic to establish a new class of expert. From this vantage point, engineers used their “mathematical reasoning,” as Ellet called it, to create a systematic, integrated political economy out of a numerical, atomized marketplace. A demonstrated capacity for mathematical reasoning, as well as their increased credibility as arbiters of the public good, gave civil engineers the power to shape American political economy. The application of their mathematical knowledge to public problems, from where to build a canal to how to value an aqueduct, led them to think systematically about national commerce. But they did more than imagine commercial spaces and interactions. Once they came to understand regional political economy through the placement of interlocking roads and canals in space, engineers were in a position to materially make it so. As a result, antebellum America began to resemble a grand system of interlocking parts. Civil engineers’ mathematical reasoning produced a representation which, in turn, yielded a new material reality. In this way, antebellum debates about what types of mathematics should be considered useful, and how they should be learned, took on further weight. Civil engineers’ mathematical knowledge and social authority helped shape the practical, spatial dimensions of everyday economic life in antebellum America. Civil engineers pointed toward a new way of seeing economic life, one that grew out of their education, professional experience, and of course, calculations. In addition to advancing their own authority, they also began to directly shape the way that markets operated in the United States. They did this in the most literal sense possible: by deciding what kinds of bridges, roads, canals, and railways would be built, where they would be built, how much distance they would cover, and 167 how much they would charge. As a result, antebellum civil engineers developed a specific view of how commerce should operate. In projects like the Boston aqueduct, they prioritized “economy” in all things. “Economy” did not mean solely taking in more revenue than cost, or spending the least amount of money possible, although engineers did care about both. Rather, to them, it meant producing the most public and private welfare from a single line of infrastructure, and distributing those benefits as widely as possible. To do that, they relied heavily on their mathematical training, most essentially by applying the reasoning inherent in geometry.62 Overall, Charles Ellet Jr. was an ordinary civil engineer. He saw his essay as an outgrowth of the consulting ethos in which he and his peers specialized. In it, he emphasized his devotion to practicality, being “unremittingly engaged in… plans of practical utility.” Although he insisted that that his laws had been “singularly neglected” in public works plans, and inveighed against other engineers for preferring one proposed project over another “without one reference to the influence with the difference of the changes on the two lines would have on the quantities which they would respectively convey,” he still nevertheless relied on his social position, mathematical education, and spatial view of trade to write the Essay. And ultimately, his “primary goal” was one that engineers had been pursuing for decades: “to determine the value” of internal trade by way of 62 In this, engineers combined the early modern usage of the word “economy,” meaning the management of resources, often with reference to the household or homestead, with a growing sense of their own political economic vision, which emphasized increasing the material foundations of trade and therefore spreading the ability to participate in commerce across the United States. It would be too much, I think, to argue that they were using the word in the modern sense, as identified by Timothy Mitchell and others. However, the systematic political economic vision engineers like Charles Ellet developed in the late antebellum period does gesture to a more managed and discrete (and, of course, mathematical) understanding of economic activity than contemporaneous ideas, including both popular understandings of market society and classical economic theory. See: Mitchell, Timothy “Fixing the Economy,” Cultural Studies, 12, 1 (1998): 82–101; Paul K. Conkin, Prophets of Prosperity: America’s First Political Economists (Bloomington: Indiana UP, 1980). 168 “transportation on lines of artificial communication.” Ellet called his idea “the economy of public improvements,” a systematic vision of mathematical commerce.63 For Ellet, the most advantageous toll had to be calculated from structures larger than individual traders. His Essay focused on the toll because he assumed that any merchant wanting to use an improvement would make a decision primarily based on the cost of transportation—he would “put his estimate in dollars.” In this, Ellet assumed traders would compare arithmetically the cost of transporting his goods with the expected gain from selling them at the other end. But his goal was to understand the point at which the balance of the toll and the number of traders using the line would create maximum profit for the corporation. To do so, he relied not on “the mere question of value obtained by quotations from the price current,” which he saw as merely anecdotal, but on the tools of his trade: lines, angles, and triangles. Figure 2. Image from Charles Ellet, Jr., An Essay on the Laws of Trade, in Reference to the Works of Internal Improvement in the United States (New York: Augustus M. Kelley, 1966) As shown in this figure from the Essay, Ellet believed individual economic action stemmed not solely from “desire for gain,” but also from traders’ spatial position within larger structure of 63 Ellet, Essay on the Laws of Trade, p. 12., p. 27. 169 trade.64 He sought the “dividing point” of a region: the literal place at which nearby traders would choose to use to one line of trade instead of another, to know how to move it.65 When he came to formulae, moreover, Ellet created expressions that made his everyday concerns into symbols to find a “general solution” to the problem of trade. He used variables to represent distances, weights, and tolls to understand how far commodities would be carried along certain lines. But rather thank think about trade happening over time, Ellet often described it as a triangular relationship, and used that reasoning to build solvable expressions. This way, he could find the greatest distance a particular article would travel on the canal, the limit of the charge on a commodity, or the toll at which articles would be excluded. Cost variables could be analyzed with geometry just like literal spatial ones, although he did not always distinguish very clearly between the two. Ellet also noted of “the shape of the country” around the hypothetical canal and explained that it, too, could be understood as a triangular relationship of considerations: the distance to travel to get to the line in relation to travel along it. The “produce of the country” would thus move “within the triangles” as it traveled from point to point along lines of trade.66 Ellet did not invent the concept that roads and canals would bring prosperity both to the corporations behind them as well as to entire regions. That idea had animated interest in state- sponsored infrastructure since at least the eighteenth century. As William Tatham had phrased it in 1794, infrastructure projects “render countries, through which they pass, more rich and fertile” and would bring “very comfortable advantage” to merchants who lived at the terminuses of the 64 Ibid, p. 23. 65 Ibid., pp. 23- 26. 66 Ibid, p. 55. 170 line.67 Infrastructure would also make it possible for a growing number of people to export their goods to major cities, even ultimately to ports, as well as purchase goods coming in from other regions of the country or foreign markets. This had been an animating idea of political economy in England and colonial America, and domestic and foreign trade had long been seen as necessary to a functional state. Even Jeffersonians, who wanted to see every American man make his living by farming land that he owned, recognized the importance of commerce as a “handmaiden” to farming, and supported building the roads and canals that would facilitate that commerce.68 And other civil engineers, including Loammi Baldwin Jr., reflected in print on the importance of public works in facilitating trade, and therefore in building national prosperity.69 Nevertheless, though civil engineers readily agreed with the essence of these arguments, they also brought a unique view of balanced space and precise measurements to an older doctrine of widespread prosperity through internal trade. The mathematization of America’s infrastructure boom, as led by engineers, went beyond arithmetic accounting practices, because what Andrew Ellicott had called their “system and habit of thought” pushed them to think in terms of geometry. Where arithmetic deals in single solutions to concrete numerical questions, geometry does not necessarily require numbers at all. It allows us to understand problems of size and scope without 67 Tatham, Political Economy of Inland Navigation, p. 8. Although Tatham’s work is very much in line with classical political economy, he did include at least one forward-looking element by compiling the most up-to-date statistics he could into long tables detailing American population, trade, and wealth, especially from the 1790 Census. Using population data, land valuations, and a few uncited assumptions (for example, that the population increases in the compound ratio of 3.5%), he attempted to show that the value of land, trade, and capital in the United States had been rising along with population, and argued that this was the direct result of infrastructure. 68 Drew McCoy, The Elusive Republic: Political Economy in Jeffersonian America (Chapel Hill: UNC Press, 1980). 69 Loammi Baldwin Jr., Thoughts on the Study of Political Economy: As Connected with the Population, Industry and Paper Currency of the United States (Cambridge: Hilliard and Metcalf, 1809). 171 being bound by the strict magnitude of numbers. As the Common School Assistant put it in 1840: “We would laugh at the judgment of a child that would always prefer two apples to one, without regarding the size; and yet we frequently see men acting with little more wisdom respecting things of importance for want of understanding geometry.” In geometry, it was “relative quantities” that mattered, not single numbers.70 This was the mathematical reasoning that civil engineers brought to public works: how many more people would be helped by a particular plan, what proportion of people or places might be served, and how much could be built for what cost. The importance of geometry to engineers’ economic reasoning went beyond construction. In particular, geometry allowed engineers to rationalize space in such a way as to make it legible to commercial projects like infrastructure. Surveying had always been a crucial component of engineering, and took on new prominence in the age of useful knowledge. Engineers’ educations gave them the skills to wield the instruments, calculate the areas, and use expert judgment in the process of turning three-dimensional space into a two-dimensional map. Trigonometry helped them go beyond divisions of private property, and flattened natural topography into utility. It presented a landscape of commercial interaction that emphasized shapes, balance, and continuity. In essence, it emphasized a literal commercial space, and engineers often thought about how to best encourage commerce through a spatial understanding of domestic trade. Charles Ellet made the link explicit in his formulae, but the trigonometric practices of surveying meant engineers were constructing in much the same way, if not as self-reflectively. 70 “Calculation: Number and Magnitude” Common School Assistant (Apr 1840), p. 57. The article continued, “Indeed, without some knowledge of this science, no one can have any correct idea of the relative quantities of surfaces, or of bodies of matter; and all decisions on the subject… are nothing but guesses, and calculations in arithmetic might almost as well be neglected, and the results guessed at in the same manner.” 172 Engineers understood that the products of their labors would have a material impact on the way trade operated. The Virginia Board of Public Works cautioned against a new canal in 1836, arguing that while it “would lessen the distance to which the produce must now be transported,” it would “run very near the Dismal Swamp Canal, and… it is always injudicious to construct two improvements which may compete for the same project.”71 For his part, Ellet argued that “no work can be constructed in an improved country without meeting a rival,” and the resulting competition would simply draw traders away from each.72 Engineers wanted their employers to make money, but their geometrical vision led them to conclude that thoughtful management of improvements, rather than competition on price, would lead to widest prosperity and the greatest participation. Similarly, some looked askance at risky financing plans. George Whistler complained to Joseph Swift that his new project in New York was of “great importance” and “permanent character,” and must be built “upon sounder principles than stock speculation.” Under no circumstances, he said, should “stock speculation… be substituted for the skill of the engineer.”73 Nevertheless, if Ellet had expected to revolutionize the management of internal trade in the United States, he likely felt disappointed. His effort “to reduce the subject of internal commerce to a system adapted to the application of mathematical reasoning,” and his claims that trade could be understood “within the reach of general investigations” met silence, confusion, or both.74 He 71 Reports of the Principal Engineer, of his Operations in the Year 1826: Summary Report. “The Eleventh, Twelfth, and Thirteenth Annual Reports of the Board of Public Works, to the General Assembly of Virginia” (Richmond: Samuel Shepherd & Co, 1829). Library Company of Philadelphia (Philadelphia, PA). 72 Ellet, Essay on the Laws of Trade, p. 27. 73 George Whistler to Joseph Gardner Swift, October 23, 1839. Joseph G. Swift Correspondence. New York Public Library (New York, NY). 74 Ellet, Essay on the Laws of Trade, pp. 40-41. 173 almost immediately published a “popular” version of the Essay, stripped of mathematical formulae and most figures in an attempt to expand his readership, which more closely resembled a traditional political economy treatise.75 It is also not clear that any other engineers read or used either text. Ellet himself went on to become a canal lobbyist, publishing papers in forums like the Journal of the Franklin Institute favorably contrasting the economy and efficiency of canals to alternatives: specifically, and increasingly, railroads.76 But although his Essay failed to gain much prominence, the text synthesized many of the assumptions of civil engineers of his time, and pointed toward a new understanding of the relationship between mathematics and commerce. A Numerate Elite In essence, Ellet argued that the “apparent irregularity of the distribution of trade” in the United States was “more imaginary than real.” He claimed his own ideas were “simpler, and more 77 worthy of reliance,” than most others than engineers used, including those of physics. Unlike Tatham or Baldwin, however, Ellet did not see his text as one of political economy; he pointedly distinguished his practical advice from such treatises. And he did not argue that these principles would be easy to implement, or that they would make engineers obsolete. Quite the contrary: he insisted that in the management of public works, “sufficient latitude should be given to them who 75 Charles Ellet, “A Popular Exposition of the Incorrectness of the Tariffs of Toll in Use on the Public Improvements of the U.S.” (Philadelphia: Sherman & Co., 1839). 76 Conversational Meeting Volume, 1843-1847. Clippings from 1870 Scrapbook, Records of the American Institute of the City of New York for the Encouragement of Science and Invention, 1808-1983. New York Historical Society (New York, NY). He also oversaw the construction of the Wheeling Suspension Bridge in (West) Virginia, which for a brief period in the 1840s held the superlative of being the longest suspension bridge in the world. 77 Ellet, Essay on the Laws of Trade, p. 21 174 are entrusted with the responsibility of governing the affairs of the institution.”78 If trade took place most efficiently and effectively in a well-planned, geometrical economic space, then board rooms and legislatures alike would continue to need civil engineers, and engineers would in turn have a constant claim to authority over the economy that they had literally built. Men like Ellet and Baldwin made themselves indispensable to the American infrastructure boom in the antebellum decades. By turning political questions into mathematical ones, they made themselves into perpetual experts. They did so because they believed scientific disinterestedness was the best means to the public good, and that they were the most capable and disinterested men of science to do that work. Many envisioned themselves as public servants who prioritized science over politics, for the benefit of the national public. They did their best to create accurate reports, stay on budget, and create lasting, useful infrastructure. At the same time, however, they pushed back on the democratic objectivity of numbers. Just as they had learned to see battlefields through descriptive geometry, American engineers came to see commerce not as a market defined by open participation, but as a landscape in need of management. By making mathematics the tool to settle ongoing political debates over economic authority, and in their efforts to depoliticize the public good, they argued for a rationalized, top-down political economy. Unlike earlier and contemporaneous proponents of using mathematics for entrepreneurial or commercial ends, antebellum civil engineers did not view mathematics as serving a democratic ideal. For them, mathematical rules were not abstract community standards, but concepts that they alone understood and controlled. They understood that their position existed largely to produce 78 Ibid., pp. 67-68. 175 trustworthy numbers so that taxpayers and boards of directors would support any given project. But they also knew that a trader on a canal did not need to know the mathematics behind the slope of the banks or the width of the channel, nor did he need to know why a canal had been built in a certain way, or in relation to any other project. So, too, did Ellet dismiss the need for any individual trader to understand the mathematics he had used to predict their behavior. In that, antebellum civil engineers started the historical process by which the public accountability of numbers would fall away, but mathematical reason would only grow in economic importance. 176 Chapter 4: Corporate Calculators In 1858, the state legislature of Massachusetts passed “An Act for the Better Establishment of the Board of Insurance Commissioners,” a bill first put forth by Elizur Wright. Wright was then best known as an anti-slavery advocate, but he had supported himself by working in life insurance, first through computational work, and later traveling to England to research that country’s more developed actuarial practices. Energized by what he found, Wright returned to the United States eager to reform its expanding, and largely unregulated, life insurance industry. State legislators in his home state of Massachusetts were skeptical, and unwilling to impose on the industry; the bill was voted down multiple times over the 1850s. Eventually, however, supporters of its regulatory aims found the votes, and the Massachusetts Insurance Commission was founded. Legislators did attempt to give the two Commissioner positions to political insiders, but no one wanted a job that required so much calculation. Begrudgingly, they appointed Wright instead.1 The fate of Wright’s commission, as it quickly became, would be fundamentally altered by coming events. The Civil War and its aftermath reshaped Americans’ relationship with the federal government, and altered their expectations of it. Waging, arming, and financing the war required the considerable expansion of the national government, particularly into the realms of industrial development and economic regulation. The massive dislocations of war and emancipation created an expectation of obligation on the part of the central government to provide security as much as protect liberty. The resulting postbellum industrialization, too, convinced Americans of the need 1 On the Massachusetts commission, see: Lawrence B. Goodheart, Abolitionist, Actuary, Atheist: Elizur Wright and the Reform Impulse (Kent, OH: Kent State University Press, 1990), p. 148; Sharon Murphy, Investing in Life: Insurance in Antebellum America (Baltimore: Johns Hopkins University Press, 2010), p. 255. 177 for state protection against corporate behemoths that unleashed unfamiliar, seemingly dangerous technologies on the nation.2 Life insurance lay at the crossroads of these intersecting anxieties and expectations. The industry expanded rapidly during and after the war: total policy value more than doubled during the war years, and rose from $159 million in 1862 to almost $1.3 billion in 1870.3 As more Americans encountered new financial securities—life insurance policies, workmen’s compensation, home mortgages—they came to expect government regulation to provide security against instability and fraud. However, as Wright would quickly find, regulating a mathematical industry like life insurance required more than legislative power. It meant watching and evaluating the knowledge made and used by privately-employed actuaries.4 As a result of the postbellum life insurance boom, actuaries developed immense economic influence. Their calculations relied on algebra and variables, which pushed them to conceptualize a mathematical economy that legitimized abstraction. Actuarial work required algebraic formulae. With so many policies in use at any given time, all of which required the same basic calculation with different inputs, actuaries tended to construct a few formulae to use for calculating individual policies and the state of the firm overall. Over time, they began to hoard this knowledge. Attempts to describe life insurance to the public tended to omit any explicit formulae, explaining them as 2 On the Civil War’s effect on American political economy, see: Richard Franklin Bensel, Yankee Leviathan: The Origins of Central State Authority in America, 1859–1877 (Cambridge, UK: Cambridge University Press, 1990); Barbara Young Welke, Recasting American Liberty: Gender, Race, Law, and the Railroad Revolution, 1865-1920 (New York: Cambridge University Press, 2001); Drew M. Faust, This Republic of Suffering: Death and the American Civil War (New York: Vintage Books, 2009); George M. Fredrickson, The Inner Civil War: Northern Intellectuals and the Crisis of the Union (New York: Harpers & Row, 1965). 3 Murphy, Investing in Life (2010), p. 274. Murphy describes the Civil War as a “watershed” for life insurance. 4 On the significance of postbellum insurance companies in redefining American political economy, see Jonathan Levy, Freaks of Fortune: The Emerging World of Capitalism and Risk in America (University of Chicago Press, 2012) and Dan Bouk, How Our Days Became Numbered: Risk and the Rise of the Statistical Individual (University of Chicago Press, 2015). 178 “mathematical devices” designed to decrease “the necessary labor” of the actuary, upon whom the solvency of the company depended. In private, actuaries developed systematized formulae, which not only insured lives, but also undergirded a new market of financial instruments.5 These rules satisfied actuaries, and regulators, that corporations were following fair and objective standards, but actuaries made little effort to explain themselves to the public. Rather, they claimed that turning a life table into a policy was too complex for public understanding, but the “mathematical skill and nice discrimination” of the actuary would ensure total accuracy.6 Although actuaries wielded notable economic influence in the United States’ increasingly financial economy, they also represented a larger shift in the position that mathematical expertise held in economic life. The postbellum decades witnessed the rise of corporate calculators, men employed by private corporations to perform in-house mathematical work. Though these experts did not always agree with one another, they all became increasingly protective of their data and calculative labor. Together, they worked to privatize the mathematics of economy authority in the postbellum United States. Corporate calculators paid lip service to accountability and scientific disinterestedness, but primarily they served to ensure the continued prosperity of the corporation.7 At the same time, changes to the social and cultural position of mathematics within the larger structures of postbellum society winnowed the field from which Americans could critique it. In 5 See, for example, Sheppard Homans and Elizur Wright’s correspondence in April, 1863, in which they debate the proper level of explication in policy formulae. EWWBP, Carton 1, Folder 7: Letters, 1854-1864 [H]. 6 J.H. Van Amringe, A Plain Exposition of the Theory and Practice of Life Assurance (New York: Charles A. Kittle, 1874). 7 On the importance of the Civil War to the modern corporate form, and on the changing nature of “accountability” during the transformation of antebellum corporations into modern ones, see William G. Roy, Socializing Capital: The Rise of the Large Industrial Corporation in America (Princeton: Princeton University Press, 1997), pp. 44, 129. 179 particular, arithmetic calculation, once the mark of an independent man, came to represent menial labor, now best suited for women. As mathematical commerce came to rely on private calculators, “useful” mathematics moved beyond general public knowledge. As a result, mathematics’ powers of obfuscation began to outweigh its potential for accountability. “The good men in the business” Whereas antebellum civil engineers had claimed their positions of economic authority by way of explicit appeals to the public good, American actuaries were largely corporate calculators from the start. In the United States, the invention and development of the actuarial profession relied on corporations’ perceived need for actuaries. That did not exist at the beginning of the century, nor did it spread inevitably through corporate ranks as the industry expanded. Rather, the history of American actuarial science suggests a symbiotic process between insurance firms and actuaries, or at least, men who felt actuarial science should be used. Under Elizur Wright, the Massachusetts Insurance Commission furthered this process by holding up the need for mathematical expertise in life insurance. By insisting on firms’ need for actuaries, Wright’s Commission both consolidated the actuarial profession and convinced life companies of their actuarial needs. It shaped not only the insurance business in New England, but national practices as well. Unlike England, early nineteenth-century America counted few actuaries in its population.8 One modern historian estimates that only twenty-seven people worked for more than five years as 8 The early history of American actuaries is extremely limited, in part because so few individuals were seen as—or saw themselves as—actuaries, as opposed to accountants or clerks. The most comprehensive work is E.J. Moorhead, Our Yesterdays: The History of the Actuarial Profession in North America, 1809-1979 (Schaumburg, Ill.: Society of Actuaries, 1989). See also Murphy, Investing in Life (2010) and Bouk, How Our Days Became Numbered (2014). 180 actuaries before the Civil War.9 These men, including Nathaniel Bowditch in Massachusetts, and William Bard and Nicholas de Groot in New York, did not have specialized training in insurance or probability. Like their British counterparts, they worked for insurers as private calculators, who made or improved actuarial tables and valued policies. However, American insurance firms were not initially convinced they needed an actuary. Many smaller companies relied only on a staff of clerks, who often treated insurance payments as static transactions, even paying clients back the “surplus” of their payment once the insurer had paid out the necessary amount, or the need had ended. They made little effort to reinvest policy payments, pay out with annuities, or grow their companies. In 1898, actuary Walter Nichols scoffed that these early firms had treated insurance as an “ordinary mercantile venture, requiring only the skill of the accountant.”10 When the Institute of Actuaries was formed in London in 1848, however, the few interested men in the United States began trying to follow suit. Bowditch, who would later be claimed as the original American actuary, had already died, but the next generation was ready. They included the young Elizur Wright, who had held brief positions with the Massachusetts Hospital Life Insurance Company and New England Mutual. Like others, Wright had no actuarial training, but he had held a position as a mathematics teacher, proof of his mathematical acumen.11 Like Bowditch and others before him, Wright used mathematics to gain work in the insurance industry. But unlike Bowditch, Wright entered at a time when the life insurance industry was becoming increasingly important to American economic life, and had begun to reconsider its relative lack of actuarial sophistication 9 E.J. Moorhead, Our Yesterdays (1989), p. 2. 10 Quoted in Moorhead, Our Yesterdays (1989), p. 3. 11 Goodheart, Abolitionist, Actuary, Atheist (1990), pp. 26-7. 181 compared to their English counterparts. Having orchestrated widespread public relations campaign to convince Americans of the industry’s stability before the Civil War, postbellum insurance firms began to feel the need to back that claim up by hiring an actuarial staff. The Massachusetts Insurance Commission marked the first organized actuarial institution in the United States. It was the result of more than a decade of advocacy from insurance reformers, who wanted greater institutionalization of actuarial knowledge. These men, who were primarily northeastern actuaries, advanced a regulatory vision in which a company would be judged by the quality of its mathematical practices. But this handful of actuaries did not elevate their profession independently. During and after the war, insurers increasingly believed that business depended on the mathematical accuracy of their policies, to ensure there was always enough money coming in to pay any unexpected victims. If actuaries could help them guarantee that stability, they would cooperate with regulatory efforts like Wright’s. As the industry expanded in the 1860s, American insurers adopted actuaries’ language of mathematical stability. They became convinced of the benefit of employing an actuary to value their policies and reserves. As a result, actuarial science became the standard of both good business and good regulation, and actuaries were empowered to define the terms on which both these public benefits would be evaluated. Like antebellum consulting engineers, American actuaries consolidated around scientific disinterestedness to institutionalize their profession and lay claim to economic authority. Into at least the 1870s, life insurance firms wanted mathematical reassurance in their advertising, but they did not especially care where it came from. Mathematics professors were as good as actuaries for this role, perhaps even better, as their claims to calculative expertise were clear to most people in a way that actuaries’ may not have been. Some, like Harvard professor Benjamin Peirce, did formal 182 work for insurance companies. Others might be asked to briefly explain policy valuation or tables, in texts published by insurance companies to reassure the public of the industry’s stability. Over time, however, consulting mathematicians ceded their expertise to employed actuaries, who found that they could claim the same type of authority as mathematical authorities, but with the additional layer of expertise in the business itself. As early as the 1850s, some larger life insurers advertised their “skillful actuaries” who would keep the firm on an even keel.12 Even more than other numerical experts of the mid-nineteenth century, actuaries got by on their mathematical skill. Rather than rely on English data, they built probabilistic mortality tables based on American figures. They developed algebraic formulae that simplified the computational labor of creating many different insurance policies. These allowed the industry to expand, as the calculations could be done by bookkeepers while actuaries developed the larger models. Even as more business-oriented knowledge became part of the efforts to professionalize actuarial science, the idea that it was a fundamentally mathematical job remained essential in determining who could become an actuary and what kind of expertise they should command. As a result, insurance became an essentially mathematical industry, one that bragged about its reliance on mathematical experts and professed its scientific nature at every opportunity. This mathematical foundation would make life insurance actuaries central to postbellum debates over economic authority. Nevertheless, the effort to professionalize American actuarial science lasted a long time. During the postbellum years, the professional associations that developed around insurance were not exclusive to actuaries; they often included agents, underwriters, and managers in addition to 12 Anon., Considerations on Life Insurance: By a Lady (New York: Mutual Life Insurance Company, 1855). 183 actuaries. English institutions and publications also remained central to American actuarial science throughout the nineteenth century. The Actuarial Society of America was founded in 1889 in New York, but before 1900 its members were admitted by invitation, not examination.13 During the postbellum years, actuaries remained a largely self-appointed group, without official credentials beyond professional experience. Wright himself only began to identify as a “consulting actuary” after 1860. Their corporate origins meant that, unlike consulting civil engineers, actuaries never had an easy claim to scientific disinterestedness or public accountability. Nevertheless, they saw themselves as detached experts, “freer from business jealousies than the presidents or managers” of their companies.14 To prove it, they insisted on the absolute rule of mathematics in their industry. Wright’s commission, like the professional and regulatory bodies that succeeded it, established mathematical knowledge as the primary currency of the insurance industry. It created the need for actuaries even absent a defined professional structure to produce them. Elizur Wright’s Massachusetts regulatory commission both reflected and reinforced life insurers’ perceived need to have an actuary on staff. For his part, Wright strongly believed that the industry’s stability required mathematical actuarial science. He decided that his office’s provision to “visit and examine” firms meant that he should not only report back to the state legislature about companies’ activities, but also determine their financial solvency based on their books, and if need be, use his regulatory power to put them out of business. For their part, insurers, desirous to assure Americans of their stability at a time when mathematical expertise had become closely tied to 13 Hans Bühlmann, “The Actuary: The Role and Limitations of the Profession since the Mid-19th Century” ASTIN Bulletin, 27 (2), 1997, p. 166. 14 T.B. Macaulay, “The Actuarial Society of America,” Journal of the Institute of Actuaries (1886-1994), Vol. 29, No. 6 (January, 1892), pp. 544-547. 184 objective commercial authority, saw the benefit in playing along. By November of 1858—seven months after Wright’s appointment to the Insurance Board—insurance firms both in and outside of Massachusetts praised “the mathematical reputation” of the commission, and of the individual at its head.15 A religious man and avid reformer, Wright fretted over the possibility of unsound life insurers disappointing the families, widows, and children who depended on insurance, especially during wartime.16 To avoid this outcome, Wright did more than check companies’ books at their request. He also sold calculations, on the grounds of shoring up the industry. Wright’s justification for selling his tables and his time to life insurance companies both in and outside of Massachusetts was that he “consider[ed] it so very important to educate aright all who are entrusted with the management of life insurance.”17 But rather than disseminate his tables to existing insurance boards like his own in other states, such as New York, Wright elected to “put [the tables] into the market” and solicit payment from insurance companies or state commissioners who wanted to use them.18 The result was an additional income to his $1500 annual salary. William Barnes, Superintendent of the Insurance Department of the State of New York, offered $250 for a copy (and duplicates) of Wright’s Valuation Tables in 1861. In addition, Barnes offered Wright the opportunity to purchase from him the tables of the New York insurers under his purview, for a “$366.66 subscription arrangement.”19 Others offered higher or lower sums, depending on how 15 F.S. Winston to Wright and Sargent, November 1, 1858. Elizur and Walter Wright Business Papers [EWWBP], Carton 1, Folder 16: Letters, 1854-1864 [W-Z]. Baker Library, Harvard Business School (Boston, MA). 16 The association between life insurance and the protection of widows and children was consciously made by insurers in the antebellum period, as Sharon Murphy shows. For reformers like Wright, it was a useful doctrine for criticizing “bad” insurance companies, as the industry depended so much on maintaining a positive image. 17 J. Eadie to Elizur Wright, Nov 12, 1859. EWWBP, Carton 1, Folder 1: Letters, 1854-1864 [A]. 18 F.B. Bacen to Wright, Oct 12, 1861. EWWBP, Carton 1, Folder 2: Letters, 1854-1864 [B]. 19 William Barnes to Elizur Wright, October 2, 1861. EWWBP, Carton 1, Folder 2: Letters, 1854-1864 [B]. 185 informed they were of the market rate for reliable mortality tables. Whether purchasing a Wright table made an insurer more likely to pass inspection is hard to say, but one would be forgiven for speculating. Regardless, Wright continued the practice throughout his tenure. After the initial boom in the valuation table market, Wright turned to a more specific, and as he saw it, effective form of reforming life insurance: selling calculation itself. For Wright, his mathematical knowledge and actuarial experience made calculation a form of skilled labor, one he proved very willing to sell. When asked by the Penn Mutual in 1862 to calculate the total value of all their standing policies, Wright responded that the work could probably be done in about two weeks, but until he saw the data, it would be hard to determine “the labor of valuation.” Still, he did not think it would exceed $200. Perhaps recognizing that this might seem an exorbitant sum for mere calculation, Wright added that charging less would be “hardly just to other actuaries… for though the work itself it short, it is the result of long and expensive preparation” if it was to be done with “anything approaching accuracy.”20 He received similar requests from insurers across the country, and nearly always accepted. Even some companies who already employed an actuary called on Wright to assist with a particularly technical problem. While Wright clearly considered himself to be a bold reformer, his single-minded effort to transform his commission into a powerful instrument of both regulation and self-enrichment did not enamor him to the Massachusetts legislature. He was dismissed in 1866 under charges of 20 W. Lovering Carter to Elizur Wright, May 17, 1862; Wright to Carter, May 21, 1862. EWWBP, Carton 1, Folder 3: Letters, 1854-1864 [C]. Wright’s primary aim was ensuring that firms had sufficient reserve funds to pay out all their outstanding policies, in the unlikely by theoretically possible event that every one of their policyholders died at the same time. To determine this, he calculated firms’ real assets based on their current policies, which all involved different schedules and premiums. Some firms found Wright’s approach too conservative, but others saw the value in advertising their stability, as assured by an expert, to their governments and customers. 186 corruption, specifically for taking bribes from insurance companies. Wright insisted that he needed the extra income because he had employed his children to help him with clerical work, and his state salary did not cover those expenses. But the legislature was unmoved, and insisted that the consulting that Wright did for companies he was supposed to be regulating constituted corruption, although no one could prove that he had ever bent the rules for a corporate customer. That technical innocence haunted Wright, who remained furious about the dismissal for the rest of his life.21 How could life insurance agencies be held to strict mathematical standards without advanced technical calculations, and why should they be prevented from getting that from the best available source? And without mathematical standards, how could insurance be trusted? Wright did not retire from the world of life insurance reform; on the contrary, he kept up both his consulting business and his legislative efforts. In 1867, he told George Stone, an insurer in Wilmington, that should the company want to publish his name as a “consulting actuary,” he asked for an annual salary of $500, for which he would deliver calculations and advice on more than 500 policies. He was also willing to work without the publication of his name, and charge only $10 to $100—but he knew that the employment of an actuary, even one consulting from a distance, mattered to the image that insurers needed to project.22 Wright envisioned insurance regulation based firmly in the same mathematics as the industry itself would persist, and he insisted that only people with both knowledge and experience could do that regulating. The targets of his energies, meanwhile, found themselves caught between annoyance at government overreach and 21 Goodheart, Abolitionist, Actuary, Atheist, p. 156. 22 Wright to George Stone, October 26, 1867. EWWBP, Carton 1, Folder 29: Letters, 1864-1868 [S]. 187 an awareness that mathematical accuracy, especially if assured the presence of an actuary, would remain a necessity both to their financial future and their public image. Between 1858 and his downfall in 1866, Elizur Wright embodied the contradictions that the life insurance industry would face in the following two decades. Companies had promised that they were mathematically sound, and state governments had begun to show an interest in holding them to that promise. At the same time, the tools to evaluate financial solvency, whether within a company or by its regulators, remained in the hands of actuaries, who were seen as the only people with enough mathematical and industry knowledge to tell a financially solvent company from one on the verge of ruin. In 1867, that a National Bureau for Life Insurance was proposed to do similar work to the Massachusetts Commission on a national scale. A.W. Kellogg of Northwestern Mutual Life in Milwaukee wrote to Wright that he supported the choice of an actuary as the agency’s head. “It seems to me,” Kellogg said, that to make the new agency the most useful, they should ensure that “the good men in the business control” it. He asked for Wright’s help in creating the Bureau, and suggested insurer would support it so long as they got a seat at the table.23 The Massachusetts Insurance Commission contained a fundamental paradox, one that led to Wright’s dismissal and with which he would continue to struggle as a private citizen. As Kellogg said, regulating the industry would be good for insurers and customers alike, so long as “the good men in the business” remained in charge. But how could actuaries be regulated by anyone other than one another, who understood the technical specification of the business? And could actuaries be trusted to oversee actuaries? This tension remained even as Wright’s emphasis on mathematical 23 A.W. Kellogg to Wright, Nov. 26, 1867. EWWBP, Folder 24: Letters, 1864-1868 [K-L]; Murphy, Investing in Life (2010), pp. 288-289. 188 accuracy spread throughout the American life insurance industry. It pitted an antebellum vision of mathematics as a means to accountability against a growing suspicion that mathematics being done in the bowels of large corporations would obfuscate rather than clarify. How could mathematics keep actuaries honest if they were the only ones who understood it? “The confidence of the public” While he was still commissioner, this question did not trouble Elizur Wright. He believed without question that financial solvency and mathematical accuracy were synonymous. Only through careful and accurate mathematical calculation, he insisted, could an insurer be “entitled to the confidence of the public,” an honor he denied many firms.24 He wanted companies to refrain from issuing new policies unless they could show that they possessed financial assets at least equal to the net value of all issued policies. This standard that required a sophisticated understanding of the way life insurance policies worked and how they were valued, in order to gain a snapshot view of an insurer’s books. But while Elizur Wright had the mathematical ability to do that, his claim that these calculations would win the “confidence of the public” repeated a core problem of his commission, on a broader scale. How could the public be confident in something that, Wright and other actuaries believed, they did not have the tools to understand? Insurers’ claims to mathematical truth helped the industry expand, but they also constrained its social power. In this, life insurers embodied the central principles and paradoxes of the use of mathematics in the postbellum American business landscape. Indeed, perhaps no industry was 24 Wright to Gilbert Currie, April 29, 1859. EWWBP, Carton 1, Folder 3: Letters, 1854-1864 [A]. 189 more dependent on the idea that mathematics could ensure sound and predictable business, basing claims to accuracy, trustworthiness, and scientific business practices on mathematical calculations. But life insurers did not present themselves as following the arithmetic rules of accounting in a way legible to the public. Rather, they used increasingly complex calculations to value and predict their rapidly growing array of insurance policies, as well as the other financial instruments in which these firms had become involved. At the same time, their reliance on the “confidence of the public” in the very nature of their business meant that they had to acquiesce to some kind of regulation or oversight. They had to advertise that they were playing by the rules, even as they entrusted more and more of their business to the mathematical reasoning of experts. Americans retained their antebellum expectations, that mathematics should ensure fairness in economic life, into the postbellum years. Indeed, the idea that the state had a responsibility to provide security against avaricious corporations heightened the expectations for clearly articulated rules in economic life. Wright’s tenure as a regulator corresponded almost exactly with the Civil War and its immediate aftermath, and he seemed to have deeply imbibed these anxieties and desire for fairness and security. However, actuaries did not have the standardized education of engineers, nor did they publicly use arithmetical rules to explain their calculations and decision-making. What Wright and other actuaries used in the postbellum period were instead algorithmic formulae, into which they plugged their own data and adjusted as needed. These algorithms were not mutually agreed-upon between companies, nor were they advertised to the public. The postbellum vision of life insurance regulation borrowed earlier ideas about the public accountability of mathematical laws, but ones devised in private. Wright sought to maintain the political appeal of accountability, but he wanted to use his own rules, instead of common arithmetic. 190 As the insurance industry grew and expanded after 1860, so did the technical knowledge required to manage it. For the industry, especially among its actuaries, the promise of probabilistic truth was not a marketing scheme—at least, not solely. Rather, mathematical accuracy was deeply intertwined with how the company would fare. Enough policies had to be sold, to enough relatively young people, at a sufficient price, to keep the reserves of each company in good standing, so that they would be able to pay out when necessary. Many believed that an insurer who was unable to do this risked not only his company, but the shaky foundation on which the industry still rested. If a bad apple went under, it threatened to damage the image of the industry that insurers had worked so hard to build. The claims to mathematical certainty that life insurers had made in the industry’s early years now meant that accurate calculation would have to undergird their daily business. Some actuaries, like Wright, embraced this mathematical project, to strengthen and expand what they believed to be a vital social service. But others resented the encroachment of regulators into their technical knowledge, and resisted sharing information with the public. In 1863, Francis Bowen, professor of moral philosophy and political economy, wrote to Elizur Wright, who had complained about a technical error in a piece Bowen had written. Bowen claimed familiarity with the principles of the industry, having read his “Jones & De Morgan,” but he assured Wright that to have written for an audience of “actuaries or competent mathematicians would have been beside the purpose, and even injurious to the purpose.”25 He understood the error Wright had identified, but insisted that he had not exposed it “because the subject is of interest only to computers, and because it could not be explained without going into technicalities,” which 25 Francis Bowen to Elizur Wright, October 28, 1863. EWWBP, Carton 1, Folder 2: Letters, 1854-1864 [B]. 191 Bowen had “carefully avoided.” He had written his piece in a way so that “common persons” could understand, emphasizing average costs and average life expectancies. His purpose, he reminded Wright, was to “recommend the practice of insuring lives, and to teach necessary caution in the mode of doing so,” which he could do only by writing for “ordinary readers.” For Bowen, the matter was personal. He had, he told Wright, “had the misfortune” to have purchased a policy from a small company, which he later discovered did not have “one person— Secretary, President, Director, or Clerk—who was able to make the simplest computations” in the matter of life insurance. In his own heroic telling, Bowen said he had “fought [his] way out” of that company and “into a sound one,” and encouraged his friends to do the same. He saw Wright’s work in the Insurance Commission as essential. “You can do no better service,” Bowen insisted, “than by strenuously opposing these young and weak companies” that existed only to profit “self- appointed officers,” and would eventually default on the “widows and orphans” who depended on their product. Those who believed that life insurance played a valuable social role in an urbanizing, industrializing nation, still recovering from the war, put their faith in the calculators who supported the industry from within. But they also shared a belief that explaining the “technicalities” of those calculations to the public was a pointless, even counterproductive endeavor. Wright’s vision of a mathematically regulated industry met with enthusiasm from at least some companies. After all, the United States’ life insurance industry had sworn up and down for the previous three decades that their product “rests on Divine law, as its only true basis” and that far from being gamblers on human life, their efforts in fact “banish[ed] speculation from society,” 192 thanks to the laws of probability and the reputable actuaries who read the tables of mortality.26 As commissioner, Wright received hundreds of letters from companies across the U.S. “Our Company is a young but rigorous member of the brotherhood,” A.W. Kellogg wrote to Wright in 1861, “and we intend by care, prudence, and energy to put it on a par with its successful older brothers.” Kellogg assured Wright that he had “calculated our required premium reserve in accordance with the suggestion of your last report,” finding the “accumulations sufficient” and intending to “make the accurate valuation as soon as possible.” But Kellogg also asked if Wright would be willing to value his company’s 700 existing policies and evaluate the company’s financial solvency. Kellogg believed that “a valuation and endorsement by yourself would inspirit our Trustees, and give our members a higher appreciation of their own institution.”27 Even if Kellogg was flattering Wright in hopes of a favorable valuation, his request speaks to the growing faith insurers placed in mathematics. As his firm was based in Wisconsin, he did not need Wright’s approval, except to sell policies in Massachusetts. But Kellogg was likely telling the truth about the board’s trust in Wright’s calculations. Having established the close association between their industry and mathematical certainty, insurers had to—and indeed, often appeared to want to—hire an actuary to value their outstanding policies and decide whether the company was truly solvent or not. Some of the larger firms, especially in New York, hired in-house actuaries right away. Meanwhile, smaller companies struggled to keep up. Two members of the Board of Directors of the German Mutual Life Insurance Company in St. Louis asked Wright in 1863 to value their policies, admitting that the “very small” company could not “afford to pay large sums 26 Considerations on Life Insurance: By a Lady (1855). American Antiquarian Society (Worcester, MA). 27 A.W. Kellogg to Wright, April 18, 1861. EWWBP, Carton 1, Folder 9: Letters, 1854-1864 [K-L]. 193 for the service of actuaries.” They had “some little knowledge of the system and skill in figures” and had tried their best, but were disappointed when Wright told them they had far too many outstanding policies. This news would surely earn them “the active opposition of all the old school companies,” they complained, almost assuredly to Wright’s indifference.28 Not everyone liked Wright’s vision. Many firms desired secrecy, especially if requisite public accountability occurred too often or without warning. The aspect of the industry that Wright wanted to weed out—the temporary lack of sufficient funds to cover all existing policies on the assumption, or bet, that incoming premiums would erase the deficit—was central to many firms’ business strategies, but they recognized how hard this fact would be to explain to customers who had been sold a product of total security, fit for widows and orphans. “The reason why we did not state our returns examined by you,” James Dixon told Wright testily, was that they “revealed facts which alarmed us, and which if published might ruin our business.” The discrepancy in the books was a normal part of doing business, as Dixon saw it, but it was a piece that had to be kept a secret. He insisted that the company would easily recover the balance within a few months, “unless the public confidence is lost.”29 Righting the financial balance required new customers, whom Dixon was confident would come, but not if they thought the company was insolvent. Insurers wanted actuarial mathematics for financial success, not for public accountability. Insurers advertised a world in which policyholders paid into an individual account, which would someday be paid back to their families in a lump sum. But the realities of their business of reinvesting some of their holdings while paying out policies when necessary meant that the public 28 [Isidor] Bush to Wright, December 10, 1863. EWWBP, Carton 1, Folder 2: Letters, 1854-1864 [B]. 29 James Dixon to Wright, January 29, 1855. EWWBP, Carton 1, Folder 4: Letters, 1854-1864 [D]. 194 expectation was not a reality. Knowledge of this amalgamation of wealth and perpetual movement of funds within firms made men like James Dixon nervous around regulators. They believed that if the public saw their business plan, they would reject it out of prejudice, without considering the mathematics of financial services. This presumed ignorance of the public justified insurers’ desire to keep actuarial tables, formula, and calculations private from the public and their representatives in government. For their part, actuaries tended to agree with this assessment. They saw themselves as mathematical experts who performed specialized, difficult work. With their employers insisting that the public would not understand the mathematical foundation of the industry, most actuaries readily agreed that their calculations were too difficult to be widely understood, and that the best thing for the industry was to keep their calculations to themselves. Doubts about the public’s mathematical abilities pervaded both the industry and attempts to regulate it. For people like Wright, the mathematical claims of the life insurance industry meant that reputable calculators like himself should check the books of companies to make sure they were not going to defraud widows and orphans. To achieve this, experts would do the evaluation, and then publish or otherwise disseminate their results so that the public could make an informed choice. But, because they believed the necessary mathematical knowledge to be the province of their profession alone, they had to get the public to trust them. Sheppard Homans, another actuary and long-time friend of Wright’s, told him on the eve of the Massachusetts commission’s founding that he hoped Wright “will be able to convince the public generally (who are averse to statistics) of the soundness of your position.”30 For insurers, meanwhile, mathematics grounded their claims 30 Sheppard Homans to Wright, Dec. 24, 1859. EWWBP, Carton 1, Folder 7: Letters, 1854-1864 [H]. 195 to certainty, but believed that public accountability threatened their business model. They wanted a seal of approval from a mathematical expert who understood that this was not an arithmetical business of static exchanges and a perpetually even balance sheet. For Elizur Wright, the solution for public confidence in life insurance was obvious. The “significance and credibility of the figures” was inextricable from “the motives and moral dignity of the computer.”31 He believed from the beginning of his career until its end that, whatever the judgments of the Massachusetts legislature, trust in life insurance had to begin with the actuary. Only through the work of good, reliable actuaries would the industry thrive. Even in 1879, having been called as an expert witness in a hearing before the New York legislature about the Mutual Life Insurance Company, he claimed that all actuaries, “in their unbought moments,” would agree with him on a technical point about how insurers should use their reserves.32 Like the consulting engineers before him, Wright understood the dangers of mixing science and commerce, but also believed it to be a necessary evil, and one that could be combatted with the right people. He did not see a meaningful distinction between trust in numbers and trust in people—or, if he did, he did not see a way around their intermingling to secure the public confidence.33 31 Elizur Wright letter, July 5, 1860. EWWBP, Carton 2, Folder 26: Insurance Letters, 1845-1863. 32 “Remarks of Elizur Wright, Before the Judiciary Committee of the General Assembly of New York, On the ‘Rebate Plan’ of the Mutual Life Insurance Company. February 19, 1879.” EWWBP, Carton 2, Folder 57: Letters, 1877-1880. 33 Historical literature dealing with the intersections of trust, character, capitalism, and science is extensive but diverse in geography and temporality. See, for example: Steven Shapin, A Social History of Truth: Civility and Science in Seventeenth-Century England (University of Chicago Press, 1994) and The Scientific Life: A Moral History of a Late Modern Vocation (Chicago: University of Chicago Press, 2008); Theodore M. Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton: Princeton University Press, 1996); Harold J. Cook, Matters of Exchange: Commerce, Medicine, and Science in the Dutch Golden Age (New Haven: Yale University Press, 2003); Onora O’Neill, A Question of Trust (Cambridge: Cambridge University Press, 2002); Peter Dear, “From Truth to Disinterestedness in the Seventeenth Century” Social Studies of Science Vol. 22, No. 4 196 The result of Wright’s crusade for accuracy and accountability in life insurance, originally intended to weed out companies who were likely to fail those who purchased their policies, brought capitalists and regulators to a compromise: the authority and reliability of the corporate actuary. This man (in 1920, the Actuarial Society of the America counted one woman in its 260 members) would perform and evaluate the calculations not only to write policies, but to determine and protect the solvency of the company. 34 By the 1870s, moreover, actuaries managed both sides of the deal. In 1872, New York passed a law requiring life insurers to register with the state. The terms of the law stated that solvency would be tested as such. First, each company’s actuary would calculate the firm’s necessary reserve based on its outstanding policies. He would then forward his results to Albany, where a state actuary would check the calculations to determine if they accorded with the law. This regulatory model essentially required that every corporation and every state employ at least one actuary, thus allowing actuaries to define solvency itself. In the emergent financial economy, actuaries had become the new numerate elite. To fully see the extent of their influence, however, one should cast a glance to the changing role of the civil engineer in the decades following the Civil War. The actuary emerged as a corporate calculator from the outset, but by and large engineers had to transition out of their previous consulting roles into positions as private employees of corporations. The increasing postbellum dominance of the corporate calculator model reshaped engineers’ social roles, self-understanding, and mathematical practices. Faced with the growing commercial utility of “abstract” mathematics like algebra and (Nov., 1992), pp. 619-631. On commerce, character, and trust in antebellum America, see Bertram Wyatt-Brown, Lewis Tappan and the Evangelical War against Slavery (Baton Rouge: LSU Press, 1997). 34 Neva R. Deardorff, “Statistical Work for Women” (Bureau of Occupations for Trained Women, Philadelphia), c. 1920. Records of the Bureau of Vocational Information, 1908-1932, Schlesinger Library (Cambridge, MA). 197 analytical statistics, postbellum engineers begrudgingly began to change their definition of what productive and masculine work looked like. Despite their skepticism toward actuarial science and statistical accounting, engineers ultimately reinforced the corporate calculator model, and with it, the increased privatization of mathematical knowledge and skill. “The so-called ‘science of accounts’” In an address delivered to the Society of Engineers and Associates in New York on October 28, 1869, A.S. Cameron stated that across the world, strides in prosperity and improvement were the “direct results of Mechanical progress.” Mechanics and agriculture had always driven human progress, he argued, and would continue to do so. But Cameron identified a disturbing trend in the employment of young American men. Recently, the engineer declared, two ads had appeared in a Philadelphia newspaper: one for a cooper’s apprentice, and one for a clerk in a savings bank. The cooper received a single application; the savings bank, more than two hundred. To account for this bizarre discrepancy, Cameron blamed “the want of a disposition on the part of our young men to engage in Mechanical pursuits and patiently master them.” 35 He fretted that this case reflected a larger lack of respect for mechanical work in the United States. Whether Cameron’s story was true or not, his worry pointed to a growing realization among American engineers that the position they had held before the war was no longer a reality. With the massive industrial production of the Civil War and the expansion of corporate capitalism in its aftermath, engineers migrated out of their consulting positions and into managerial roles in the 35 A.S. Cameron, “On the Necessity of a Bureau of Mechanics: A paper read before the Society of Engineers and Associates, October 28, 1869” (New York: Slater, 1869) 198 1860s and onward. Instead of holding projects accountable in cost and effectiveness in the public eye, engineers increasingly used their mechanical expertise and claims to precise and accurate calculation to hold workers accountable to corporations.36 The Society of Civil Engineers had been organized in 1852, but most parallel societies for metallurgical, mechanical, electrical, and mining engineers emerged in the 1870s and 1880s.37 By the 1870s, their general purpose had shifted from the antebellum period. As William McAlpine, then the President of the Society of Civil Engineers, expressed it in 1874, “The engineer is required to follow the exact rules of mathematics, the stern deductions from science, and the rigid laws of mechanism. The wealth and prosperity of any country depends upon the skill and amount of its labor, usefully applied… It is the peculiar duty of the engineer to instruct and direct labor; his value in his calling depends greatly upon his knowledge of, and ability to instruct in, the best methods of applying either skilled or unskilled labor.”38 As McAlpine’s address suggests, managerial work relied just as much on a formal technical education as consulting, perhaps even more so. He wanted engineers to have the “highest degree of knowledge in the physical sciences, but also long practical experience and sound judgment in the application of such knowledge.” In 1879, one member of the Engineers’ Club of Philadelphia opined that there should be a national examination for engineering. He argued that men who did not meet certain standards should not be allowed to work as engineers, “any more than a lawyer 36 The literature on engineers and industrial management is substantial. Classics include Alfred D. Chandler, The Visible Hand: The Managerial Revolution in America (New York: Knopf, 1977) and David F. Noble, America By Design: Science, Technology, and the Rise of Corporate Capitalism (New York: Knopf, 1977). 37 Noble, America By Design (1977), 37. 38 William J. McAlpine, “Modern Engineering. A Lecture, Delivered at the American Institute in New York” (New York: D. Van Nostrand, 1874). Library Company of Philadelphia (Philadelphia, PA). 199 should be allowed to practice in our courts without being admitted to the bar.”39 On the question of reforming land surveying, another member suggested that Pennsylvania institute “a system of triangulation over the State,” comprising “a network of lines and angular points at convenient distances,” to make surveying easier. His idea suggests that engineers’ enthusiasm for geometrical planning had not diminished in the decades since Ellet’s Laws of Trade. But the rise of large corporations, the spread of specialized office work, and the appearance of abstract financial products—life insurance policies chief among them—threatened the position of the engineer. In the 1860s and 1870s, civil engineers, as well as their brethren in new specialized fields of engineering, still saw themselves as economically essential—even more so with the rise of industrial corporations of previously unknown size and influence. But they did not entirely trust the new professional counters. They largely still saw themselves as productive men managing an economic system based in the physical trade of real commodities, and pushed back on the growing social prestige of corporate actuaries and accountants. The reality of their managerial work, as well as the growing importance of financial securities to the American economy, created a postbellum crisis among professional engineers over what role they would play in this new abstract economy. Ultimately, most would adapt their mathematical principles into scientific management and cost accounting. Engineers eventually accepted the de-emphasis of their previously public role, thereby helping to reinforce the position of the corporate calculator. 39 “Memorial of the Engineers’ Club of Philadelphia, and Citizens of the State of Pennsylvania, to the Honorable Members of the State and House of Representatives in Legislature Assembled. 1878-9.” Library Company of Philadelphia (Philadelphia, PA). 200 In June of 1876, the American Society of Civil Engineers and the American Institute of Mining Engineers held a joint meeting at the Franklin Institute in Philadelphia, an enduring symbol of the value of practical, masculine labor. The subject of the conference was technical education: how well it worked or didn’t, how it might be improved, and how to enact the “elevation of the working-man, in our industrial trades.” With the decline of the apprenticeship system, technical education had become the linchpin of social mobility, at least as engineers understood it. They also wanted, ostensibly from purely charitable instincts, to eliminate all forms of organization that lifted some while restraining others: guilds, castes, government regulations—and of course, trade unions, which the Chairman accused of “crushing labor to a uniformity of despair or sullen indifference.” These men wanted instead to cultivate a “fellowship of knowledge” that would continue a dream from earlier in the century: a nation of working men, using their education in practical science to construct and produce the necessary items in an industrial society.40 But like Cameron, these civil and mining engineers worried that too few young men were pursuing an education in practical mechanics. In his opening address, the Chairman suggested that, especially, in smaller industrial companies, “the bookkeeper stands the best chance of promotion to the manager’s place,” not the engineer. He accused engineers of staying “only within the sphere of their own practice” and sacrificing opportunities to gain authority and impact within corporate structures. But the solution that he and others at the meeting proposed was not that more engineers should engage in bookkeeping, which they considered a chore. Rather, they argued that educators 40 “Discussions on Technical Education, at the Washington Meeting of the American Institute of Mining Engineers, February 22d and 23d, 1876, and at a Joint Meeting of the American Society of Civil Engineers, and the American Institute of Mining Engineers at Philadelphia, and June 19th and 20th, 1876” (Easton, PA: Published by the Institute, 1876). Library Company of Philadelphia (Philadelphia, PA). 201 at technical schools were too prone to forget that their core purpose was “not to produce scholars, professors, or mathematicians” but instead to teach useful skills for a life in industrial work. Civil engineer Ashbel Welch declared that “too much time is given to abstract mathematics” in most engineers’ education, which “unfits him for practical usefulness.” Napoleon, he said, “said LaPlace was good for nothing for business; he was always dealing with infinitesimal quantities.” To Welch, schools turned out too many LaPlaces, and not enough Napoleons. Furthermore, if the mathematics that had so benefited engineers in the antebellum decades had become too theoretical for the current role of the engineer, the meeting members also indicated that their colleagues had not come to grips with the new mathematical authority. Member William P. Shinn observed haughtily that the “so-called ‘science of accounts’—for it is after all only a pseudo-science—appears to be a ‘bugbear’ to engineers generally.” Shinn recalled a moment from decades past, in which an “eminent engineer” had declared, with “satisfaction,” “I have nothing to do with finances or accounts.”41 But Shinn and his colleagues at the Franklin Institute had begun to understand that their old attitudes toward corporations’ private employees, who they had once dismissed as serving capital rather than science, did not fit well in the postbellum economic world. They had to be able to maintain their disinterested credibility even if, as private employees of large corporations, they could no longer claim to be scientific consultants. 41 Ibid. The phrase “science of accounts” seems to have originated in bookkeeping manuals, and become popular in the commercial college textbooks of the postbellum period, with which these men likely would have been familiar. See: Joseph H. Palmer, A Treatise on Practical Book-Keeping and Business Transactions (New York: Pratt Woodford & Co, 1852); H.B. Bryant and H.D. Stratton, Bryant & Stratton’s National Book-Keeping (New York: Ivison & Co., 1860). 202 By the 1870s, the calculations behind the corporations driving the American economy were not merely the adding and subtracting of the antebellum clerk. Accountants, a new profession of expert calculators who had emerged from the ranks of bookkeepers, were introducing new forms of representing—and shaping—business. Accounting and auditing became a central feature of corporations in the decades after the Civil War, fueled by the need for people to handle complex calculative tasks. New methods to measure growth and depreciation, chart production and labor efficiency, and tools for variance analysis all emerged from the postbellum corporation, and shaped its outlook on economic life.42 Some engineers joined the ranks of these calculative pioneers, especially in cost accounting, but the evidence also suggests that in implementing some of these practices, they fell behind their accountant peers.43 Nevertheless, even the efforts these engineers did make suggest a fundamental turnaround from their earlier positions, and the increasing social power corporate calculators achieved through abstract mathematics. Moreover, even as industrial corporations were developing new and complex accounting methods, financial corporations were also joining the field. Life insurance firms, through their in- house actuaries, produced and anchored this market. Life policies became the financial core of a variety of instruments and businesses: insurers invested their reserves in mortgages, savings banks, commodity futures, and beyond. In 1876, the Pacific Mutual Life Insurance Company of California invested nearly all its additional reserve in real estate securities in the northeast, literally banking 42 Chandler, The Visible Hand (1977); Peter Miller, “Governing by Numbers: Why Calculative Practices Matter” Social Research, Vol. 68, No. 2, Numbers (Summer 2001), pp. 379-396; Caitlin Clare Rosenthal, “From Memory to Mastery: Accounting for Control in America, 1750-1880” PhD Dissertation, Harvard University (2012). 43 Chandler, The Visible Hand (1977), 274. 203 on those states’ higher interest rates.44 Family savings banks also became a popular source of life policies, thereby muddling the line between insurance firm and bank. Savings banks could make loans for mortgages and other investments, and could operate as commercial banks.45 The growth in financial instruments allowed life insurance firms to diversify their portfolios, but they did not advertise this to the public, continuing the cycle of mathematical secrecy. The ascendance of the science of accounts in both industrial and financial capitalism in this period unveiled the fissures of the increasingly mathematical economy. The algebra and statistics accountants and actuaries used, which turned monetary abstractions into productive and legitimate commodities, competed with engineers’ ideas of planned, rational space. Both thought themselves expert, scientific, disinterested calculators, but the mathematics in which they were educated, and found most useful, pointed them in divergent economic directions, even as they both moved into private calculating roles for corporations. But despite their professed outrage, engineers had long held a position of private expertise within the otherwise public useful knowledge economy. The rise of large corporations and specialized technical education elevated an aspect of their profession that had existed since the 1820s. They had almost always elevated expert judgment over the fixed rules of public accountability. The massive expansion of corporations after the Civil War removed their role as public representatives, allow them to become purely private experts. Meanwhile, the importance of the “science of accounts” pointed to another development: the devaluation of arithmetical bookkeeping. Whereas keeping one’s books had been a sign of 44 J. Crackbon to Wright, May 27, 1876. EWWBP, Carton 1, Folder 35: Letters, 1868-1872 [C]. 45 “Elements of Life Insurance: For the Use of Family Banks” (Boston: Wright & Potter, 1876). American Antiquarian Society (Worcester, MA). 204 economic independence in the antebellum period, with the ideal that men would all be independent proprietors of one sort of business or another, corporatization turned bookkeeping into “clerical drudgery.”46 Of course, the need for someone—or something—to keep the basic numbers in order did not vanish. Indeed, the bigger corporations got, the more numbers they produced, and the more work was involved in keeping them straight. But engineers were not alone in their prejudice against clerical work; actuaries and accountants also viewed themselves as mathematical experts. All of these corporate calculators wanted to make the rules, not follow them. As a result, the importance of arithmetic diminished during this period, with far-reaching consequences. “Nothing but the art of numbers” In 1888, Benjamin G. Buttolph looked back on his experiences working for the inspections department of a railcar factory in Providence, Rhode Island. In one instance, he had been asked by his superior to create a table of different mechanical concerns, mainly the pressures placed on the cars at various points in the curvature of the tracks. Producing detailed “computation of the tables,” Buttolph recalled, had not been “very difficult, but rather laborious.” To Buttolph, looking back at the end of the 1880s, the creation of tables and the work of computation had been drudgery, a task he agreed to do in his new position, but in which he took no joy.47 Even as corporate calculators made new advances in calculative techniques, and amassed greater and more widespread influence in the postbellum business landscape, the wider meaning of calculation in the United States was changing. Whereas fifty years prior, calculation of any sort 46 “Discussions on Technical Education” (1876). 47 Reminiscences of Benjamin G. Buttolph Covering His Apprenticeship in the Inspection Department from July 31st, 1888 to Nov. 20th, 1891. Rhode Island Historical Society (Providence, RI). 205 had been understood as a marker of economic independence, even if not everyone enjoyed it, a series of economic, cultural, and technological changes in the middle of the century had begun to change that, leading to Buttolph’s malaise. Tasks that had once indicated the business man’s self- ownership began to become those of the clerk, the secretary, or even the machine. A gap between skilled and unskilled business calculation began to open in practice and thought, pushing even corporate calculators to scramble to stay on the right side of the line. They succeeded, but at the expense of the central facets of the arithmetic economy: education in commercial arithmetic, and the idea of bookkeeping as a masculine skill of economic self-ownership. The growing need for numerical calculation in the postbellum corporation had a somewhat ironic effect in the emergence of menial calculators. A driving force behind this shift was the rise of expert, professional calculators: actuaries, engineers, and eventually accountants. Actuaries and accountants, in particular, claimed a special relationship to their numbers in analysis, sometimes referred to at the time as “interpretation.” Their professional societies, the examinations needed to enter them, and their seemingly essential status as the scientists behind corporate productivity and growth earned them the status of skilled laborers. But this small brotherhood of experts could not do all the necessarily calculations themselves, and they therefore needed to hire people to do them. In doing so, they created a new meaning for an old position: that of the bookkeeper, who continued to calculate, but without having to think about the meaning of his work, as a businessman would have had to in prior decades. This process was a gradual one—even in the 1890s, accountants were still striving to distinguish themselves from bookkeepers—but it was one with immense economic and cultural significance for American mathematics. 206 Decades of the proliferation of bookkeeping and arithmetic textbooks, manuals, and ready-reckoners had expanded the ranks of what professional accountants and actuaries viewed as the “minimally numerate” in the postbellum U.S.48 Legitimate “actuarial labor,” explained Emory McClintock in 1872, meant the complex mathematics that he and his colleagues performed. Simple calculations, on the other hand, referred to “the clerical and typographical labor involved,” which could be done by the bookkeepers and secretaries employed in large firms.49 What actuaries did, as McClintock saw it, required an advanced knowledge of mathematics, experience and training in the profession, and scientific disinterestedness. These types of knowledge justified the salaries that actuaries received and the division of labor that those salaries implied, just as Elizur Wright had justified the payments for his tables and calculations in the previous decade. Actuaries used reason, analysis, and judgment. They did not simply transcribe tables. This distinction, between calculation and mathematics, allowed men like McClintock to solidify their positions. But it had not been a natural one in the United States even a generation earlier. Just as algebra had been made useful, so too did arithmetic have to be actively made mindless. Arguably no evidence better illustrates the changing nature of arithmetic in postbellum America than the rise of women bookkeepers, and the simultaneous demotion of bookkeeping to secretarial labor. In the years between 1870 and 1930, record numbers of women joined American corporations, especially in the financial and banking industries. Insurance firms were among the first to employ large-scale clerical labor on a national scale, and in doing so adopt a gendered 48 Rosenthal, “From Memory to Mastery,” pp. 176-7. 49 Emory McClintock to Wright, April 22. EWWBP, Carton 1, Folder 51: Letters, 1872 [M]. 207 division of labor in the office that would persist well into the twentieth century.50 Elizur Wright, always ahead of his time, hired his daughters to do some of his calculations for him as early as the 1860s. And although employing his family members did not help his case when he was accused of corruption in 1866, his idea was not limited to nepotism, nor was he unique in looking to female labor. In 1860, he received a letter from a young woman seeking employment as a copyist, aware that Wright employed his daughters as calculators, and that “other ladies [are] employed in the same manner in other departments.” Miss Fletcher was partially inspired by the war, noting that “in times of political excitement there is often much such work to be done.” But she also declared that she would “be glad… to make it my ‘profession’ for life.”51 Miss Fletcher may have been particularly interested in Wright’s commission because she had heard that he employed his wife and daughter, but her awareness that women were joining this line of work was prescient. During the war, women filled clerical positions in firms, and afterward they remained as essential components of the emerging corporate office. Bookkeeping became one of the primary secretarial tasks that women performed in these spaces, especially as accounting became a supposedly more mathematically complex form of work. By the 1880s, older ideas about women’s insufficient capacity for methodical, logical calculation had reversed. In an 1888 edition of his Standard Book-Keeping for Business Colleges, prolific textbook author Ira Mayhew stated that, while keeping books was important for any self-respecting business man, he observed that in 50 Angel Kwolek-Folland, Engendering Business: Men and Women in the Corporate Office, 1870-1930 (Johns Hopkins University Press: Baltimore, 1994), pp. 2-3. 51 M.L. Fletcher to Wright, March 18th, 1860. EWWBP, Carton 1, Folder 6: Letters, 1854-1864 [F-G]. 208 many larger offices “women are preferred for book-keepers.”52 As a result of the new prominence of the corporate calculator, Americans’ relationship with mathematics shifted. What had once been a signifier of economic independence had become domestic office work.53 By the 1920s, the position of bookkeeper had largely been subsumed by that of the clerk or secretary. Rather than an essential form of economic knowledge, bookkeeping was “viewed as a specialized kind of office work” for secretaries, “which to be intelligently done should be based upon a wide knowledge of business services and subsidiary office work” and leaving calculation a near-afterthought. The modern bookkeeper would no longer be “the actual keeper of the ledger,” but rather a general office secretary with a wide, shallow knowledge of industry practices who also possessed decent typing skills and an ability to follow instructions.54 In 1920, Marguerite McNair, a statistical clerk for Consolidated Steel, made $1,500 per year “computing and combining figures” with “no interpretation.” That clause about interpretation divided the secretarial workers from their superiors. Irma Reilly, another statistical clerk, made $1,800 a year for “computing index numbers, tabulating, etc., no interpretation.” In contrast, Edith Miller at the National Bank of Commerce had an annual salary of $5,000 for “planning, executing, and interpreting data.”55 52 Ira Mayhew, Standard Book-Keeping for Business Colleges, Commercial Departments, the Counting-Room, and Self Instruction (Chicago: Buckbee & Co., 1888), p. 10. 53 On the domestication of the corporate office during the late nineteenth century, see Claudia Goldin, Understanding the Gender Gap: An Economic History of American Women (1992); Elyce J. Rotella, From Home to Office: U.S. Women at Work, 1870-1930 (Ann Arbor: UMI Research Press, 1981); Sharon Hartman Stone, Beyond the Typewriter: Gender, Class, and the Origins of Modern American Office Work, 1900-1930 (Urbana: University of Illinois Press, 1992). 54 Federal Board for Vocational Education: Selected Office and Store Occupations in the United States in 1920 and 1910. Records of the Bureau of Vocational Information, 1908-1932. Schlesinger Library (Cambridge, MA). 55 Questionnaires for Statistical Workers in Government offices: Jan 1, 1919—Dec. 31, 1920. Records of the Bureau of Vocational Information, 1908-1932. Schlesinger Library (Cambridge, MA). 209 Rather than independent reasoning, arithmetic bookkeeping now denoted “mechanical” work being performed “under the guidance of a few directing minds.”56 Although Edith Miller was hired to interpret data in 1920, the vast majority of the “directing minds” in corporate offices belonged to men. Postbellum corporate calculators may have changed what types of mathematics were seen to be useful, but they did not sever the links between commercial utility and masculinity. On the contrary, they continued to claim their inherent manly authority in economic life. Rather, the gender of mathematics itself shifted. Analytical algebra and statistics, mocked as “dear Miss Anna Lytical” by Dartmouth students only a generation earlier, transformed from effete ornament into useful, manly knowledge. That transformation paralleled the feminization of what had once been a notably masculine understanding of arithmetic calculation. The consolidation of economic power and authority by corporate calculators, themselves almost exclusively men, ensured that no matter what mathematics reigned supreme, it would be seen as masculine. In addition to the growing prominence of women in bookkeeping, the nascent but rapidly spreading prevalence of mechanical calculators also reinforced the slow devaluation of arithmetic calculation. Perhaps unsurprisingly, Elizur Wright invented a device he called an “arithmeter” for accurate calculation in insurance offices. He patented the cylindrical device in 1869, and had his son Walter take it to actuaries at large insurance firms, and explain how it worked, in hopes that they would purchase one and use it in their departments.57 Emory McClintock, after meeting with 56 Neva R. Deardorff, “Statistical Work for Women” (Published by the Bureau of Occupations for Trained Women, Philadelphia), n.d. Records of the Bureau of Vocational Information, 1908-1932. Schlesinger Library (Cambridge, MA). 57 Emory McClintock to Wright, October 5, 1869. EWWBP, Carton 1, Folder 41: Letters, 1868-1872 [M]; Sheppard Homans to Wright, March 14, 1870. Carton 1, Folder 38: Letters, 1868-1872 [H]. 210 Walter and finding himself impressed with the machine, also suggested that it be modified “for the use of banks in computing interest at a given rate” by dividing the device’s multiplying wheel into logarithms, so that each tick would “correspond to the logarithm of the interest on $1 for 300 days at 7%.”58 While Wright’s device was initially something of a novelty, life insurance firms quickly began to adopt it, thrilled at the “prospect of abridging the labor in computing our dividends,” and purchasing it at nearly the same rate as they did the typewriter.59 The mechanization of calculation had the same effect on that form of skilled labor as it has on many others. No longer did someone need an education to do the work effectively, so a high wage or salary was no longer needed to attract skilled people to the work, and wider cultural assumptions about calculation shifted away from older ideas about economic independence and began to see it as drudgery. Government offices followed industry; in 1921, most clerks at the post office used a calculating machine for their work, as did the statistical clerks at the Weather Bureau.60 Calculating machines, especially when combined with the feminization of bookkeeping and secretarial labor, and the stratification of numerical tasks within the corporation, did more than alienate skilled from unskilled calculators in the economic imagination. They also contributed to a larger breakdown in the close association of arithmetic with economic reasoning in the public eye, including within the American school system. Arithmetic, once the cornerstone of the useful knowledge economy, began to lose its perceived utility. 58 McClintock to Wright, October 5, 1869. 59 Homans to Wright, March 14, 1870; Goodheart, Abolitionist, Actuary, Atheist (1990), p. 149. 60 Questionnaires for Statistical Workers in Government offices: Jan 1, 1919—Dec. 31, 1920. Records of the Bureau of Vocational Information, 1908-1932. Schlesinger Library (Cambridge, MA). On knowledge production in the postbellum Weather Bureau, see Jamie Pietruska, “U.S. Weather Bureau Chief Willis Moore and the Reimagination of Uncertainty in Long-Range Forecasting,” Environment and History 17 (2011): 79-105. 211 On April 12, 1887, Francis Amasa Walker gave a speech to the Boston School Committee on the nature of secondary school mathematics education. Walker had been an engineer, a soldier, and a faculty member at the nascent Massachusetts Institute of Technology, and had ascended to president of the university five years prior. In the 1870s and 1880s he published two books about political economy: The Wages Question in 1876, and the college textbook, Political Economy, in 1883, which became a staple of college courses in political economy in the late nineteenth century, assigned alongside Smith, Ricardo, Mill, as well as domestic American economists. Walker would later go on to hold leadership roles in both the American Statistical Association and the American Economic Association, and become General Superintendent of the Census Department.61 Clearly, he believed in the promise of mathematics to answer the needs of both science and business. But it was not on any of these subjects that he addressed the School Committee. In his address, Walker argued that arithmetic now took up too much of students’ time in grammar and primary school. He told the assembled audience that a “false arithmetic has grown up” and crowded out “that true arithmetic which is nothing but the art of numbers.” A generation ago, he said, no doubt somewhat nostalgically, “studies in the district school were few and simple. Reading, writing, and arithmetic, a little grammar, and a little political geography made up the course of study.” But in the last two or three decades, too many new studies had been introduced, which emphasized “intellectual training” instead of practicality. Walker specifically recommended that schools eliminate compound interest, compound proportion, compound partnership, cube root 61 Richard Adelstein, “Mind and Hand: Economics and Engineering at the Massachusetts Institute of Technology” in William J. Barber, et al. (eds.), Breaking the Academic Mould: Economists and American Higher Learning in the Nineteenth Century (Middletown: Wesleyan University Press, 1988), pp. 290-317 212 and its applications, equation of payments, and rates of exchange from the general curriculum in arithmetic. He also advised that homework in arithmetic be given “only in exceptional cases,” that no more than three and a half hours a week be spent on the subject, and that examinations to move from primary to grammar school be “as simple as possible.”62 Walker complained that arithmetic had become too “technical” in its pedagogy, when its “main purpose” was “to secure accuracy and a reasonable degree of facility in plain, ordinary ciphering.” Teachers and textbooks had become too enamored with in the idea that arithmetic gave students right-reasoning skills, he said. But the logic puzzles that arithmetic problems had become made no sense when the purpose of arithmetic was to teach practical economic skills. “In a store or shop or factory, or on a railroad,” Walker said, “a lad who cannot set down figures and add them rightly every time is little better than a cripple.” He also mustered evidence from current students and parents, who complained to him and others about the amount of time children spent on their arithmetic and their parents’ struggles to keep up with the new information, blaming “the inveterate superstition of the New England mind, that it is well the child should be worried and perplexed in education” for the persistence of these problems.63 Walker shared with other mathematicians and educators of this period a “general feeling” that “the teaching of arithmetic has been overdone in our schools,” and that schools required a reversion to basic principles.64 62 Francis A. Walker, “Arithmetic in Primary and Grammar Schools. Remarks of Mr. Walker in the s, April 12, 1887” (Boston: Damrell & Upham, 1887). Massachusetts Historical Society (Boston, MA). 63 Ibid. 64 Florian Cajori, The Teaching and History of Mathematics in the United States (Washington: GPO, 1890), p. 111. This quotation is an interjection that Cajori makes into his history, reflecting on the state of mathematical education in his own time, roughly the same year as Walker’s address to the Boston School Committee. 213 In his reference to “principles,” Walker sounded reminiscent of earlier attitude toward the teaching of mathematics. But in calling for a version of the subject that was “nothing but the art of numbers,” he eliminated the self-judgment that had been championed by antebellum educational reformers. What Walker wanted was a version of arithmetical pedagogy that looked all the way back to the eighteenth century, that would produce completely accurate computers—essentially, human adding machines. He declared that “employers have, literally, no use for boys who make mistakes in numbers.” Walker’s pedagogical philosophy reflected the growing public prominence of the industrial corporation, which ran on the operation of hundreds of moving parts, both human and machine. He still believed that arithmetic should be a fundamental part of children’s education, but his emphasis suggested that it was a mere baseline for getting and holding down a job, not a symbol of an idealized democratic marketplace. In this, Walker reinforced corporate calculators’ disassociation of economic mathematics and public accountability. Walker’s attitude was also apparent in the new commercial colleges.65 These schools began emerging in the 1850s and 1860s as something in between prototypes for business colleges and clerical or secretarial schools. Their stated purpose was not unlike that of the arithmetic classes of an earlier period, although they were more formalized and included more direct education in bookkeeping, formal writing style and penmanship, and other forms of corporate record keeping. Commercial colleges claimed to cater to the future “business man,” but their primary result was to churn out the quick, accurate clerks and bookkeepers now in high demand in both government and corporate offices.66 Although commercial college textbooks did cover much of the material that 65 Walker, “Arithmetic in Primary and Grammar Schools” (1887). 66 Chandler, The Visible Hand (1977), pp. 466-7; Rosenthal, “Memory to Mastery” (2012), pp. 150-151. 214 antebellum arithmetic textbooks did, including the items that Walker wanted to see cut out of the curriculum in the 1880s, they also emphasized secretarial skills. A “practical familiarity of General Book-keeping,” Ira Mayhew argued, mattered much more than the “perfect comprehension of the mysteries of square and cube root, of arithmetical and geometrical progression, of permutations and combinations, of the summation of an infinite series, etc.”67 To that end, commercial college textbooks often dismissed higher mathematics to focus on shortcuts and tricks, prioritizing accuracy and speed over reason and analysis in such a way that would likely been distressing to old advocates of mental arithmetic. “It is not our purpose,” one explained, “to introduce any of the higher branches of mathematics, viz., Algebra, Conic Sections, Calculus,” but rather, “a system of calculation that is practical to every business man.”68 Others dismissed double entry bookkeeping as a mystery and “a scheme for swindling” that wasted clerks’ time.69 Many emphasized shortcuts to computation or ways to approximate things that might not need to be perfectly precise, especially involving interest rates—assuming 360 days per year for a 6% interest rate could make a calculation much faster without sacrificing accuracy.70 Above all, texts promised to reduce the “mental labor” involved in bookkeeping, through methods that would require “no great mental exertion,” and thus allow an individual to work “a whole day without any mental fatigue.”71 In fact, the new arithmetic required very little mental work at all. 67 Ira Mayhew, A Practical System of Bookkeeping (Boston: Bazin & Ellsworth, 1861), pp. viii-ix. 68 John E. Wade, “The Merchants & Mechanics’ Commercial Arithmetic; or, Instantaneous Method of Computing Numbers” (New York: Russell Brothers, 1872). 69 Thomas Jones, Paradoxes of Debit and Credit Demolished (New York: John Wiley, 1859). 70 George N. Comer, Book-Keeping Rationalized (Boston: Comer & Co., 1862). 71 Wade, “The Merchants & Mechanics’ Commercial Arithmetic” (1872). 215 The declining position of arithmetic in postbellum America was not the first time that this kind of calculation had come under attack; even in the United States, arithmetic had long straddled the line between mathematical reasoning and clerical drudgery.72 But when and how certain types of mathematics change their meaning depends on a set of historically contingent factors, even for arithmetic. In the United States after the Civil War, with the rise of large corporations, professional bodies for the numerate elite, new mechanical calculators, and an increasingly female workforce, commercial calculations separated into skilled and unskilled. The rise of the corporate calculators exacerbated the latent divisions in mathematical skill between expert and lay, and helped create an economic system in which only the formers’ calculations had legitimacy as economic knowledge, and the latter became a menial task. Analytic or interpretive calculation allowed those who wielded it to enter positions of commercial management, control, and independence. Those who lacked it, meanwhile, became subject to, rather than in command of, an increasingly mathematical economy, one moving further and further beyond the reach of public critique. “Bad Choctaw and worse algebra” In 1861, when life insurers surveyed the business landscape and considered the future, they concluded that “outside of public opinion, we face no difficulty.”73 That difficulty did not prove to be a small one. Despite efforts to assuage it with essays, advertisements, and other publications, 72 On the shifting meaning of “calculation” in Europe in the nineteenth century, see Lorraine Daston, “Enlightenment Calculations” Critical Inquiry, Vol. 21, No. 1 (Autumn, 1994), pp. 182-202. On the idea of clerical drudgery in American history, see: Michael Zakim, “Producing Capitalism: The Clerk at Work” in Zakim and Kornblith, Capitalism Takes Command: The Social Transformation of Nineteenth-Century America (Chicago: University of Chicago Press, 2012) and Brian Luskey, On the Make: Clerks and the Quest for Capital in Nineteenth- Century America (New York: NYU Press, 2010). 73 O.P Rice to Wright, Nov. 23, 1861. EWWBP, Carton 1, Folder 13: Letters, 1854-1864 [Q-R]. 216 public skepticism of life insurance expanded. Over the next three decades, public criticism of life insurers focused not on the potential sacrilege of predicting death, as in the antebellum period, but on the core of the postbellum life insurance industry: algebraic calculations and the actuaries who performed them. In 1874, Yale mathematics professor John Howard van Amringe identified the insurance industry’s “formulae and the numerous tables” as the culprit. An occasional consultant for insurance firms, he argued that these formulae “render the subject a mystery to many,” and sometimes causing the “unreflecting” public “to suppose that chance governs a company in the determination of its rates and the conduct of its affairs.” Amringe assured readers that this was not the case, that the “mystery is simply one of language and not of principle.” But repeated insistence on “well-known and fixed laws” did little to slow growing public worry.74 By the 1870s, insurers had become acutely aware of growing public suspicion. They fretted that too many understood the industry and its products as “an extraordinary anomaly and enigma… exciting the distrust, indignation, and execration of the public.” Some blamed consumers, warning them that it was their “incaution” in buying policies that had saddled the industry with its current, undeserved disrepute.75 Others tried to address one of the main points of contention: the idea that the firms were using mathematics to value policies that ordinary people could not understand, and feared they were being cheated in some way. Net premiums, Amringe explained in an essay on life insurance, were “simple and require for their comprehension no knowledge beyond the most elementary.” Actuaries used formulae with variables instead of arithmetic numbers because doing 74 J.H. Van Amringe, A Plain Exposition of the Theory and Practice of Life Assurance (New York: Charles A. Kittle, 1874). 75 “Elements of Life Insurance: For the Use of Family Banks” (Boston: Wright & Potter, 1876). 217 calculations for each policy would be “tedious and laborious” and make it “impossible to transact business.” Amringe stressed that the “principles” of life insurance were as straightforward as they had always been, it was just the “methods” that had become more complex.76 Amringe’s “principles” referred to older ideas about paying into an individual policy and getting it back at the time of death, but it was their algebraic “methods” that insurers worried about most in public criticism. In response, some insurers and their supporters tried to reassure the public that they were, in fact, following objective mathematical rules, rather than opportunistic profit- seeking or wanton gambling. But the realities of insurers’ business model did mean that they were not dealing in the static transactions that years of arithmetic text-books and published reports had trained most Americans to look for. Instead, they had to account over lifespans and incorporate various levels of uncertainty. Over time, actuaries and their employers increasingly read public distrust in their algebraic methods as faulty understanding of their business principles, or simply a complete lack thereof. Texts like Amringe’s essay tried to ameliorate concerns about life insurance without delving into the specific calculative techniques used by actuaries. The result was a learned mathematical helplessness in ordinary people’s encounters with the industry. That confusion, in turn, reinforced experts’ lack of confidence in their mathematical abilities. In private, some firms despaired at the task of reconciling the mathematical needs of their business and the public’s unforgiving standards. In 1866, an insurer in Ohio told Wright that while he understood Wright’s concern that the firm’s books did not indicate a sufficient reserve fund for the current outstanding policies, he begged Wright not to publish the information. The public, he 76 Amringe, A Plain Exposition (1874). 218 said, “will understand nothing,” and the punish the company unduly for what was in reality a minor indiscretion.77 In 1871, another individual complained to Wright that “in these days of newly awakened distrust on the part of the public,” which he blamed on “the demoralization of some of the new companies,” his Hartford firm simply had to present a more favorable statement to the public than internally to the Board of Directors.78 The daily running of the business required a certain degree of uncertainty, managers and actuaries agreed, but they maintained that there was no other way to successfully run a life insurance company, especially when every other company was doing the same thing, some with larger staffs or higher reserves. One response to this claim was the boom in fraternal collectives in American towns and cities. By the end of the 1880s, at least half of those Americans who had some kind of life policy had gotten it from a cooperative organization, perhaps more, and there is little if any evidence that they were any less successful than private corporations in managing their members’ common risks in accident or life policies. They did so not through creating mathematically tiered policies for as many members as possible, as private corporate insurers did, but by insuring a small group of like people with similar risks.79 Fraternal organizations expanded rapidly after 1860 not only because they were integrated into individuals’ communities and workplaces, and thus local and accessible, although that was immensely important. Over time, the fact that these types of organizations did not boast any mathematical backing also became a point in their favor. Rather than link policies to 77 J. Mills to Wright, June 9, 1866. EWWBP, Carton 1, Folder 25: Letters, 1864-1868 [M]. 78 Rodney Dennis to Wright, January 10, 1871. EWWBP, Carton 1, Folder 36: Letters, 1868-1872 [D-E]. 79 Robert Whaples and David Buffum, “Fraternalism, Paternalism, the Family, and the Market: Insurance a Century Ago” Social Science History, Vol. 15, No. 1 (Spring, 1991), p. 103; Witt, The Accidental Republic (2004), p. 72; Dan Bouk, “The Science of Difference: Developing Tools for Discrimination in the American Life Insurance Industry, 1830—1930” Enterprise & Society, Vol. 12, No. 4 (December 2011), p. 723. 219 age or health, as private insurers did, and which often priced especially vulnerable workers out of their protections, fraternal organizations emphasized a simpler and seemingly more objective way of protecting their members, without any actuaries needed.80 These associations sought to provide an alternative to the algebraic, actuarial science of commercial life insurance. M.W. Hackett, of the Ancient Order of United Workmen, a fraternal organization that developed a tontine-style insurance plan for its members, declared in the 1870s that actuaries were “false scientists.” He and others like him believed that the algebraic calculations behind life insurance policies were nothing more than trickery designed to line the pockets of the insurers at the expense of working men and their families. The AOUW also boasted to its members that they had no corporate personnel on the payroll—especially actuaries, who they held in special disregard as the main purveyors of wanton speculation and corporate profit. Any proposed method that had “too much of insurance methods” about it was likely to be rejected.81 These organizations were not explicitly religious, excepting cultural or ethnic ones for Catholics or Jews. They objected to life insurance not because they felt the business itself was amoral, but because they refused to risk their livelihoods on mathematics that they did not trust. In 1886, the Travelers Insurance Company condemned fraternalism as “a revolt against the multiplication tables.”82 Facing such significant competition, many life insurers condemned these 80 Whaples and Buffum, “Fraternalism, Paternalism, the Family, and the Market” (1991), p. 104. See also George Emery, A Young Man's Benefit: The Independent Order of Odd Fellows and Sickness Insurance in the United States and Canada, 1860-1929 (Montreal: McGill-Queen’s University Press, 1999); Jason Kaufman, For the Common Good? American Civic Life and the Golden Age of Fraternity (New York: Oxford University Press, 2002); Mark C. Carnes, Secret Ritual and Manhood in Victorian America (New Haven: Yale University Press, 1991); Mary Ann Clawson, Constructing Brotherhood: Class, Gender, and Fraternalism (Princeton University Press, 1989). 81 Levy, Freaks of Fortune (2012), pp. 194-204. 82 Quoted in Levy, Freaks of Fortune (2012), p. 214. 220 “tontine schemers” as existential threats to the stability and reputation of the industry.83 Certainly the competition irritated everyone in the private insurance business, but the fraternal organizations’ assault on the credibility of actuarial calculations stung most sharply for people like Elizur Wright, who believed that clear and accurate algebra was the only means to preserve the necessary social safety net that life insurance provided. Insurers attacked fraternal organizations as the source of instability in life insurance, as they lacked a scientific foundation, and were not legally enforceable in the same way a corporate insurance contract was. They held that fraternal societies who offered policies without actuaries had no respect for “mathematical axioms,” and in doing so threatened “real” insurance business.84 Of course, when fraternal organizations were forced to adopt statistical practices in the twentieth century, actuaries were prepared.85 Elizur’s son Walter offered valuation tables to fraternal organizations from his Boston office for $5 each.86 Elizur, for his part, did not see fraternal organizations as the only threats to life insurance. Indeed, he opposed them in part for the same reason he distrusted other kinds of small or otherwise disreputable life insurance firms: because they did not undergird their business with sophisticated mathematical techniques. But although he was especially dedicated to this cause, he was not alone in wanting to see the business hew closely to mathematics in its dealings. As early as the 1850s, some onlookers had railed against new forms of insurance that seemed to threaten safe, established principles, or otherwise seemed to be trying to cheat the mathematical laws of insurance. An 1851 83 R.L. Day to Wright, April 22. EWWBP, Carton 1, Folder 48: Letters, 1872 [D-G]. 84 “Connecticut Report, Part Three: Fraternal Insurance” in Journal of the Institute of Actuaries, Volume 28 (1898), p. 355. 85 On fraternal organizations shifting to more mathematical practices, see Levy pp. 228-229. 86 “Valuable tables prepared especially for the use of Fraternal Associations. By Walter C Wright, Consulting Actuary” (n.d.). EWWBP, Carton 2, Folder 9: Printed Announcements. 221 screed accused mutual firms of being “experimenters, who desire to make two and two five, instead of four, as generally considered” by what the author deemed “as fixed for all practical purposes as those which govern the movement of our planet.” He declared that mutual life companies lacked “enough science to keep them alive during the next ten years”—a prophecy that did not, of course, come to pass, as they became the bedrock of the industry in the ensuring decades.87 Nevertheless, public faith in life insurers’ mathematics both helped and constrained insurers. Like Elizur Wright, others fretted that firms that were “very unsound” might nevertheless “present to the eye a goodly array of figures,” or that a company might steal or squander the money invested in it “and show no obvious symptoms of its insolvency for a generation.”88 As early as 1859, actuary Nicholas DeGroot warned his colleagues that sufficient reserve funds held “utmost importance to the public,” because life insurers were essentially acting “like savings banks” and therefore its patrons should be able to withdraw their investments at any time. Without “adequate reserves,” DeGroot said, the entire financial system around life insurance “must eventually prove a public delusion.”89 As the industry grew, many members became increasingly worried that a few bad eggs—as they saw it—would bring down the entire industry. The public’s growing skepticism, one insurer complained to Elizur Wright in 1871, stemmed from the “demoralizations” of many of the “new companies.” As these corporations played greater roles in the larger financial universe, the more consequential each individual failure seemed to insurers.90 87 Pro Bono Publico, “Life Insurance. Credit System. Being a Review of an Official Document of the Mutual Benefit Life Insurance Company of New Jersey” (1851). American Antiquarian Society (Worcester, MA). 88 Nicholas DeGroot to Wright, March 19, 1860. EWWBP, Carton 1, Folder 4: Letters, 1854-1864 [D]; Amringe, A Plain Exposition (1874). 89 DeGroot to Joseph Collins, December 21, 1859. EWWBP, 90 Rodney Dennis to Wright, January 10, 1871. EWWBP, Carton 1, Folder 36: Letters, 1868-1872 [D-E]. 222 DeGroot would ultimately prove correct. In the late 1860s, the life insurance market, after years of massive expansion, contracted severely. Firms had invested their income liberally, even wildly, creating profoundly risky portfolios across the American financial landscape. When the securities markets weakened in the early 1870s, insurers’ assets declined sharply. The bank panic of 1873 delivered a final blow, and by 1877, nearly two-thirds of American life companies had declared bankruptcy.91 As life companies and banks failed in September of 1873, actuary Charles Hibbard bemoaned that the “rottenness of life insurance co’s is daily being exposed.” He warned Elizur Wright that if the public could not trust insurers to invest their money wisely, and if policy- holders had no power to withdraw their deposits at will, “the security of life insurance companies will be at the least questionable.”92 Meanwhile, victims and onlookers railed against the insurers who had risked—and lost—the savings of husbands and widows because they lacked the sufficient reserves for which some had long advocated. Newspapers condemned actuaries as possessing “the miserable skill to enrich themselves out of the common ruin.”93 The accusations lobbed at actuaries primarily involved their mathematics. Obviously, this group must have made some kind of mistake, the thinking appears to have gone, otherwise the life insurance industry would not have collapsed so spectacularly. T.S. Lambert, an actuary who had always disliked the turn in his profession toward more abstract mathematics, seethed in 1875 that the “tricks and dupery” of life companies’ actuaries, who were “barnacled upon life insurance as its wiseacres and helmsmen,” had ruined an industry he vehemently believed to be a safety net for 91 Murphy, Investing in Life (2010), p. 287. 92 Charles Hibbard to Wright, September 19, 1873. EWWBP, Carton 1, Folder 59: Letters, 1873-1875 [H]. 93 “Elements of Life Insurance: For the Use of Family Banks” (Boston: Wright & Potter, 1876). American Antiquarian Society (Worcester, MA). 223 widows and orphans. “For such fictions to be called scientific,” he fumed, “is enough to make a tolerably intelligent man sick of his kind.” 94 But as furious as Lambert was that these ‘tricks and dupery’ could be passed off as “the vocation of mathematics,” the industry had built its foundations on the secret mathematics done by its corporate calculators. They had made mathematics a mystery to the public, and thus bore the general wrath against their profession. Actuaries like Charles Hibbard jumped to defend their position, to distinguish themselves from those “men who pretend to be scientific” who were truly to blame.95 They insisted that they should receive no more blame for the panic than ship captains navigating a storm, and that “many life companies… would have been saved if the warning of the Actuary had been heeded and obeyed.”96 Some had done more than speak out. Sheppard Homans was dismissed from New York Mutual in 1872 when he refused to validate the firm’s books for regulators, on the grounds that they were dangerously inaccurate.97 But for the most part, actuaries doubled down on their work. While some blamed corporate managers, many also despaired that the incident proved the public did not understand the industry. Hibbard implored Elizur Wright to “do what you can to enlighten the public on the mysteries of life insurance,” while Homans reflected moodily that he wished the “insuring public would do a little more of their own thinking” instead of trusting company agents.98 In general, they believed, the public was irrational, and mathematically-illiterate. 94 T.S. Lambert, “Fictions & Realities of Life Insurance” (1875?). American Antiquarian Society (Worcester, MA). For more on Lambert, see Bouk, How Our Days Became Numbered (2014), Chapter 1. 95 Charles Hibbard to Wright, September 19, 1873. EWWBP, Carton 1, Folder 59: Letters, 1873-1875 [H]. 96 Quoted in Levy, Freaks of Fortune (2012), pp. 198-99. 97 Goodheart, Abolitionist, Actuary, Atheist (1990), p. 172. 98 Hibbard to Wright, 1873; Homans to Wright, April 21, 1876. EWWBP, Carton 1, Folder 69: Letters, 1875-1879 [H]. 224 Meanwhile, another reaction to the economic downturn emerged among insurers: the idea that it was not a lack of regulation, but in fact, too much regulation upon life insurance companies that had crashed the market. In his 1875 address to the Underwriters’ Association of the South, E.A. Hewitt mocked the public skepticism of insurance and blamed regulators for turning people against the industry. He complained bitterly about all the “deputies and clerks and complicated machinery” that regulatory commissions had summoned to use against the insurance industry. He mocked the concern of these commissions that life insurance companies were hiding insecurities or outright falsehoods behind their mathematical calculations—“all this algebra and mystery,” as Hewitt called it. But, he told his audience, when the commissioners looked deep into one firm, they discovered that far from the intrigues of wily fraudsters, most of “the mathematical work of the department” was found to be “done by girls of 16 and upward!” Hewitt’s skepticism toward the government was not entirely about life insurance; although the southern actuary did not mention Wright by name, he noted with scorn that insurance regulation had begun in Massachusetts, and likened it to the “expression at Washington in the idea that white can be made black and black bleached white by law.” The insistence “that insurance companies need watching, and insurance capital will bear plundering” was foolish, Hewitt insisted, and it had been government regulation that started the “panic which shook the land as by an earthquake and is paralyzing all our industries today,” not insurers. “It is thought by many,” he said, “that there is some dark and difficult process used in life insurance calculations,” that necessitated intervention of state officials. But in the first report of the Massachusetts Commission, were learned dissertations about the mathematical adjustment of the feathers on a bat’s wing, and the geometrical lathe work on a beetle’s ear; pages of cabalistic figures telling him when and how he ought to die; the whole ending with a long 225 appendix of fearful hieroglyphics, looking for all the world as if they were construed of bad Choctaw and worse algebra. These “perilous calculations and terrible formulae,” Hewitt said, were a solution in search of a problem. Worse, they presented a false justification for establishing a state “vicarship” for the safety of the community when, in reality, no one was in danger of anything except the excessive interference of overreaching state and federal governments. Nothing “in the nature of the business” of life insurance made it any different from any other business, and therefore required no special commissions or bureaus to regulate it. Like any other business, insurance should be regulated by those “who have both knowledge and experience of the business; whose entire fortunes are staked upon it; and who have nothing to do but mind their own business.”99 Hewitt’s racially charged comparison of life insurance regulation to the federal efforts to grant civil rights to freedmen speaks to the close link between public desire for state regulation of industry, the reorganization of postbellum American society, and the economic anxieties produced by the Panic of 1873. But in his reference to mathematics, Hewitt’s difference with Wright become clear. Within the southerner’s critique of the former abolitionist also appears a growing divergence between those who believed that the state should hold life insurers to mathematical rules, and those who believed those rules were nonsensical burdens, designed to inhibit individuals’ liberty to seek profits from their business ventures. This divide was not confined to any regional divide. The Panic of 1873 exacerbated suspicions that life insurers and actuaries had already held about the nature of their mathematical expertise and the public’s inability to understand it. In the years that followed 99 “Address of E.A. Hewitt” (1875), pp. 310-312. 226 they turned away from trying to explain their methods, closing ranks around their private science and condemning its critics as misinformed—even Elizur Wright himself. In 1877, a reviewer in The Insurance Times took aim at one of Wright’s recent publication, provocatively titled, “Traps Baited with Orphan, or What is the Matter with Life Insurance?” He called the text an “outrage” and accused Wright of deceiving his audience. Most insurers were by then familiar with Wright’s “barbarisms,” he said, but the public would not be prepared to parse his exaggerations and even lies. Wright’s worst sin, according to this reviewer, was his insistence on proving his claims with calculations. The reviewer lamented that readers would understand his “series of figures” only “when each and every one of them is an actuary.” Until that distant time, they would hear only Wright’s “sneers and flings” while remaining “unable or unwilling to follow the computations which might… expose their falsehood.”100 The review pointed to an increasingly firm attitude among insurers. Public accountability was all well and good, but if the public did not understand the calculations, they would have no way to evaluate which ones were true. Better to avoid them altogether, and stick to the written word alone. Alternative forms of insurance, the outcry over the crash, and a rash of scandals in the life insurance industry between the 1870s and 1910s indicated to many insurers the value of Hewitt’s position, that mathematical state regulation served neither the industry nor the public. Publications promising to publicly explain how policies were calculated diminished, and actuaries worked more closely with, and increasingly subordinately to, their office managers. In 1890, insurers convinced New York state to pass a law prohibiting policyholders from requesting an accounting of their 100 Untitled, The Insurance Times, October 1877, pp. 645-647. EWWBP, Carton 2, Folder 21: Folder 21: Announcements & Articles. Baker Library, Harvard Business School (Boston, MA). 227 insurance fund without first getting approval from the state attorney general, a restraint that never materialized.101 Nonetheless, assurances of the precise, scientific, trustworthy, and mathematically accurate work that life insurers did continued apace. Even as debates over how to precisely value policies continued within the actuarial profession, their ranks closed around protecting the idea of mathematical accuracy, and the wisdom of experienced practitioners. Life insurance companies continued to invest widely and diversely, blurring lines between life insurance firms, savings banks, and commercial banks.102 By the time of the famous Armstrong Investigation in 1905, widely considered a turning point in the development of life insurance in the United States, life insurers were reporting profits of close to $642 million, up from $25 million forty years earlier, and spending $230 million. Life insurers invested in mortgages, savings banks, government bonds, and railroad securities, diversifying their investments and profit sources.103 Nevertheless, they continued to depend on actuarial tables to ensure that they would be able, at least in theory, to eventually pay the policyholders who—whether they knew it or not—funded the transformation of many life insurers into commercial investors. As much corruption as the Armstrong Investigation exposed to the nation, however, and as many new regulations were placed 101 Levy, Freaks of Fortune (2012), p. 220. 102 Douglass C. North, “Life Insurance and Investment Banking at the Time of the Armstrong Investigation of 1905- 1906” The Journal of Economic History, Vol. 14, No. 3 (Summer, 1954): 209-228. On the Armstrong Investigation, see also: North, “Life Insurance and Investment Banking” (1954); Bouk, How Our Days Became Numbered (2009); Megan J. Wolff, “The Myth Of The Actuary: Life Insurance And Frederick L. Hoffman's Race Traits And Tendencies Of The American Negro” Public Health Rep, Vol. 121 No. 1 (2006 Jan-Feb): 84–91; Roger L. Ransom and Richard Sutch, “Tontine Insurance and the Armstrong Investigation: A Case of Stifled Innovation, 1868–1905” The Journal of Economic History Volume 47, Issue 2 (June 1987): 379-390. 103 North, “Life Insurance and Investment Banking,” p. 210. 228 on the insurance industry, actuaries’ importance to the creation of the American financial system had already been realized, and would continue into the new century. Elizur Wright, for his part, never gave up his fight. By the end of his life, he had made as many enemies as friends in the industry he had worked so hard to build and stabilize—more, even. “There seems to be a mystery” about life insurance, he wrote in 1877, the result of “methods of figuring which truly only the high priests of the order can unveil.” He insisted that “the veil must be rent and the working become more plain to ordinary mortals” or the whole system would fail. He was never entirely clear, however, about how this would occur. As he aged, Wright’s frustration with the industry grew. He criticized life insurance firms that he believed “too large for comfort or economy” and publicly accused them of proposing “to throw the mathematical laws of the game overboard” in pursuit of “unmitigated aristocracy.”104 Until he died, Wright continued to insist that if the public understood the mathematics of the industry, and regulating actuaries kept corporations honest, the life insurance industry would thrive—at least, he quipped in a letter to the Boston Herald, “till corporations get powerful enough to repeal the Rule of Three.”105 “The old man’s ghost” By the time Elizur Wright died in 1885, even some of his old friends and allies felt some relief, although they were not sure they would ever truly be rid of him. W.S. Smith, an officer at John Hancock, told Sheppard Homans in 1896 that “Elizur’s blatant and explosive fulminations” 104 “Remarks of Elizur Wright, Before the Judiciary Committee of the General Assembly of New York, On the ‘Rebate Plan’ of the Mutual Life Insurance Company. February 19, 1879.” EWWBP, Carton 2, Folder 57: Letters, 1877-1880. 105 Wright letter to the Editor of the Boston Herald, 1880?. EWWBP, Carton 2, Folder 57: Letters, 1877-1880. 229 had placed undue burdens upon the Massachusetts life companies, which could no longer compete with those of New York and the western states. Despite Wright’s death, Smith sighed, “the burden has remained and whatever the old man’s ghost indicates has been accepted and borne.”106 Wright, for his part, likely would have despaired to see the fate of the industry. He had complained in 1877 that “science” was not given sufficient “responsibility of running the business,” and that instead “so called” business men “merely employ scientific men to calculate chances and premiums.”107 He no doubt would have hated seeing actuaries be pushed out of managerial positions by financiers over the next twenty years.108 Wright’s faith in the power of mathematics against corporate power would not be borne out in the industry to which he had dedicated his life. But in many ways, Wright had helped build this new mathematical industry, which required the constant supervision of privately employed experts. The privatization of corporate calculation, the rise in abstract models, and the entangling of life insurance with other financial instruments all served to obscure accountability to the public and limit the state’s regulatory power. Some of these developments Wright supported; others he critiqued, sometimes harshly. But despite his eventual despair at the path of the life insurance industry, he had been a quintessential corporate calculator. He was protective of his calculations, charged for his labor and results, fretted that the public would never understand the industry, and held fast to the belief that mathematical accuracy was crucial to the functioning of American corporations. Wright felt that commercial calculation belonged in the hands of experts—but not out of an explicitly anti-democratic position. Indeed, Wright worried 106 W.S. Smith to Sheppard Homans, October 1, 1896. EWWBP, Box 3, Folder 2: Correspondence, 1894-1897. 107 Untitled, The Insurance Times, October 1877, pp. 645-647. EWWBP, Carton 2, Folder 21: Folder 21: Announcements & Articles. Baker Library, Harvard Business School (Boston, MA). 108 Bouk, How Our Days Became Numbered (2015), p. 98. 230 throughout his career that life insurers who did not adhere to mathematical rules did not deserve the confidence of the public. And yet, his efforts contributed to a system in which these rules were written by experts who hoarded and hid the knowledge to use them. This paradox was not of Elizur Wright’s making. It had always present throughout the growth and development of the mathematical economy. The specialized, reified, absolute nature of mathematics had long conflicted with its promise to provide the simplicity, accountability, and stability that almost everyone wanted from economic life. With the rise of life insurance companies and the consolidation around corporate calculators, tensions finally began to crack. Wright did not believe that mathematizing markets and risk meant that they were self-regulating; on the contrary, he believed regulation had to come from conscious calculation. But to the public eye, the line that separated regulators and those they regulated seemed vague at best, especially when mysterious mathematics led to a massive financial crash. Combined with shifts in public education, the field from which to contest these changes grew smaller. The mathematical economy had been imagined as a participatory one, in which everyone followed the rules to guarantee fairness in commercial life. Some, like Wright, believed it still could be. But others had given up on that notion, and were reconciling themselves to the idea that individuals did not need to know mathematics to be part of a mathematical economy, so long as the right people were in charge. 231 Chapter 5: The Mathematical Economy On July 8, 1888, John Rankin wrote to his colleague John Bates Clark to thank him for sending Rankin a copy of his new book, Capital and Its Earnings. Rankin professed himself “under great obligation” for the work, and enthused that he hoped “to see it become a pioneer for bringing in a new era in the science which now most needs recasting.”1 He spoke, of course, of their shared discipline, economics. The “recasting” Rankin spoke of was just beginning in the United States, as the nineteenth century study of political economy transitioned into its modern form, complete with a new name and a new set of tools. With American universities reshaping themselves into a form more akin to the German research model than the old English finishing school, the drive among academics to clearly define and differentiate their fields intensified. Between 1890 and 1920, a new generation of academic economists emerged to fundamentally recast their field in a new form. What shape it would take, however, remained up for debate. The characters, institutions, events, and arguments presented in this chapter are no doubt accustomed to being the first act in a work on the history of economic ideas, not the final one. The men discussed herein are some of the first American neoclassical economists, and the intellectual great-grandfathers of the modern economy.2 More precisely, they are the first modern economists, 1 J.S. Rankin to John Bates Clark, 8 July 1887. Folder 4, Series I: R, 1887-1930. Box 3, Series I: Correspondence, 1875-1955 and Series II: Unpublished Scholarly Materials, circa 1865-1936. John Bates Clark Papers, Columbia University Rare Books & Manuscripts Library (New York, New York). 2 The terminology around this period of economics is not entirely settled, and historians arrange individuals differently across the intellectual spectrum of economic thought. In this chapter, I am particularly focused on the introduction of calculus into economic science and the consequences of that shift for the ideas of the wider discipline. Marginalism or marginalist economics is most closely associated with calculus, and is therefore the term I primarily use, although not all the individuals in this chapter would have used it. “Neoclassical” is the general term for modern economics, which is largely—but not exclusively—defined by the advances made by marginalists in the late nineteenth century. At the time, however, “neoclassical” was often used to describe any modern economics. In this chapter, I use “neoclassical” to describe the now-hegemonic economic paradigm of utility maximization, which 232 meaning that, among other characteristics, they were among the first to use mathematics to study the economy from a scientific distance, like the cosmos, rather than treat it as a realm of natural philosophy or of daily business dealings. They did not come up with these ideas on their own; the “marginal revolution” in economics began in Europe, and was imported, with varying degrees of enthusiasm, into American economics departments. In hindsight, historians and economists share a rare agreement that these pioneers introduced something new into the ontological framework of “the economy.” They built a foundation that would undergird the history of economic thought and policy for the rest of the twentieth century, and perhaps beyond.3 Nevertheless, I hope that Professor Clark and his colleagues would not be offended to find themselves at the end, rather than the beginning, of this story. While the study of political economy in nineteenth-century America was almost entirely non-mathematical, this narrative has shown how other types of people advanced both the idea and practice of the mathematical economy. In one sense, the questions that American academic economists debated at the outset of the twentieth century simply constitute one more instance in which the proper relationship of mathematics to economic life was up for debate, with consequences for commercial life, mathematical pedagogy, stemmed directly from the marginalists’ adoption of calculus, although not all twentieth century neoclassical economics consciously or explicitly used calculus. 3 See, for example: Daniel Breslau, “Economics Invents the Economy: Mathematics, Statistics, and Models in the Work of Irving Fisher and Wesley Mitchell” Theory and Society, Vol. 32, No. 3 (Jun., 2003); Walter A. Friedman, Fortune Tellers: The Story of America’s First Economic Forecasters (Princeton University Press: Princeton, 2014); Philip Mirowski, More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics (Cambridge: Cambridge University Press, 1989); Timothy Mitchell, “Fixing the Economy,” Cultural Studies, 12, 1 (1998): 82– 101; Mary S. Morgan, The History of Econometric Ideas (Cambridge: Cambridge University Press, 1990); Margaret Schabas, A World Ruled by Number: William Stanley Jevons and the Rise of Mathematical Economics (Princeton, 1990); Martin J. Sklar, The Corporate Reconstruction of American Capitalism, 1890-1916 (Cambridge: Cambridge University Press, 1988); Yuval P. Yonay, The Struggle Over the Soul of Economics: Institutionalist and Neoclassical Economists in America Between the Wars (Princeton: Princeton University Press 1998). 233 and social relationships. Like prior numerate elites, economists used mathematics to develop new political economic concepts, and to claim authority over economic life. Like those predecessors, economists built specialized expertise out of the apparent objectivity of mathematics, first within their own professional world, and eventually in business and policy. In understanding the rise of neoclassical economics as another iteration of the developing mathematical economy, we also find a new kind of mathematics taking center stage. The adoption of differential calculus as the language of economic thought had profound implications for how economists imagined economic life. It drew in some ways on the financial abstractions pioneered by actuaries and accountants, and viewed economic activity and society as a systematic whole, as civil engineers had. But the epistemological interdependence between the “margin” of marginal utility theory and the derivative of the differential calculus fundamentally altered the assumptions that economists made. Calculus profoundly impacted the way marginalist economists understood the role of individuals in the economy. To say they inaugurated a new economics because they used “mathematics” is insufficiently explanatory. Mathematics had long been a part of economic life. What made economists’ worldview different was their adoption of calculus. The past century had created widespread belief in the importance of individual calculation as the foundation of economic participation, but it had also created an expert elite. Americans had argued over the purpose of economic expertise, the correct type of mathematics to use in different commercial situations, whether mathematics was appropriate in economic life at all. The rise of the modern mathematical economy centuries changed all of that. From their positions as supposed complete outsiders, economists consciously strove to make themselves the only economic experts: on business, on policy, even on the behavior of individuals they had never met. The invention of 234 the modern mathematical economy in academic economics eclipsed the old one, in which the act of calculation had defined economic participation, knowledge, and skill. This idea had originated in the political economic crucible of the early republic, but it had been steadily undermined by the numerate elite. Neoclassical economists presided over its obsolescence. In addition to universalizing their historically specific, calculus-based vision of economic activity, economists erased the long pre-history of the mathematical economy. Their new science naturalized a vision in which some people with specialized mathematical skill conceptualized and managed economic life for a public that did not, even could not, understand its technicalities. At the same time, they envisioned a universal economic man. Yet this theoretical individual was far from universal. Rather, he was imbued with the social markers that commercial mathematics had long implied: independent, reasoned, productive, market-oriented, and male. Homo economicus amalgamated a hundred years of historical specifics around social difference, business practices, and educational theories into an ahistorical concept. In inventing him, academic economists ended the longstanding tension between expertise and democracy in mathematical economic life. They declared that there was no difference between different mathematics in economic life, or between objective rules and reasoned judgment, because they all people were constant, uniform calculators. Thus, expert rule did not undermine participation or public accountability. For economists, a nation of implicit calculators was still a democratic one, as long as they had their say. Domesticating Marginalism The shift of American political economy into economics in the late nineteenth century was never obvious or inevitable, but rather the result of significant changes in university structures, ideas about scientific progress, international academic communication, commercial realities, and 235 social relationships. Mathematical economics emerged from a more concentrated set of concerns about the proper way to understand economic life, and the position of the economist in theorizing it. The first mathematical economists were not a cohesive group, and did not agree about how to mathematize the study of political economy. The most influential ones turned out to be those who embraced marginal utility theory, who used differential calculus as their mathematics of choice. These so-called marginalist economists are most often credited with starting and encouraging the transformation of classical political economy into modern neoclassical economics. Marginal utility theory laid the groundwork for the essentials of modern economics, including the universality of market forces, the emphasis on individual consumers driving economic action, and the rejection of the longstanding search for a material definition of economic value.4 Nevertheless, the embrace of marginalism in the United States was also made possible by the prior century of economic mathematization. From elementary school textbooks to emerging financial instruments, mathematics was crucial to every aspect of American economic life by the end of the nineteenth century. Indeed, the only area it had not penetrated was the study of political economy, which held fast to classical notions of land, labor, and value until at least the 1870s, and made almost no effort to incorporate mathematical reasoning. We might even consider it surprising that American economists resisted mathematics for as long as they did. Although they did look to European ideas in the 1880s and 1890s for the new trends in economics—abandoning, for the first time in American intellectual life, the idea of American economic life as exceptional—and while 4 Donald Winch, “Marginalism and the Boundaries of Economic Science” in R.D. Collison Black et al, The Marginal Revolution in Economics: Interpretation and Evaluation (Durham: Duke University Press, 1973), p. 59; Jeffrey Sklansky, The Soul’s Economy: Market Society and Selfhood in American Thought, 1820-1920 (Chapel Hill: UNC Press, 2002), pp. 172-176; Mary Morgan, The History of Econometric Ideas (1990), pp. 2-3. 236 structural factors were essential, marginal economics took hold in a country where mathematics had long been part of economic life.5 The early adopters of mathematical economics may have been a small minority, but their numbers expanded rapidly, and their ideas spread widely, within a few decades, a testament to the United States’ readiness to accept a fully mathematical economy, as described by academic experts with advanced mathematical training. The success of mathematical economics in late nineteenth-century America was a striking reversal from fifty years prior. In the eighteenth century, European intellectuals had argued that society was not a space of unpredictable chaos, but one that could be studied systematically, as the natural and physical sciences were. Men like François Quesnay, Adam Smith, Thomas Malthus, Auguste Comté, Jacques Turgot and others studied and theorized society and all its attributes, especially the proper use of government policy to encourage economic prosperity, fair distribution of wealth, and commercial freedom. They saw human interactions as no different than the natural world, at least in its ability to be understood through reasoned discourse, and presented themselves as expert mediators between government, society, and nature.6 What they hailed as liberalism in its highest form, the unshackling of individual human freedom, others saw as the death of a purer, more religious world. Edmund Burke blamed the French Revolution and its violence on these new 5 On Anglo-Atlantic cooperation and intellectual cross-fertilization in this period, see Daniel T. Rodgers, Atlantic Crossings: Social Politics in a Progressive Age (Cambridge: Harvard University Press, 1998). 6 On Enlightenment intellectuals’ use of natural history to theorize the political economic world specifically, see: Fredrik Albritton Jonsson, “Rival Ecologies of Global Commerce: Adam Smith and the Natural Historians” The American Historical Review, Vol. 115, No. 5 (December 2010), pp. 1342-1363; Margaret Schabas, The Natural Origins of Economics; Emma Spary, “Political, Natural and Bodily Economies” in N. Jardine, J.A. Secord, and E.C. Spary (eds.) Cultures of Natural History (Cambridge University Press, 1996). 237 ideas. With prescient terminology, though a bit prematurely, he lamented that “the age of chivalry is gone; that of sophisters, economists, and calculators has succeeded.”7 Americans may not have embraced Burke, but the useful knowledge economy of the early national and antebellum periods encouraged skepticism toward abstract, mathematical economics. Halsey Wing, in his address to the young men of Albany in 1832, warned explicitly of the dangers that mathematical thinking posed to the management of society. To explain why a singular focus on mathematics threatened to undermine good judgment, Wing turned to Turgot. When called by the King of France to manage the national treasury, the great mathematician came equipped only with his great mathematical knowledge and “puerile ignorance of men and things.” According to Wing, Turgot’s mathematical training led him to the spurious conclusion “that political economy presented a suitable field for the application of the unyielding standard of arithmetic and geometry.” But his efforts to “subject human affairs to the precision of mathematical problems” ended in a way that, Wing assured his listeners, “the plainest common sense could have predicted”: utter failure in all his “clever” projects. Defeated, Turgot fell from grace with nothing to show for his efforts, save his distinction as “a statesman mathematically mad.”8 American political economists of the nineteenth century largely shared Wing’s suspicion of mathematics as an appropriate field for the study of economy and society. They consciously did not see themselves as physicists, chemists or other natural scientists. While they did often refer to their discipline as a “science,” they did so in the expansive way of the early modern period, to 7 Edmund Burke, Reflections on the Revolution in France (1790), quoted in Theodore M. Porter, “Thin Description: Surface and Depth in Science and Science Studies” Osiris, Vol. 27, No. 1 (2012), p. 216. 8 Halsey R. Wing, “Essay on the Moral and Intellectual Effects of Studying the Mathematical and Physical Sciences; and on the Application of these Sciences to the Arts” (Albany: Young Men’s Association, 1834). 238 mean a comprehensive field of inquiry that was understandable and knowable through observation and human reason. Political economists studied human society, not the natural world. The subject of their study was not flora or fauna, but intelligent beings imbued with moral purpose. That meant that they would rely on moral rather than natural philosophy, and their empirical observations and descriptions would take a different form.9 Most eschewed numbers entirely, except as occasional anecdotal evidence. Rather, their “data” stemmed from observing human relations and interactions and then theorizing both the state of the political economic world, and what kinds of government policies should be enacted to make it operate most naturally.10 In the late nineteenth century, however, a series of structural and ideological factors led some American economists to reconsider the place of mathematics in their field.11 Marginalism had many fathers, especially because the field was defined and named after the fact rather than during its conception, but most scholars consider the trifecta of Léon Walras in France, William Stanley Jevons in England, and Carl Menger in Germany to be the founders of marginal utility theory and modern mathematical economics.12 At the time, too, observers such as Simon Patten noted that the old school of “objective economics based upon the physical facts of the objective 9 Paul K. Conkin, Prophets of Prosperity: America’s First Political Economists (Bloomington: Indiana UP, 1980), p. ix. On classical thought in American political economy, see also Stewart Davenport, Friends of the Unrighteous Mammon: Northern Christians and Market Capitalism, 1815-1860 (Chicago: University of Chicago Press, 2008). 10 On observations in classical political economy, see Harro Maas, “Sorting Things Out: The Economist as an Armchair Observer” in Daston and Lunbeck (eds.), Histories of Scientific Observation (Chicago: University of Chicago Press, 2011). 11 Some have suggested, compellingly, that Thomas Kuhn’s theory of “simultaneous discovery” model is the best way to understand the emergence of marginal economics across Europe and the United States during this period. See Mark Blaug, “Was There a Marginal Revolution?” in Collison Black et al, the Marginal Revolution in Economics (1973); Thomas Kuhn, “Energy Conservation as an Example of Simultaneous Discovery” in Margaret Claggett (ed.), Critical Problems in the History of Science (Madison: University of Wisconsin Press, 1969). 12 See articles by Mark Blaug, Richard S. Howey, A.W. Coats, and William Jaffé in Collison Black et al, The Marginal Revolution in Economics: Interpretation and Evaluation (Durham: Duke University Press, 1973). 239 world and the natural laws which regulate them” had found competition in “the new school of economists, led by Jevons and Menger.”13 Insofar as a “marginal revolution” existed in the 1870s, it was in these unrelated economists combining differential calculus with utility maximization, and in doing so, beginning to turn the field into a mathematical, deductive science.14 Although the United States did not house a Jevons, Walras, or Menger during the earliest days of marginalism, it was not immune from factors that encouraged mathematical economics to develop elsewhere. After the Civil War, American universities began to transform themselves into entities more akin to German research universities than the liberal gentlemanly schools, on the British model that they had followed since the eighteenth century. They began to require doctorates for faculty, and created graduate programs for students who wanted to pursue a life of the mind— whether to become faculty, or simply to continue to pursue the art or science they had studied in college. Disciplinary boundaries became harder, more standard, and more professionalized, with organizations like the American Historical Association and the American Economic Association organizing annual conferences and aggressively reaching out to interested or potentially relevant individuals to build their membership. American universities developed disciplinary personalities and strengths in their faculty and graduate students, so that one might identify the economists at Columbia as being different than the ones at Harvard.15 13 Simon N. Patten, “The Educational Value of Political Economy” Publications of the American Economic Association, Vol 5, No. 6 (Nov. 1890), p. 15. 14 Mark Blaug, “Was There a Marginal Revolution?” in Collison Black et al., The Marginal Revolution in Economics (1973), pp. 3-4. 15 John R. Thelin, A History of American Higher Education, 2d ed. (Baltimore: Johns Hopkins University Press, 2013); Roger L. Geiger, To Advance Knowledge: The Growth of American Research Universities, 1900-1940 (New York: Oxford University Press, 1986); Laurence R. Veysey, The Emergence of the American University (Chicago: 240 Furthermore, the embrace of mathematics in economics also reflected the concerns that fueled the rise of the social sciences in the late nineteenth century. American academics had begun to confront the apparent complexity of industrial society, and the social, economic, and political problems that seemed to attend it. These questions led outward in many directions: social reform, professionalization, federal policymaking, and more.16 For young economists in this era, deductive reasoning from mathematical principles, rather than the formulation of theories based on the inductive collection of evidence, appealed. The abstractions involved in mathematical economics, rather than observed data, arguably avoided some difficult issues. Questions about labor and capital, the distribution of wealth, the role of government in taxes and tariffs, and other such issues could be put aside, in favor of a morally neutral examination of what the economy was, not what it should be.17 In this, they were drawn to the objectifying power of mathematics, now to sidestep the stirring of proto-Progressive confrontations around economic justice. A third key factor in the rise of marginalism in the United States was the growing interest in “pure science,” as well as the rising scientific prestige of physics. In 1883, American physicist Henry A. Rowland insisted, in a widely-reprinted address, that what American science needed was to shed its former commercial trappings and focus on research purely for the sake of knowledge. University of Chicago Press, 1965); Frederick Rudolph, The American College and University: A History, 2d ed. (Athens: University of Georgia Press, 1991). 16 The literature on social scientific responses to industrialization in this period is significant. See: Rodgers, Atlantic Crossings (1998); Dorothy Ross, Origins of American Social Science (New York: Cambridge University Press, 1992); Jeffrey P. Sklansky, The Soul’s Economy: Market Society and Selfhood in American Thought, 1820-1920 (Chapel Hill: University of North Carolina Press, 2002); James Livingston, Pragmatism and the Political Economy of Cultural Revolution, 1850-1940 (Chapel Hill: University of North Carolina Press, 1997); Thomas L. Haskell, The Emergence of Professional Social Science: The American Social Science Association and the Nineteenth-Century Crisis of Authority (Chicago: University of Illinois Press, 1977); Jonathan Levy, Freaks of Fortune: The Emerging World of Capitalism and Risk in America (Chicago: University of Chicago Press, 2002). 17 Ross, Origins of American Social Science, p. 179. 241 Rowland commended his predecessors, whose applied science had built the United States to its industrial glory, but warned that satisfaction with application would stall American progress. He wanted to decisively cut the trappings of commercial application, through funding from the federal government.18 In arguing that science should not be driven by its practical applications, Rowland broke decisively from the tenets of the useful knowledge economy. But this changing vision did not dampen the wider enthusiasm for physics, at least among academics. Observers in the ensuing years noted the enthusiasm among the “educated classes” for physical science, and some wondered aloud if the social sciences could attain the same popularity and prestige.19 None of these factors meant that the adoption of mathematical economics in the postbellum United States was inevitable, nor did they necessarily define the direction of a more mathematical economic science. Those American economists who adopted marginal economics began as a small minority, and for a time, they worked completely at odds with the American political economic tradition. However, certain historical conditions—ones both specific to the exact period, and those created by nearly a century of overlap between mathematics and commerce—laid the groundwork for marginalism to take hold in the United States. Although American political economists had not yet explicitly adopted them, ideas around managed, top-down political economy, the abstraction of economic goods and concepts, the expectation of mathematical skill for economic authorities, and the centrality of calculation to economic life were all familiar to American social scientists, 18 Henry A. Rowland, “A Plea for Pure Science” Science, Vol. 2, No. 29 (Aug. 24, 1883), pp. 242-250. 19 Brinton Coxe to Richard Ely, December 29, 1890. Folder 2: Incoming Correspondence, 1890-1891. Box 4: Correspondence, Incoming, 1888 March-1896 February. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 242 and to Americans generally, by 1890. With new institutions to house and sustain it, marginalism immigrated easily to the United States in the late nineteenth century. Between 1890, when Irving Fisher began his dissertation on “Mathematical Investigations in the Theory of Value and Price,” despite professing that he had never heard of “mathematical economics,” and the 1920s, when he served as President of the American Economic Association, marginal economics became the dominant paradigm in American economics departments.20 That transition did not happen overnight, nor was it uncontested. Over these three decades, economists and other interested parties fought bitterly about the appropriate role of numbers, mathematics, observation, deduction, and policy in their constantly changing discipline. The transformation of economics from a science of historical facts, numerical statistics, and government policy into one that treated economic life as a self-contained system akin to the cosmos, best studied with calculus, ultimately had profound implications for the relationship between mathematics, data, business, and American expectations for their economic lives. “The business of pure economics” In 1899, Edwin Seligman—a partial founder of the American Economic Association and lifelong professor of political economy and economics at Columbia—fretted to the Association’s Secretary, Walter Willcox, about the state of the AEA. Although the organization had been around for fewer than fifteen years, Seligman noted with concern that its “finances seem to me to be on the decline” and predicted that without “energetic measures,” the Association would likely have 20 Allen, Irving Fisher, p. 53; Ross, Origins of American Social Science, p. 173. 243 to be dissolved. The American Historical Association, he noted, had reached 1,200 members, while the AEA membership continued to decline. He wanted the Executive Committee to strategize about increasing membership, warning that “if we cease to advance, the end is not far off.”21 While some cared a great deal about making disciplinary divisions within universities, the distinctions were less obvious to potential members. Any professor of history, economics, political science, or sociology in the 1890s might be inundated with letters asking them to join these organizations and publish in their journals. Every discipline needed something to distinguish itself in the competition among the social sciences for members, money, publications, and prestige. As marginalists like John Bates Clark and his allies tried to make economics a distinct and influential social science, they had to overcome the old ways of academic economics.22 This earlier school, which came to be known as “historicism” once it had to be distinguished from the normal way of doing things, had emphasized concrete observations alongside larger, classical questions of value and labor. The push to incorporate mathematics into the discipline started a debate among economists about the value of data versus mathematics in economic science. Was the purpose of scientific economic knowledge to quantify and measure, or was it to interpret and evaluate? Was the role of the economist to observe, or to theorize? Historicists saw data as objective information. 21 Edwin Seligman to Walter Willcox, February 15, 1899. Folder 7: Feb.- Oct., 1899. Box 8: Incoming Correspondence, 1896-1900. Papers of the American Economic Association, David M. Rubenstein Library (Durham, NC). 22 Unlike Irving Fisher, Clark was not a mathematician by training. Furthermore, he was trained in the historical school, which his graduate work reflects. These factors have caused some historians (particularly those who study Irving Fisher) to categorize Clark with more enthusiastic historicists, and skeptics of mathematics, like Edwin Seligman and Richard Ely. Nevertheless, Clark’s papers from the 1890s and onward, as well as his correspondence and teaching materials, demonstrate an obvious interest in using calculus in economic thought. That his published work did not make as explicit use of mathematics as some others does not, in my view, mean he was not a marginalist. Nevertheless, his example is a useful reminder that the discipline was deeply in flux, and categorizing individuals into discrete schools is perhaps less helpful than looking for broad ideological paradigms. 244 They used numbers primarily as rhetoric, not as bases for computation. But some younger, more radical economists wanted to use mathematics to conceptualize the whole economy, without being bound to objective facts. They wanted to use mathematical reasoning to interpret observations, and build models that would be structural, universal, and predictive. In this debate, economists played another round in the longstanding conflict between reason and rules. In 1896, Clark lamented that he could find “almost nothing definitely mathematical” in the publications of the AEA.23 He was disappointed, but he could not have been surprised. Many if not most American economics professors of the 1880s and 1890s had done their graduate study at German universities, where historicism reigned supreme. These economists understood the study of economics to be primarily inductive. They looked at historical data on prices, wages, taxes, and other measurable forms, and used these numbers to support their more general theories regarding value, production, and labor. They were not the first economists to take this approach; one can find statistics in economic thought as far back as the seventeenth century.24 Nevertheless, it had become widespread in American economics by the 1880s. Historicists were open to—even enthusiastic about—the inclusion of numbers in their work, but most were strongly anti-theoretical, and thus strongly anti-mathematical. In the United States, perhaps ironically, the economists who were most comfortable employing numerical evidence in their work were the ones who most strongly rejected the turn toward using mathematical models in their discipline.25 23 John Bates Clark to J.W. Jenks, February 18, 1896 and February 29, 1896. Folder 1: Feb. 1-Sept. 1, 1896. Box 8: Incoming Correspondence, 1896-1900. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 24 On the “political arithmetic” of William Petty and John Graunt, see Peter Buck, “Seventeenth-Century Political Arithmetic: Civil Strife and Vital Statistics” Isis, Vol. 68, No. 1 (Mar., 1977), pp. 67-84. 25 Morgan, History of Econometric Ideas, p. 3; Allen, Irving Fisher, p. 52. 245 This discrepancy, which might seem somewhat paradoxical to the modern reader, is better understood through a clearer definition of what nineteenth-century Americans meant by the word “statistics.” Before 1900, they did not mean a mathematical field measuring variance, distribution, error, and so on. Instead, “statistics” generally meant lists of numbers compiled by government or other public body that were purely descriptive. People did not assume that these numbers had been produced by a method other than counting, and any further calculations done with them tended to be basic arithmetic. The field that today we refer to as statistics was still nascent, and would likely have been read as algebra or analytics to most Americans. Indeed, statistics and mathematics were often understood to operate in entirely distinct domains.26 The data available for historical analysis was always incomplete, given the limitations of data collection at the time. Instead, most historical economists used it anecdotally, as part of a broader effort to teach students about economics by way of past examples, which were often only intermittently numerical. In its earliest American iteration, economics was taught very much like political economy, as a kind of economic history class. Economics classes tended to move through American (and, to a lesser degree, English and European) history, showing the important developments in economic change, such as the development of water mills, the expansion of the railroad system, and the rise of large industrial corporations. Lecture notes from student indicate that figures were sometimes presented in lecture—cotton exports between 1790 and 1860, for example, or the depreciation of 26 Morgan, History of Econometric Ideas, pp. 2-3. Even modern statistics, which involves a great deal more analysis than the kind discussed here, is still not considered by all economists or mathematicians to be a field of mathematics, due to its necessary reliance on observed data rather than purely conceptual relationships. 246 currency in wartime.27 In addition to attending these historical lectures, students also read texts in economic and commercial thought. These included some classic treatises by Europeans, such as Adam Smith and John Stuart Mill, as well as newer works by both American and European authors, including Alfred Marshall, Richard Ely, Francis Walker, and John Elliott Cairnes.28 These courses emphasized both the supposedly universal liberalism of free trade and rational social science, while also specifically tying the material to the national history. They gave American economics a link to European intellectual trends while also maintaining its exceptionalism.29 Nevertheless, its robustness did not make American economics homogenous or unified in either content or methodology. Depending on the background of the professor, who might have a degree in any of the social sciences, students at different universities could learn not only different content, but different approaches to the study of economics itself. What material counted as political science versus economics versus sociology was still hotly debated among academics, and even once a disciplinary line was agreed on, the appropriate texts varied a great deal. A student at one university might learn classical economics from The Wealth of Nations; another, elsewhere, might read Alfred Marshall, an English economist whose 1890 textbook used a both geometry and calculus to explain concepts like supply and demand, production value, and perfect competition.30 27 William Pickman Wharton, Notes in Economics 6, 1901–1902; Clarence A. Bunker, Notes in Political Economy IV, Lectures by Prof. Dunbar. H.U. 1886-7. Harvard University Archives (Cambridge, MA). 28 Syllabi, Course Outlines and Reading Lists in Economics, 1895-1979. Harvard University Archives (Cambridge, MA); Box 2: Course Notes for Economics with Professor Wicker, 1901-1902, Forrest Joslin Hall Papers. Rauner Special Collections Library, Dartmouth College (Hanover, NH). 29 Dorothy Ross argues that one of the primary goals of American social science in this period: to catch up to and adopt European liberalism, but also to show that the exceptional history and culture of the United States made it the most natural home for these ideas. Ross, Origins of American Social Science (1991). 30 Alfred Marshall, The Principles of Economics (1890). 247 As a result, Davis Dewey complained in 1909, college students emerged from economics courses “with but a hazy notion of the science as a whole”—and worse, without having “made an adequate gain in mental power through the training of his faculties in abstract reasoning.”31 Dewey’s fascination with the training of mental faculties in abstract reasoning mirrored a growing sense among some social scientists that real science was mathematical, and that perhaps they should be thinking more along those lines. Simon Patten opined in 1890 that of all the classical studies, mathematics held “an unquestioned place in the college curriculum.” He believed that the discipline was “a model science” and a “standard to which all sciences must conform and by which progress must be measured.”32 Sociologist Lester F. Ward echoed this idea, calling mathematics “a standard to which all other sciences are to be referred” in 1895.33 The role of mathematics in the physical sciences, and even to a lesser degree the natural ones, did not necessarily indicate to social scientists that they too should adopt it. For many, it raised questions about how to define the social sciences as distinct from the natural and physical sciences, especially if, like their political economist predecessors, they saw their field as something very distinct from physics or astronomy. For those who were dissatisfied with the state of economics, however, and wanted to see it more clearly defined in the social sciences, it provided a blueprint for change. Those economists who wanted to use mathematics in economics disagreed that data should be collected first, before deciding whether a mathematical treatment was appropriate. They argued 31 Davis R. Dewey, “Observation in Economics: Annual Address of the President” American Economic Association Quarterly, 3rd Series, Vol. 11, No. 1 (Apr., 1910), p. 34. 32 Simon N. Patten, “The Educational Value of Political Economy” Publications of the American Economic Association, Vol 5, No. 6 (Nov. 1890), p. 8. 33 Albion W. Small, “The Relation of Sociology to Economics” Publications of the American Economic Association, Vol. 10, No. 3, (Mar., 1895), p. 113-14. 248 instead that empirical data would always be imperfect, and therefore mathematical models should lead, and then be checked by data—under the presumption that, if it did not, the fault could very well be in the data. Indeed, some early mathematical economists held back from fitting equations to their curves, for want of sufficient numerical data.34 As early as 1890, Simon Patten suggested that simply because “a mass of facts do not correspond to the conclusions which may be drawn from a given theory,” that theory was not necessarily wrong. Indeed, Patten wanted all “problems in which theory and fact are at odds” to “be reserved for graduate work, when the student has acquired such confidence in his reasoning.”35 Patten’s claim, that it was reasoned judgment that should define economic science, and not the presentation of objective facts, positioned marginalist economists in the longer history of numerate elites. They believed that mathematics represented objective truth, but only if trained professionals interpreted it. The counterintuitively non-numerical nature of early mathematical economics can be seen in some of the graphical representations used to explain economic phenomena. In a 1909 article on collective bargaining, John Bates Clark used a series of graphs with essentially no numbers to describe the movement, as he understood it, of various factors across time. The figures are intended to explain the relationship of wages, production, and time in determining potential losses from a worker strike, according to Clark’s theory of marginal productivity: 34 Frederick C. Mills et al, “The Present Status and Future Prospects of Quantitative Economics” The American Economic Review, Vol. 18, No. 1, (Mar., 1928), p. 31. 35 Patten, “The Educational Value of Political Economy,” pp. 24-8. 249 Figure 3. Potential losses from worker strike, from J. B. Clark, “A Theory of Collective Bargaining” American Economic Association Quarterly, 3rd Series, Vol. 10, No. 1, (Apr., 1909), pp. 24-39. The graphs were not based in any observed data, and Clark did not assign numbers to them as though they were. Rather, he presented a mathematical relationship between variables that could explain any strike, regardless of its particulars. For mathematical economists like Clark, particulars distracted from the fundamental laws that they sought. Assigning numbers to a problem threatened the purity of economic science by distracting from the larger conceptual work of explanation and prediction, and holding back progress. Instead, Clark based his analysis of collective bargaining in the relationships between the mathematical concepts of productivity, wage loss, and individual utility maximization. Whether he described an actual strike or not was beside the point; this theory could describe the general outcome of any strike, at least according to Clark. Economists admitted, especially among themselves, that theory and reality did not always align. Indeed, to many, a good theory sometimes had hardly anything to do with reality, where the conditions could never be controlled, the examples always had to be qualified, and exceptions were seemingly always the rule. “Needless to say,” James Rossignol explained in 1917, “actual wages 250 are never exactly equal to theoretical or normal wages,” and to this fact he attributed critics’ claims that theories of wages and “the marginal employer” were little better than “myth.” But “economic fictions,” as Rossignol proudly called them, offered much more than mere observation. Doubters might claim that wages “are not fixed by supply and demand… but by custom, tradition, caprice, monopoly,” avarice, and poverty. But to take this view, in Rossignol’s opinion, was “to despair of any rational explanation of economic phenomena and to throw away the clew that might guide the perplexed investigator out of the maze.”36 Economics would do better to rely on careful deductive reasoning, he suggested, than on the faulty whims of empirical observation. Naturally, many older American economists professed a deep skepticism toward this way of understanding economic life. Those who believed in the inductive approach found mathematical approaches overly abstract, and believed that the embedded assumptions were implausible at best, and disturbing at worst. Albion Small, voicing a concern shared by many fellow sociologists, opined in 1895 that “mathematical economists have tended to overlook both the necessity and the difficulty of precise knowledge of extra-economic phenomena,” instead elevating “abstractions” to the height of science.37 Those of a historical bent professed even more alarm and disappointment with mathematical methodologies. In 1902, Henry Charles Adams groused to Seligman that that “there is no such thing as a marginal producer of any sort.” Like Small, Adams saw no validity to abstractions, deductions, or claims to absolute truth in economics. But he also noted resignedly 36 James E. Le Rossignol, “Some Phases of the Minimum Wage Question” The American Economic Review, Vol. 7, No. 1 (Mar., 1917), p. 253. 37 Albion W. Small, “The Relation of Sociology to Economics” Publications of the American Economic Association, Vol. 10, No. 3, (Mar., 1895), pp. 106-7. 251 that this view challenged “the present trend in economic theory,” and he worried that his sweeping criticism would not be welcome in academic economics journals.38 Some skeptics of the mathematical turn also disliked the abstraction of economic decision- making that mathematical models inaugurated. Increasingly sophisticated knowledge of statistics among academics led to new conversations about how to understand numerical data in economics. Stung by accusations from the new camp that “the use of odd facts, a few numbers, or individual cases” were little use in probing the complexities of economic behavior over time, some partisans of statistical knowledge sought a deeper understanding of the relationship between numbers and society.39 Ernst Gryzanovski, a professor in the largely historicist Harvard economics department, argued that statistical patterns did not mean that humanity was inevitably shackled to certain rates of crime, suicide, or industrial accident. Algebraic statistics, he explained, could show correlations between anything, and thus had to be used appropriately by practiced hands. And even when the experts pointed to unhappy results, economic or otherwise, Gryzanovski insisted that it was “more rational to mend our ways… than to look out for sun-spots and cycles.” Statistics were not fate; the regularity of its cycles could be “destroyed” with concerted action.40 38 Henry C. Adams to Edwin Seligman, 14 May 1902. Folder 10: President Seligman’s Correspondence, 1902, Box 9: Correspondence, 1900-1902. Papers of the AEA, David M. Rubenstein Library, Duke University (Durham, NC). 39 Morgan, The History of Econometric Ideas, p. 16. 40 Ernst G. F. Gryzanovski, “On Collective Phenomena and the Scientific Value of Statistical Data,” Publications of the American Economic Association, 3rd Series, Vol. 7, No. 3 (Aug., 1906), pp. 46-7. Here Gryzanovski is almost assuredly making reference to William Stanley Jevons’ infamous attempt to predict economic cycles by way of sun spots, under the theory that the astronomical phenomena might influence crop harvests. Although it was not a theory Jevons himself took particularly seriously, it was one that critics of the mathematical turn frequently pointed to, and that advocates of analytical statistics like Gryzanovski felt the need to disavow. 252 American marginal economics did not only challenge the individual economic theories of those like Small and Adams, although it did over time shift the discipline away from certain types of assumptions and questions and towards others. The mathematical turn also threatened to upset the essential nature of formal economic knowledge in the American university system, and exclude many of the people who had formerly laid claim to expertise in the discipline. The combination of historical and political narrative, publicly available statistics, and classical economic theory had long allowed professors of history, political theory, natural philosophy, and more, to teach and be authorities in economic knowledge. This in turn had made economic knowledge a contingent part of a larger system of political, philosophical, and scientific knowledge about the way that society and nature operated. But between the increasingly rigid delineations between academic disciplines, and the slow but tangible growth in the mathematical knowledge necessary for graduate work in economics, the circle of economic experts began to close. Mathematical economists prioritized reasoned judgment and mathematical models over the presentation of supposedly objective numerical data in order to consolidate professional authority over a discipline that they believed was in desperate need of new leadership and new ideas. Their opponents pushed back using the language of objectivity, accusing mathematical economists of misrepresenting economic reality, and indeed, creating economic ideas out of whole cloth. Unlike previous contests over the position of rules and reason within economic mathematics, however, no one in this fight felt the need to be publicly accountable. Historicists might have gestured to older ideas about democratic accessibility, but in general, they did not point to public accountability as a central reason to preserve their methods. In the era of pure science and the research university, the contest between historicists and marginalists played out in the realm of academic economics. 253 Nevertheless, mathematical economists’ conscious, strategic elevation of theory over practice in their quest to claim professional expertise would have larger consequences, particularly when it came to exerting their influence in business and public policy. The disconnect between mathematics and statistics in turn-of-the-century debates over the use of numbers in economics gestured to a larger question about the purpose of the new science. For proponents of mathematical economics, “the business of pure economics” was “to explain, not to justify or condemn.”41 They shared this attitude with some of their classical predecessors, and with many of their fellow social scientists. Crucially, moreover, they also shared it with some of more direct but less recognized predecessors, in the engineers and actuaries of the numerate elite. These men had also argued that their disinterestedness was crucial to national prosperity. But the absorption of their mathematical expertise into corporate structures had led to a more homogenous “business” interest, one being formally institutionalized in this period. As a result, business posed an unexpected challenge to the changing orthodoxy of academic economics. “The right class of business men” At the thirteenth annual meeting of the American Economic Association, Edmund T. James explained to his audience the relationship of higher education to “commercial education” and the potential for both to gain by their association. “Modern business,” he declared “is becoming more complex,” and therefore, like law and medicine, deserved its own professional schools and degree accreditation. By attracting “a higher order of talent” and “a higher degree of preparation” the new 41 G. R. Wicker, L. C. Marshall and J. H. Hollander, “Outlines of a Theory of Wages: Discussion” American Economic Association Quarterly, 3rd Series, Vol. 11, No. 1, (Apr., 1910), pp. 159-60. 254 business schools would support the United States’ industrial growth and social prosperity. James wanted a largely practical education for these students—he warned against looking down on book- keeping skills—but also believed that “economics should be accepted as the fundamental element in any such course” in business education. Indeed, he said, the student “who grapples in earnest with problems of economics” would attain “a mental discipline which may well be compared with that which the study of mathematics or other abstruse subjects may give.” He admitted that some of his peers believed it foolish for a young man to spend years in the study of such abstruse subjects as “Latin, Greek and mathematics,” but James believed that the combination of mental reasoning with practical skills would best educate America’s future businessmen.42 James’s optimism about cooperation between the distinct sides of commercial education— theoretical economics on one side and practical business on the other—was widely repeated in this period. Rhetorically, advocates of professional business education insisted that new schools would easily reconcile the mental and cultural benefits of a liberal education with the practical skills and knowledge taught in commercial colleges.43 But in practice, just as many economics departments were beginning to embrace greater deductive theory and mathematical models, business schools (and for a time, business-oriented economics departments) moved in the other direction. Even into the 1920s and beyond, some observers still distinguished between “commercial” as opposed to 42 Edmund T. James, “Relation of the College and University to Higher Commercial Education” Publications of the American Economic Association, 3rd Series, Vol. 2, No. 1 (Feb., 1901), pp. 144-165. 43 On the early history of American business schools, see Rakesh Khurana, From Higher Aims to Hired Hands: The Social Transformation of American Business Schools and the Unfulfilled Promise of Management as a Profession (Princeton: Princeton University Press, 2010). 255 “economic importance” when it came to teaching in business schools.44 The result was a system of education that professed unity and practiced competition between economics departments and business schools. In disagreements around the use of numbers and mathematics, economists and businessmen resurrected a time-honored debate in the mathematical economy over the proper role of theory and practice in defining economic authority. In arguing that economics should be observed and not practiced, academic economists of the early twentieth century began to claim authority over the mathematical economy at the expense of businesses and businessmen. In this, they broke from previous ideas about the relationship of mathematics to commerce in the United States, but not without precedent. Engineers, accountants, and actuaries had based their claims to mathematical authority on the widespread notion that the primary economic actor was the calculating businessman, the individual proprietor who managed his books and his business in a democratic economy. At the same time that they had no doubt that they were participants in economic life, numerate elites had also always presented themselves as disinterested observers. But by the end of the nineteenth century, such experts’ tenuous positions as not-quite-participants had begun to lose credibility. As corporations grew, consultants turned into employees and managers. Economists therefore filled the gap that had been left when formerly disinterested experts became corporate calculators. From their research universities, economists could, and did, proclaim themselves the only truly objective observers. On the surface of the conversation, both economists and business leaders proclaimed that they were committed to working together, and that there need not be any gap—let alone argument 44 George S. Roorbach, “The Teaching of Importing in Schools of Business”. Folder 39, Series II. Writings, 1909- 1934. George S. Roorbach Papers, 1909-1934. Baker Library, Harvard Business School (Boston, MA). 256 or competition—between their two approaches. All other sciences relied on some combination of experimental data and inductive reasoning with theoretical deduction. Surely economics could be the same. The “true course” of economics, according to one economist in 1906, lay in “that union of observation and speculation which the progress of every science vindicates.”45 Economists tried to reassure their listeners that there existed “no jealousy between these two co-workers, theory and observation” and that both were essential to the science of economics. But some economists could not help but betray that they agreed with Jevons’ statement that empirical knowledge was “of slight importance compared with the well-connected and perfectly explained knowledge” that defined “an advanced and deductive science.”46 Without a designated laboratory, or even an agreed-upon scientific method, economists found that the exact relationship of speculation to observation was very much up for debate at the outset of the twentieth century. One cause of this division was the prominence of engineers in the early American business school landscape. The economics curriculum at MIT, for example, remained strictly practical well into the twentieth century, with classes emphasizing banking and finance, industrial organization, railroad economics, labor relations, and economic history—all crucial skills to the managerial class that had founded and supported the school.47 Insofar as these institutions created or had inherited a mathematical tradition, it tended to be in the static, spatial, geometrical ideas of the engineering 45 Jacob H. Hollander, “The Present State of the Theory of Distribution” Publications of the American Economic Association, 3rd Series, Vol. 7, No. 1 (Feb., 1906), p. 44. 46 Jevons quoted in Davis R. Dewey, “Observation in Economics. Annual Address of the President” American Economic Association Quarterly, 3rd Series, Vol. 11, No. 1 (Apr., 1910), p. 29. 47 Richard Adelstein, “Mind and Hand: Economics and Engineering at the Massachusetts Institute of Technology” in William J. Barber, et al. (eds.), Breaking the Academic Mould: Economists and American Higher Learning in the Nineteenth Century (Wesleyan University Press, 1988), p. 315-17. 257 profession. Francis Amasa Walker, whose stint as MIT president transformed the university into a modern research institute, did have a mathematical understanding of economic life, as evidenced by his textbooks on political economy. But although he shared some assumptions with the marginal economists, particularly around the idea of market equilibrium, his model was fundamentally static and geometrical, conceiving of equilibrium as something reached through a spatial balancing act, rather than a constantly moving target.48 Engineers’ enduring prominence in positions of industrial and corporate authority meant that these distinct conceptualizations of economic space and time, based in distinct mathematics, survived into the twentieth century. How the American Economic Association would relate to businessmen introduced another space of contention into the concurrent professionalization of both economics and commerce. The union of the two seemed like an obvious solution to some, like the AEA member who asked the Secretary in 1894 to send “everything we have on Municipal ownership” to the proprietor of a petroleum business in upstate New York, because he was “a prominent man… making a fight against the gas monopoly.”49 In 1904, member Freddie Howe opined that the struggling association might gain support and become more useful if it would only “identify itself more closely with industrial and social questions.” While he appreciated the academic rigor of recent meetings, Howe pointed to the success and influence of the National Municipal League, and suggested that, at least to his “non-academic mind,” this association of supposed economic experts should shed “some 48 Ross, Origins of American Social Science, p. 84. 49 E.A. Ross to the American Economic Association, 10 Feb. 1894. Folder 7: Incoming Correspondence, Dec. 1893- March 1894, Box 4: Correspondence. Incoming, 1888 March-1896 February. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 258 definite light on these questions instead of upon matters of purely speculative economy.”50 After all, he pointed out, the AEA comprised “leading public officials, business men, lawyers, bankers and other public spirited citizens,” not just academic economists.51 But Howe’s advice raised hackles among many academic economists who saw themselves as pure scientists, whose aim was to observe and explain, not advise or make judgments. Thinking about the future of the AEA in 1899, John Bates Clark suggested that while it might “desirable to interest the right class of business men in our association,” he did not want to appear as though the economists were “abrogating our own position in favor of them,” and therefore disagreed with the idea of electing a businessman to the association’s presidency. Clark believed the AEA had much to offer businessmen, and would be happy if they were to “avail themselves” of it, but he also felt that too many “practical men” believed “that anything that a business man may say on an economic subject is worth more than anything that a man from the schools can say.” This attitude Clark did not want to “assist in any slight degree.”52 Other economists were more accommodating; Frank Taussig, a professor at Harvard and a vocal proponent of historical economics, believed that a 50 Freddie C. Howe to the American Economic Association, 21 Sept. 1904. Folder 4: Feb.-Aug., 1904, Box 10: Correspondence, 1903-1908. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 51 AEA to Earle Adams Koghlinger, 20 October 1901. Folder 5: Correspondence, Sept. — Nov., 1901, Box 9: Correspondence, 1900-1902. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 52 Clark to Henry Hull, 15 December 1899. Folder 8: Oct. 1899-Jan. 4, 1900, Box 8: Incoming Correspondence, 1896-1900. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 259 businessman might help “secure additional outside members in the business world.”53 In the end, however, the Association presidency remained in academic hands. Even when economics departments made active efforts to engage local businesses, the lines of communication could be disrupted by the two camps’ differing approaches. In 1919, the Brown University economics department established the “Bureau for Business Research” to create closer ties between the university’s economists and the surrounding Rhode Island business community. The Bureau’s efforts largely consisted of sending surveys to local businesses, particularly factories and other large-scale industries, and asking for statistical data, especially around labor. Professor William Berridge spearheaded the effort, writing everyone from the Builders Iron Foundry to the Metropolitan Life Insurance Company. His success was middling. Berridge received responses explaining that “figures in relation to turn over” mattered less to firms than the proportion of those who left to those who stayed, preferring static data to “records of changes.”54 In return, he found himself reassuring firms that his analysis would give “identical weight to each establishment regardless of its size” when they insisted they were too small to be useful.55 Berridge believed that his work would allow every businessman to “compare his own curve with the composite average” in labor statistics, but he overestimated the demand for his analysis.56 53 Walter Willcox to Hull, 12 December 1899. Folder 8: Oct. 1899-Jan. 4, 1900, Box 8: Incoming Correspondence, 1896-1900. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 54 Z. Chafee to William Berridge, 24 Feb. 1926. Box 2: Correspondence, Bureau of Business Research records, 1919-1939. John Hay Library, Brown University (Providence, RI). 55 William Berridge to Martin-Copeland Co, 18 May 1926. Box 2: Correspondence, Bureau of Business Research records, 1919-1939. John Hay Library, Brown University (Providence, RI). 56 William Berridge to Samuel M. Nicholson, 9 Jan. 1926. Box 2: Correspondence, Bureau of Business Research records, 1919-1939. John Hay Library, Brown University (Providence, RI). 260 Similarly, research on the “business cycle” highlighted different opinions about the utility of mathematics for business professionals. In the 1870s, Jevons had famously put forth a theory of business ups and downs that was tied to sunspot cycles. His statistics did not convince his peers of the connection—and indeed, became a ready example for critics of the mathematical turn in the ensuing decades—but it did lead to a wider interest among economists in using mathematical and analytical statistical tools to forecast business conditions. However, in the forecasting industry that emerged from this interest, divisions remained. Mathematical economists like Irving Fisher sought to create a causal model through deductive reasoning, rather than data collection, as he viewed his work as more akin to physics than business.57 But the popular forecasters were those who worked with historical data, including those with no connection to academic economics at all. Others held positions in historicist economics departments, such as Harvard, where Frank Taussig held sway until Joseph Schumpeter’s arrival in 1933.58 Eventually this disconnect would be ameliorated by the development of econometrics, but not until at least the 1930s.59 That so many business leaders and advocates looked askance at mathematics did not mean they saw no place at all for it, especially as it became more engrained in economic science. Some business schools began to offer mathematical classes in the 1920s, particularly in finance, where the mathematics need was perceived to be greatest.60 Others continued to make room for an older, geometrical vision of economic life still preferred by engineers. In 1925, professor of economics 57 Walter Friedman, Fortune Tellers: The Story of America’s First Economic Forecasters (Princeton University Press, 2014), pp. 52-3; Allen, Irving Fisher, pp. 181-2. 58 Friedman, Fortune Tellers, p. 132. 59 Morgan, The History of Econometric Ideas, p. 259. 60 C.H. Forsyth, Mathematical Theory of Life Insurance (New York: Wiley & Sons, 1924), p. v. Rauner Special Collections Library, Dartmouth College (Hanover, NH). 261 and sociology Joseph Folsom argued that the universities should learn from business schools. He praised economics departments, like Harvard’s, that collected “actual cases of business situations and problems… instead of improved hypothetical cases.” He mocked “childish faith in the efficacy of language and arithmetic as tools for the transmitting of economic ideas,” when real examples were sorely needed. Folsom had attained a degree in civil engineering before getting his doctorate, and now saw students struggling with graphics that represented only abstract economic concepts, “such as demand and supply curves,” instead of “concrete things like the forms of business and the circulation of money.” He advocated greater “connection with engineering departments” and more use of “charts, economic maps, and pictures” in economics classes.61 The gap in philosophies between economics departments and business schools sometimes spilled into disputes over policy. Economists increasingly echoed their classical predecessors in calling for free trade, though now “on dynamic grounds,” as Clark put it in a lecture to his students at Columbia.62 But at business schools, their industrialist founders and supporters did not line up for this tenet of economic orthodoxy. Joseph Wharton believed years spent “grappling with the intricacies of dead languages and of unapplied mathematics” would not produce good business men, and sought another path.63 But when he donated $100,000 to the University of Pennsylvania in 1881 to establish a business school, he specifically retained the right to reclaim his gift should the school abandon its commitment to teaching the benefits of protectionism. The solution, largely, 61 Joseph K. Folsom, “What College Economics Departments Can Learn from Industry” The American Economic Review, Vol. 15, No. 3 (Sep., 1925), pp. 475-478. 62 “Lecture 12” Folder 18, Series II: “Conditions of Prosperity” 1914, Box 3, Series I: Correspondence, 1875-1955 and Series II: Unpublished Scholarly Materials, circa 1865-1936. John Bates Clark Papers, Columbia University Rare Books & Manuscripts Library (New York, New York). 63 Joseph Wharton, Is A College Education Advantageous to a Business Man? (Philadelphia, 1890). 262 was further separation at the Wharton School between economics and business. The school largely ignored economics, apart from a few nonessential courses in classical theory, and instead added more instruction in accounting, finance, marketing, and management.64 Disagreements over economic theory did not stem solely from self-interest. The growing prevalence of calculus in academic economics shifted the intellectual discourse and the paradigm of economic research away from questions of production, value, and labor, to issues of individual consumption and utility maximization. The mathematical reasoning embedded in the marginalist turn emphasized the decision-making of individuals and aggregated these discrete instances into a whole, systemized theory of economics. John Bates Clark explained to his students in 1907 that in most cases, normal economic forces acted “atomically,” on individuals.65 The academic goal to conceive of what Schumpeter called “a system of undefined ‘things’ that are simply subject to certain restrictions” and then “to develop a perfectly general mathematical logic of systems,” left little room to consider the place of necessarily associational and complex corporations, who often saw their own concerns as unique to their industry or business model.66 It would not be until the late 1930s that economics departments returned to look for a “theory of the firm,” although even then, such considerations never dominated academic economic science.67 64 Steven A. Sass, “An Uneasy Relationship: The Business Community and Academic Economists at the University of Pennsylvania” in Barber et al. (eds.), Breaking the Academic Mould, p. 227-30. 65 John Bates Clark handwritten teaching notes. Folder 1, “Economic Theory,” 1907-1908, Box 4: Series II, Unpublished Scholarly Materials, circa 1865-1936. John Bates Clark Papers, Columbia University Rare Books & Manuscripts Library (New York, New York). 66 Joseph Schumpeter quoted in Donald Winch, “Marginalism and the Boundaries of Economic Science” in Collison Black, The Marginal Revolution, p. 69. 67 The scholarship best associated with the turn in business studies is Ronald Coase “The Nature of the Firm” Economica 4:16 (1937), pp. 386-405. See also R. L. Hall and C. J. Hitch, “Price Theory and Business Behaviour” Oxford Economic Papers No. 2 (May, 1939), pp. 12-45 for a marginalist analysis of the problem of firm behavior. 263 Eventually, too, business schools adopted some of the mathematical models developed in economics departments as part of their broader obsession with economic forecasting. By the 1930s, the last of the historical or institutional economists had been largely boxed out of the profession, or absorbed by the same positivist assumptions about market forces, and the neoclassical paradigm became dominant throughout American universities.68 Frank Knight, an economist who had been critical of the marginalist approach in the early part of the century and held out for historical methods, conceded in 1924 that he now believed economics to be “a true, and even exact, science, which reaches laws as universal as those of mathematics and mechanics.”69 At business schools, faculty did not embrace mathematical economics wholeheartedly, still believing that “ingenious schemes of a mechanical or mathematical nature” would always be less effective than “the scrutiny and thorough investigation of the expert who is trained in the particular field under investigation.” But they too admitted that some of the “characteristic features of the scientific worker” were worth adopting, particularly as they related to “the problems of forecasting.”70 The uneasy relationship that American economists of the early twentieth century held with their ostensible allies in corporations and emerging business schools stemmed both from practical considerations about their own academic expertise, and fundamental differences in the way each approached economic questions, including their views of mathematics and numbers. Economists feared, as Clark put it in 1899, “any yielding to the view that economic wisdom resides outside of 68 Ross, Origins of American Social Science p. 407. 69 Ibid., 426. 70 C.H. Forsyth, “Business Statistics” (c. 1926). Rauner Special Collections Library, Dartmouth College (Hanover, NH). 264 the school and inside of the counting house.”71 They believed that they possessed peculiar expertise that warranted greater consideration from the public and policymakers than professional business men and their allies in business schools. And they believed their discipline, as queen of the social sciences, championed the tenets of individual rationality inherent to modern liberalism, an attitude that was reinforced by—indeed, one that arguably stemmed from—the collective decision to use calculus as the primary mathematics of economics.72 As the marginalist framework developed and entrenched itself in American economics, a rationalization developed alongside of it to justify its separation from business affairs. Only economists, this line of thinking went, had the expertise and capability to truly understand economic life as a mathematical system. The growing influence of the marginalist economists and their pursuit of a purely scientific and mathematically advanced economic discipline, at the expense of allies in business and even in their own departments, continued to undermine the once broad, if contested, meanings of the mathematical economy. However much these economists claimed to describe rather than prescribe in matters of economic policy, and despite their growing comfort with mathematical abstractions in marginal utility theory, many continued to press for a public role. In 1909, Leon C. Marshall advised his fellow economists that “our theories are not framed for the intellectual delight of the priests of the temple, but rather for the guidance… of that great body called the public.”73 But what form that guidance would take was not immediately obvious, especially as economists had worked 71 Clark to Henry Hull, 23 December 1899. Folder 8: Oct. 1899-Jan. 4, 1900, Box 8: Incoming Correspondence, 1896-1900. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 72 On marginalism and liberalism, see Ross, Origins of American Social Science, p. 173. 73 G. R. Wicker, L. C. Marshall and J. H. Hollander, “Outlines of a Theory of Wages: Discussion” American Economic Association Quarterly, 3rd Series, Vol. 11, No. 1, (Apr., 1910), p. 161. 265 so hard to distinguish their work from that of their “practical” colleagues in business schools and industries. If the point of this new, mathematical discipline was to observe and explain, would economists have a role in advising or criticizing policymakers? In general, the marginalist and neoclassical economists agreed: yes. Many of them wanted to see their journal be “broad enough in its scope so that it would be of use to those who direct political affairs.” The goal of this class of article would be to formulate those “generally accepted economic principles” insofar as they affected political issues “under consideration by our officers and representatives in state and nation.” 74 As early as 1895, the American Economic Association sent letters to both the Democratic and Republican National Committees asking that the leadership direct their “attention to some publications of the American Economic Association which are likely to be useful to you in the present campaign.”75 At the time, debates in academic economics over the use of mathematics still raged, and plenty of more traditional political economists interested in governance held influential positions. But even once the mathematical turn began in earnest, the aim to provide useful advice remained a central feature of economics. With mathematical methods becoming the new orthodoxy, however, additional problems with economic policy advocacy presented themselves. Economists believed it was—and perhaps more frankly, wanted it to become—“natural and proper for the public mind to turn to the scientific economist for specific and definite guidance” on the political issues of the day, as Jacob Hollander 74 J.H. Arnold to J.H. Hollander, c. April 1902. Folder 9: Correspondence Regarding the Proposition for the American Economic Association to Establish an Economic Journal, April 1902, Box 9: Correspondence, 1900-1902. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 75 AEA to Democratic and Republican National Committees, c. 1895. Folder 2: Letter Copybook, Nov. 11 1895 — Dec. 12 1896, Box 6: Correspondence. Outgoing, 1894-1898. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 266 put it in 1906. But they struggled to communicate that guidance, unwilling to sacrifice their hard- won academic prestige, as they saw it, by simplifying their publications or by popularizing their theories. In the same breath, Hollander continued that “the economic life of today in its range and complexity has utterly passed beyond the mental compass of the casual onlooker—be he economist or man of affairs.”76 Hollander had no doubt what the appropriate role for economists should be. The various facets of economic life had become so complicated that they had surpassed the conceptual abilities of those who participated in it, but did not have time to make a careful study of it. A dedicated coterie of disinterested, mathematically scientists would henceforth be necessary to study it, and everyone else would understand it by way of their analysis. The emphasis on mathematical deduction among the marginal economists convinced them that, as nineteenth century economist Richard Whatley explained it, “the looker-on often sees more of the game than the players.”77 In the professional context of early twentieth century academic economics, this philosophy meant that the boundaries within which economic knowledge could be interpreted, and by whom expertise could be wielded, narrowed sharply. The shift to mathematical emphasis made the “practical men” of business schools, and other participants in commercial life, less credible and influential as economic experts.78 Professional economics now meant only one thing: those in academia attempting to describe economic reality as it was through pure scientific reasoning, not those managing firms, compiling actuarial tables, or arguing over taxes and tariffs. 76 Jacob H. Hollander, “The Present State of the Theory of Distribution” Publications of the American Economic Association, 3rd Series, Vol. 7, No. 1 (Feb., 1906), pp. 29-30. 77 Whatley quoted in Maas, “Sorting Things Out,” in Daston and Lunbeck (eds.), Histories of Scientific Observation, p. 212. 78 Winch, “Marginalism and the Boundaries of Economic Science” in Collison Black, The Marginal Revolution, p. 76. 267 Nevertheless, the old core of the mathematical economy remained; the ideal of an objective, rule- based, “democratic” economy complicated economists’ efforts to declare their ultimate authority. Could such a system simply be imposed on an unsuspecting public? The Domain of Calculation In an article published in the American Economic Review in 1912, Allyn Young posed a mild criticism of William Stanley Jevons. One of the only faculty at Harvard then willing to teach mathematical economics, Young posited that, contrary to what Jevons had suggested in The Theory of Political Economy, consumers’ pursuit of maximum pleasure in their decision-making was not limited to the most rational and educated actors. Instead, Young suggested, the idea of “marginal significance” was as valid “when instincts and habits are counted among the forces governing men in their economic relations, as when only ‘economic men’ actuated solely by a reasoned pursuit of a maximum of pleasure, are postulated.”79 That is, Young believed that central tenets of marginal utility theory applied to all economic actors, whatever their “instincts and habits,” and not just the theoretical class of hyper-rational beings that Jevons had deemed “economic men.” Economists did not need to worry about the psychology of people engaged in economic relationships, he said, because the neoclassical paradigm extended to every economic actor, regardless of how effectively he engaged in “reasoned pursuit” of maximum utility or productivity. Young’s reference to “reasoned pursuit” in his description of how economists assumed that “economic men” approached their economic lives gestures to a much longer tradition of rational 79 Allyn A. Young, “Jevons’ ‘Theory of Political Economy’” The American Economic Review, Vol. 2, No. 3 (Sep., 1912), p. 582. On Young as the outlier at Harvard, see Friedman, Fortune Tellers, p. 131. 268 calculation in defining economic behavior than even he likely recognized. The calculating people had been a feature of American economic thought and practice for decades, continually reinforced by repeated claims that numerical calculation was what made American economic life democratic. Civil engineers had based their authority in published financial reports. Actuaries had insisted they were holding financial corporations to fair standards through calculation. Postbellum commercial colleges continued the long tradition of making arithmetic central to business education. As much as Young’s argument that marginal significance could be attributed to any economic actor, without regard to his intentions, was new, it was nevertheless based in longstanding American ideas about the relationship between calculation and economic life. For decades, this idea had been a place of contestation—over who could and should learn to calculate, what calculation should be used for, and more. What Young, and marginalist economists generally, argued was that there was no need for contest, because all individuals were a rational, calculating actors. Economic rationality is a difficult concept to historicize. On the one hand, some idea of the “reasoned pursuit” of economic good, whether focused on the self, firm, or community, has been at the heart of most western economic theory dating back to the seventeenth century, if not further. Moreover, the importance of rationality has been an ongoing debate in academic economics since it first took its current form in the 1920s and 1930s. From Keynes’ “animal spirits” to the modern persistence of behavioral economics, the precise nature of economic rationality has not been settled in economics departments. However, with those caveats in mind, it does appear that with the rise of the neoclassical economists in the early twentieth century, a mostly new and generally accepted orthodoxy around rationality arose. It was, as John Bates Clark’s son John Maurice put it in 1921, 269 “The rational foresight of individuals is at the basis of individualistic economics.”80 Individuals’ “rational faculties” might differ in extent, but were “essentially identical as to stuff.”81 Economists, therefore, could assume that identical “stuff” in making their models. Exactly how this vision of rationality according with calculation, however, is generally less well understood. The idealized subject of neoclassical economics, the so-called homo economicus, has an instinctive rationality. As historian Theodore Porter puts it, an economically rational actor makes “subtle (though tacit) calculations of self interest,” but his decisions lie “beyond the reach of explicit quantitative reasoning.”82 The marginalist revolution introduced a notion that became central to modern economic thought: that individuals are constantly making choices to maximize their own interest, and that because this behavior is fundamentally rational, it can be modeled from the outside. But of course, what goes in people’s heads is hard to know. Economics came to rely on the idea that people make small calculations every day, while excising the explicit calculations done by experts, academic or commercial. The marginalist economists turned the mathematical economy from one that relied on conscious economic calculation, into a system explicitly intended to exist beyond the calculative ability of participants in commercial exchange and other economic activity. They did this through the introduction of differential calculus. In 1912, Joseph Schumpeter joked to John Bates Clark that he had begun to describe his economic theories as “dynamic” primarily “to humour German readers,” who, he said, “kick at 80 John Maurice Clark, “Soundings in Non-Euclidean Economics” The American Economic Review, Vol. 11, No. 1 (Mar., 1921), p. 136. 81 Frederick C. Mills et al, “The Present Status and Future Prospects of Quantitative Economics” The American Economic Review, Vol. 18, No. 1, (Mar., 1928), pp. 29-30. 82 Theodore Porter, “Locating the Domain of Calculation” Journal of Cultural Economy, Vol. 1, No. 1 (March 2008), p. 39. 270 the word.”83 The sentiment was true in America, too; a decade prior, Henry Charles Adams insisted that “the distinction between static and dynamic” was “fruitless” and “illogical.”84 Dynamism was crucial to the marginalists’ vision of economic life, a code to suggest new, marginalist, deductive, and mathematical economics. Crucially, it was tightly linked to the kind of mathematics that they had begun to use to conceptualize economic activity: differential calculus. Menger, Walras, and Jevons had all applied differential calculus to existing ideas about utility, and this idea had directly produced their understanding of utility as something to be maximized, something that delivered a diminishing return of utility or pleasure.85 American economist Simon Patten identified this key aspect of marginalism when he explained in 1890 that what these new economists valued were the “subjective estimates which man places upon material commodities.”86 What Patten observed was the emphasis of marginal utility theory on the natural tendency of every person to act as an economic utility maximizer, and to identify the value of actions or commodities for himself, rather than adhering to a universal theory of value based in labor or land. With calculus, every economic problem could be solved by finding the maximum point on a curve representing the diminishing utility an individual found in more of the same.87 In this way, calculus 83 Joseph Schumpeter to John Bates Clark, 10 March 1912. Folder 7, Series I: Schumpeter, Joseph, 1907-1912. Box 3, Series I: Correspondence, 1875-1955 and Series II: Unpublished Scholarly Materials, circa 1865-1936. John Bates Clark Papers, Columbia University Rare Books & Manuscripts Library (New York, New York). 84 Henry C. Adams to Edwin Seligman, 14 May 1902. Folder 10: President Seligman’s Correspondence, 1902, Box 9: Correspondence, 1900-1902. Papers of the AEA, David M. Rubenstein Library, Duke University (Durham, NC). 85 Richard S. Howey, “The Origins of Marginalism” in Collison Black et al, The Marginal Revolution in Economics, p. 25; Robert Loring Allen, Irving Fisher: A Biography (Cambridge: Blackwell, 1993), p. 54. 86 Simon N. Patten, “The Educational Value of Political Economy” Publications of the American Economic Association, Vol 5, No. 6 (Nov. 1890), p. 15. 87 Richard S. Howey, “The Origins of Marginalism” in Collison Black et al, The Marginal Revolution in Economics, p. 25; Robert Loring Allen, Irving Fisher: A Biography (Cambridge: Blackwell, 1993), p. 54. 271 allowed the mathematical invention of the economic man. According to marginalist theory, people constantly acted in such a way as to maximize their happiness or pleasure, or minimize their losses or pain. Thus, for the marginal economist, every economic problem became a question of finding the maximum point on a curve, which defined the functional relationship of the consumer to the pleasure he gained from purchasing further iterations of a commodity. Maxima and minima can be easily found at spot where the first derivative of a function is equal to zero, thus equating the derivative with the actor’s rational choice.88 Indeed, by the 1930s, economists simply referred to “the differential, or, in the older phraseology, at the margin.”89 Calculus became engrained in economic knowledge as a result of the marginal revolution, which itself resulted from historical factors specific to the late nineteenth century. And yet, the assumptions that it delivered, especially around the amalgamation of individual economic activity and the central assumption of utility maximization on the part of all actors, became lost—or was misplaced, perhaps purposefully—in the larger battles over the use of mathematics in professional economics, and the public role of economists more widely. The increasingly prevalent assumption of implicit calculation meant that, even as more and more economists relied on ideas that stemmed from calculus, they also thought less and less about whether anyone outside their profession could understand their mathematical reasoning. Like their predecessors, they assumed mathematics was too difficult for ordinary people, an assumption that conveniently obscured their own elitist role in the economy. Unlike previous numerate elites, however, marginalist economists did not see that 88 Allen, Irving Fisher, p. 54. 89 G.R. Davies, “The Significance of Economic Law” The American Economic Review, Vol. 21, No. 3 (Sep., 1931), p. 454. 272 disconnect as a problem. Their growing insistence that rational human faculties did not differ “as to stuff” alienated the mathematical economy from its historical context. The obscuring of calculus through the doctrine of implicit calculation began to seep into both economics and business school classrooms. Some textbooks were quite explicit about the fact that although the mathematical reasoning behind the material had originally been based in calculus, only the economic material was necessary, not the original mathematics. A college textbook in business statistics from the mid-1920s explained that while “the quadrature theory in economics is based solidly upon the fundamental principles of the calculus,” students did not need “special technical knowledge of the algebraic workings of those principles to grasp the essentials of the theory.” Mathematics might “perhaps add something toward a more complete and satisfactory understanding” of the economic principles, but the author had his doubts. In another textbook on the mathematics of finance, he had opined that “too many mathematical principles often serves to estrange the student rather than help him in the analyses of the problems,” and thus consciously omitted “extensive algebraic theory or derivations.”90 Although the specifics of calculus had been essential to the development of marginal economics, the mathematical foundations of the theories gradually eroded, leaving behind only the economic assumptions it had created. Meanwhile, investment in using explicit commercial calculations in mathematics education continued to decline in the early twentieth century. In 1904, mathematics teachers from across the United States met for a conference at Dartmouth College. In a paper on preparing students to enter 90 C.H. Forsyth, “Business Statistics” (Hanover, c. 1926). Rauner Special Collections Library, Dartmouth College (Hanover, NH); C.H. Forsyth, Introduction to the Mathematical Theory of Finance (New York: Wiley & Sons, 1928). Rauner Special Collections Library, Dartmouth College (Hanover, NH). 273 high school mathematics classes, one teacher told the audience that he felt it “needless to multiply examples to show the futility of much of the time-honored instruction in arithmetic.” While he agreed with the general principle that arithmetic was the appropriate mathematics for students in elementary school—especially as efforts to introduce minimal algebra had been tried and failed during the previous decade—the speaker also wanted greater pedagogical change. He lauded the “increasing tendency to omit… problems in interest, partial payment, and compound proportion” in school rooms, and echoed Francis Walker’s decades-earlier call for a constant “insistence on accuracy” above all else. Now, however, this was in the service of preparing students not for a life as a shop-keep or bookkeeper, but to enter high schools. There, those teachers agreed, “the weight of evidence is decidedly in favor of algebra” as a core curriculum.91 How much the changes in secondary and higher education mathematics pedagogy was tied to concurrent changes in mathematical commerce and economics is hard to know. But they do at least suggest that broad understandings in the United States about the purpose of mathematics, in education and in commercial life, were again shifting. A 1919 high school mathematics textbook stated that the “central element in human thinking is the ability to see relationships clearly.” Thus, the main function of a high school mathematics course was to teach students that skill by giving them the “ability to recognize relationships between magnitudes, to represent such relationships economically by means of symbols, and to determine such relationships.”92 This philosophy on the purpose of mathematics education, which emphasized mathematics as a tool to understand the 91 “Report of the Conference of Teachers of Mathematics in Secondary Schools, Held at Dartmouth College, May 12, 13, 14, 1904” Rauner Special Collections Library, Dartmouth College (Hanover, NH). 92 Harold O. Rugg and John R. Clark, Fundamentals of High School Mathematics: A Textbook Designed to Follow Arithmetic (Chicago: World Book Company, 1919), p. vii. 274 relationships between quantities, not calculation itself. It taught students to become comfortable with the use of “abbreviations and letters, instead of words, to represent numbers.”93 But it also shied away from practicality, promising general “problem-solving” skills instead of the utilitarian focus of the previous century. If mathematics was to be a realm of economic knowledge, it would no longer be so in American classrooms or mathematics textbooks. Some historians have accused neoclassical economists, and their intellectual descendants, of the “willful mystification” of economic knowledge.94 Their use of mathematics often features in such accusations, as do heaps of scorn on the idea that economists engaged in pure science and only described economic life without affecting it. The latter seems somewhat justified. From the turn of the century onward, and especially after the 1910s, economists’ science was hardly pure; it consistently engaged with the dominant economic issues of the day. Its practitioners engaged in financial speculation and sold business forecasts, and, after 1929, fought with one another over the correct course for the government to take. They believed themselves the only true safeguards of the nation’s prosperity, because they believed that ordinary people, “either individually or through democratic government,” offered no foundation “for an enlightened administration of the social income.”95 Having been born, along with its social scientific siblings, in a moment of anxiety over the state of industrial society, economics’ claims to neutrality often rang hollow. 93 Ibid., p. 3. 94 This phrase taken from Augustine Sedgewick, “Against Flows” History of the Present, Vol. 4, No. 2 (Fall 2014), p. 153. 95 G.R. Davies, “The Significance of Economic Law” The American Economic Review, Vol. 21, No. 3 (Sep., 1931), p. 460. 275 However, the issue of mathematics is more difficult. To say that the mathematical economy was necessarily mystifying suggests that calculus is beyond the understanding of ordinary people. Among other concerns, this claim legitimizes Jacob Hollander’s 1906 claim that understanding the economy was “beyond the mental compass of the casual onlooker,” an argument that emerged from a historical moment of conflict over economic expertise. Mathematics had long been a part of understanding economic life, albeit never one that was universally agreed-upon. For economists to lay claim to the “domain of calculation” in their field, they had to both command a disinterested expertise, one presumed to be beyond the capabilities of businessmen and citizens, and naturalize the specific mathematical economy they had developed, separating it from its historical context. The mystification of economic life did not occur because it was mathematized in the 1870s with a field that no one understood. Rather, decades of inculcated mathematical ignorance created room for economists to ignore public mathematical knowledge altogether, and insist that it made no difference to whether they acted in accordance with mathematical models. Neoclassical economists followed and amplified the steady belief among the numerate elite that mathematics beyond arithmetic was beyond the reach of ordinary people. The AEA began to send missives to the DNC and RNC, flattering politicians with the idea that their economics articles were “hardly of the character suited for general circulation among voters,” but might nevertheless be of some use to their representatives.96 Even those who professed fears about the new methods in economic thought undermined economists’ confidence in the public. Leon Marshall warned his 96 AEA to Democratic and Republican National Committees, c. 1895. Folder 2: Letter Copybook, Nov. 11 1895 — Dec. 12 1896, Box 6: Correspondence. Outgoing, 1894-1898. Papers of the American Economic Association, David M. Rubenstein Library, Duke University (Durham, NC). 276 colleagues that the public “look upon our discussions as doctrinaire and confusing”—but he also argued that “we cannot expect [the public] to master our terminology.” Marshall wanted to scale back the messy range of new terms and methods, but he also professed a lack of faith in the public’s mathematical abilities. In the common refrain that “industrial phenomena are becoming more and more complex,” Marshall felt that “the plain people need guideposts as plain and simple as may be.” 97 But most of his colleagues wanted to understand economic life entirely, not water down its scientific research for the benefit of a “plain and simple” public. Economists’ hemming in of the domain of calculation, however, did not only remove the mathematical tools of economic life from public hands. In that, they kept company with ancestors in many expert professions before them, from bookkeeper to actuary. Instead, after claiming their economic expertise by way of mathematics, the neoclassical economists then hid the mathematical foundations of their science. They denied that the use of calculus, of any mathematics, affected the kind of knowledge they produced. As they found themselves suddenly in positions of enormous influence in the 1930s, economists embraced mathematics more tightly. “The complete working out of the field as a whole,” G.R. Davies enthused in 1931, “may eventually require equations as complex as those of the relativity theory.” But he dismissed the persistent worries about using mathematics to study economic life. Davies believed that economic analysis might be done without the use of mathematics, but he did not see any reason to do so. Mathematics, he claimed, was “the natural language” to express complex economic relationships.98 97 G. R. Wicker, L. C. Marshall and J. H. Hollander, “Outlines of a Theory of Wages: Discussion” American Economic Association Quarterly, 3rd Series, Vol. 11, No. 1, (Apr., 1910), pp. 166-67. 98 G.R. Davies, “The Significance of Economic Law” The American Economic Review, Vol. 21, No. 3 (Sep., 1931), pp. 450-51 [footnote]. 277 The idea that there was no meaningful difference between expressing economic knowledge in words and expressing it in symbols, and that mathematics was no more than a language through which to express economic theories, became the watchword of twentieth century economics. No longer would economists fight about the correct balance between the qualitative and quantitative sides of their disciplines. As early as 1928, they observed that qualitative and quantitative methods were “becoming so interwoven… that it will soon seem pedantic to question the indispensability of either.”99 British mathematical economist Alfred Marshall went so far as to argue that Ricardo merely lacked the language to express his theories correctly: “the terse language of the differential calculus.”100 Reassessment of classical economics, and questions about how to mathematize those older theories, became a new cottage industry for economists. They insisted that mathematics was the right tool because it accorded with observed reality. It did not occur to them that their theories had been shaped by the logic of calculus, not the other way around. A century after Halsey Wing had mocked the “mathematically mad” Turgot, mathematics had become the language of economic knowledge. At the sixty-fourth meeting of the American Economic Association in 1952, MIT economics professor Paul A. Samuelson delivered a paper on the place of mathematics in economics. He insisted that although some of his older colleagues still complained, mathematics had become a contingent part of economics. But Samuel urged them not to despair. “Mathematics is language,” he insisted; as tools to express economic ideas and theories, the two media were identical in every way. For Samuelson, economics expressed in mathematics 99 Frederick C. Mills et al, “The Present Status and Future Prospects of Quantitative Economics” The American Economic Review, Vol. 18, No. 1, (Mar., 1928), p. 41. 100 Marshall quoted in N.B. de Marchi, “Mill and Cairnes and the Emergence of Marginalism in England” in Collison Black et al, The Marginal Revolution in Economics, pp. 80-81. 278 were no different than those expressed in French: fundamental ideas would not change. Whether by ignorance or willfully, scientific economists forgot how influential the introduction of calculus had been to their discipline. They ignored, or never considered, the mathematical economies of the past that had depended on the type of mathematics used to understand them. By 1952, one could “hardly tell a mathematical economist from an ordinary economist.”101 The metaphor of language entirely obscured the process by which economists had created an ahistorical discipline out of the historical process of mathematization—business practices, shifts in culture and pedagogy, ideas about who should and could wield economic authority, and the role of mathematics in a democratic nation. By making calculation implicit, they purported to solve the problems of the increasingly mathematically complex economy in such a way that would preserve the supposed distribution of economic knowledge through mathematical knowledge, an idea that had been part of American political economy since the beginning of the nineteenth century. Their claims of implicit calculation, of mathematics as language, and of their perfect disinterestedness to commercial activity, naturalized the idea that this distribution of authority could be achieved through a general, implicit, nonspecific mathematical calculation on the part of all people, whether they had ever learned calculus or not. With this compromise in place, expert economic knowledge could coexist seamlessly with a democratic economy. 101 Paul A. Samuelson, “Economic Theory and Mathematics—An Appraisal” The American Economic Review, Vol. 42, No. 2 (May, 1952), pp. 56-66. Samuelson would become famous as the first American to win the Nobel Memorial Prize in Economics; he won in 1970, shortly after the award’s invention. 279 “Utility, or futility” In the early 1960s, a decade or so after Samuelson’s address to the American Economic Association, graduate students at Harvard found themselves faced with the following question on their qualifying exams to advance to doctoral candidacy: Write an essay on the use of mathematics in economics. Include in your discussion the statement of an economic problem, its reformulation and solution mathematically. Relate your example to the general question of the use and utility, or futility, of mathematics in economics.102 Perhaps it was the spirit of Frank Taussig still haunting the hall at Harvard that raised the qualms in this exam about the possible futility of truly mathematical economic science. Or perhaps the question merely reflected the never-ending debates within economics about the proper use and potential misuse of mathematics in their otherwise well-established discipline, ones that continue, even today, to circulate among academic and practical economists alike. Ongoing debates among micro-economists, macroeconomists, and econometricians over the appropriate use of mathematics in their discipline are beyond both the scope of this dissertation and the limited expertise of its author. Nevertheless, it is clear from the last century of economic history, and the history of economics, that mathematics has become an essential feature of the discipline, bolstering its core claims to its scientific legitimacy and political utility, as well as the expertise of its practitioners in universities, government, and other organizations. They may debate the correct mathematical models for different situations, or question the assumptions that go into new ones, but Samuelson’s paradigm remains. Mathematics is just a language, one that describes 102 Qualifying Exam, c. 1961. Folder 1: Qualifying Exams, Economics Dept: Sample Examinations, Records of the Department of Economics, 1900-1969. Harvard University Archives (Cambridge, MA). 280 economic reality as neutrally as any other, but ultimately more effectively. Regardless of how the mathematical economy operates, it does not matter where it came from. The history of the marginal revolution demonstrates that this assumption is not true, and so does the long history of the mathematical economy. The contest for economic expertise in the first decades of the twentieth century illustrates how the specific choice in mathematics that the neoclassical economists made ushered in a depersonalization of economic calculation, squeezing participating economic actors, from the shop-keep to the large corporation, out of the narrow realm of mathematical economic expertise. They chose not to consider the way that differential calculus had so profoundly shaped the ideas that they now passed down as the conclusions of observation and deduction, and ignored the mathematical economies that had preceded them. The invention of our mathematical economy happened in much the same way as its predecessors: through contests over calculation and expertise, a specific mathematical foundation, and a vision for economic life that stemmed from both factors. Its superior institutionalization has given it a longer life than some of its ancestors, but its history proves it no more natural or inevitable. 281 Epilogue In the aftermath of the recent financial crash, some commentators in the American media hastened to blame a sinister culprit: mathematics. “Recipe for Disaster,” a Wired piece declared in 2009, promising a full treatment of “the formula that killed Wall Street.” The article described a new mathematical tool that had become popular among investment banks in the years leading up to the crash. Like its ancestors going back to Black-Scholes, this mathematical method of assessing and distributing financial risks relied both on mathematical economic assumptions about investors’ utility-maximizing tendencies and on the advanced algebraic calculations of experts within banks and other financial institutions. Wired focused on the Gaussian copula function recently developed by financial expert (and trained actuary) David X. Li. The article displayed a complex, variable- laden equation with the caption, “Here's what killed your 401(k).”1 Figure 4. Image from “Recipe for Disaster” Wired Magazine (2009) The problem, as Wired saw it, was that the “quants” who performed the mathematical work of financial investment had misused Li’s formula, which it said was not inherently flawed, simply 1 Felix Salmon, “Recipe for Disaster: The Formula that Killed Wall Street” Wired Magazine, February 23, 2009. See also Dana MacKenzie, “Mathematics and the Financial Crisis” in What's Happening in the Mathematical Sciences, Vol. 8 (Providence, RI: American Mathematical Society, 2010), pp. 28-47. 282 vulnerable to abuse. But the piece also noted that the very idea of using mathematics in this line of work might itself be inherently risky. The elegant, even excessive, simplicity of Li’s model may have made it easier for investors and banks to mix and match increasingly risky securities, hidden by the variables of the model—but in a way, that was the point of all mathematical models, at any level of simplicity. Even framing the model as an equation, Wired argued, caused both quants and their managers to ignore the “surprising amount of uncertainty, fuzziness, and precariousness” of the “real world.” Probability theory could only take one so far. According to this narrative of the crisis, the financial world that the quants had been building up since the 1980s was a ticking time bomb. Mathematical finance was bound to fail eventually. Wired was not the first publication to advance the idea that the financial crisis had been born in the crevasse between mathematics and reality. “In Modeling Risk, the Human Factor Was Left Out,” The New York Times opined on November 4, 2008, in the earliest days of the panic.2 It pointed to “financial engineering — a blend of mathematics, statistics and computing” as the locus of the crisis. Within two years, a Wall Street Journal reporter published a book unsubtly entitled, The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It; his article version in the Journal promised an insight into “the minds behind the meltdown.”3 Much was made in mainstream media outlets of Warren Buffett’s advice, delivered in an apologetic letter to Berkshire-Hathaway’s disappointed investors, to “beware of geeks bearing formulas.”4 Buffett’s 2 Steve Lohr, “In Modeling Risk, the Human Factor Was Left Out” The New York Times, November 4, 2008. 3 Scott Patterson, The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It (New York: Crown Publishing, 2010) and “The Minds Behind the Meltdown: How a swashbuckling breed of mathematicians and computer scientists nearly destroyed Wall Street” The Wall Street Journal, January 22, 2010. 4 David Segal, “In Letter, Warren Buffett Concedes a Tough Year” The New York Times, February 28, 2009. 283 narrative was clear: these geeks, with their advanced degrees in mathematics, physics, computer science, and mathematical economics, had built a financial castle on algebraic sand. As for their managers, they must have been too ignorant or greedy to stop it. Of course, there was pushback. “Don’t Blame the Quants,” groused Forbes, as panic raged in October of 2008. Yes, the desperately insecure securities that had toppled the financial markets had been invented by experts in quantitative finance, but the problem was that they had been used so incorrectly and so wantonly. “When a bridge collapses,” it said, “no one demands the abolition of civil engineering.” It insisted that the solution to such a problem was more, better engineering, not less.5 The following year, the Society for Industrial and Applied Mathematics sniffed that, faced with the complexities of financial markets, the media had opted “to fuel public skepticism” by blaming the crash on the quants and calling for them “to be burned at the stake.” SIAM deemed this media-fueled outrage a “witch-hunt” and insisted that the people really to blame for the crisis were the traders, who were not sufficiently mathematically trained to use models like Li’s. They should be held responsible for their own “grossly irresponsible” mistakes.6 As the panic and furor settled down into both economic and cultural depression, the blame moved away from the quants and toward the traders. Hollywood helped. The 2011 film “Margin Call” depicted a pre-crisis Wall Street in which a young quant discovers that the firm’s financial assets rest on a knife’s edge; he finds that the more senior the person he must convince of this fact is, the simpler his mathematical explanation must be. Even more explicitly, the 2015 film adaption 5 Steven Shreve, “Don’t Blame the Quants” Forbes Magazine, October 8, 2008. 6 René Carmona and Ronnie Sircar, “Financial Mathematics ‘08: Mathematics and the Financial Crisis” SIAM News, Vol. 42, No. 1 (January/February 2009). 284 of Michael Lewis’s The Big Short made a hero out of mathematical savant Michael Burry and the other quants who realized the American economy was in peril, and saved its outrage for the traders and regulators who wouldn’t listen to the numbers.7 Both point to a shift in the cultural narrative of the crisis: moving the blame away mathematics and the quants, and toward the fat cats who wanted to test the time-honored adage that mathematics doesn’t lie. Progressive politicians latched onto “The Big Short” as an explanatory device for what had gone wrong in the American economy: that it was a crime for which someone should be punished, not the failure of mathematical finance. No mentions of David Li or Gaussian copula formulas were made.8 Meanwhile, a kind of disappointment settled on Americans, as media outlets looked for a new narrative about the relationship of mathematics to the financial crash. “Did Poor Math Skills Cause the 2008 Financial Crisis?” one outlet asked in 2013. It pointed to a recently published study by the National Academy of Sciences that had starkly concluded that “Numerical ability predicts mortgage default.”9 In 2014, CNBC insisted that “Math skills add up to financial literacy”; in 2015, Quartz implored its readers to “Teach kids money-management, not just abstract math.”10 Indeed, there seemed to be a silver lining to the economic calamity, in the hope that math could, finally, be made “relevant” to American students. In 2012, the organization behind PISA, an international standardized test, added a “financial literacy assessment” to the high school exam, which seeks to 7 Margin Call, dir. J.C. Chandor (Hollywood, CA: Lionsgate, 2011); The Big Short, dir. Adam McKay (Hollywood, CA: Paramount Pictures, 2015). 8 Ted Johnson, “Bernie Sanders Endorses ‘The Big Short’” Variety, January 5, 2016. 9 Nsikan Akpan, “Did Poor Math Skills Cause The 2008 Financial Crisis: Fed Study Argues Yes” Medical Daily, Jun 24, 2013; K. Gerardia, L. Goette, S. Meier, “Numerical ability predicts mortgage default” Proceedings of the National Academy of Sciences of the United States of America, 2013 Jul 9; 110(28): 11267–11271. 10 Kelli B. Grant, “Simple equation: Math skills add up to financial literacy” CNBC, July 9, 2014; Chris Mettler, “Teach kids money-management, not just abstract math” Quartz, July 8, 2015. 285 test a combination of quantitative and qualitative abilities.11 The PISA shift supported the claim that Forbes had made only a few years prior, but had seemed so outside the norm: that the solution to a financial panic caused by mathematics was in fact, more mathematics. Today, more universities than ever are offering dual-degree programs in mathematics and economics, and advertising new and improved curricula in quantitative finance. The formula that killed Wall Street has been retired, but plenty remain to take up its work, particularly as many of the regulations passed after the crash are undone or otherwise evaded. David Li may never win a Nobel Prize, but the award has continued to go to mathematical work, as the interdependence of economics, mathematics, statistics, and computer science continues to grow. If the Panic of 2008 offered Americans an opportunity to discuss the relationship between mathematics, business, and economic life, we do not seem to have taken it for long. It has already receded into history, fodder for political posturing, Oscar bait, and suggestive epilogues. The mathematical economy continues to develop and expand in university halls and corporate offices. In our defense, the intersection of mathematical education, financial literacy, mathematical economics, quantitative politics, and American democracy is a Gordian knot of the modern politics of knowledge. Cultural productions like “The Big Short” offered a simple solution to a complex problem: heroes and villains instead of Gaussian copulas. If the problem was lying, then the liars could be found out, expelled, and replaced by non-liars. But if the problem was mathematics, the solution looks more complicated. In that case, fixing the problem requires answering some difficult questions. What kind of mathematics is necessary for a loan? A mortgage? An insurance policy? 11 OECD, PISA 2015 Results (Volume IV): Students' Financial Literacy (OECD Publishing: Paris, 2017). 286 How much of it should a homeowner or policyholder know? If the quants aren’t lying, but instead are making calculative mistakes, who should be the ones to check them? Do we all need to know the mathematics behind our financial lives? Are we capable of that? Together, these questions raise a bigger one: is the mathematical economy democratic? Can it be? The nineteenth century story of the mathematical economy can begin to put these and other of our recent questions and debates in historical context. It illustrates that the concept of “quants” did not first emerge in the 1980s, only the terminology. It shows us that our instinct to blame fraud or failure for economic crisis, to preserve the inherent truthfulness of mathematics, has been around for much longer than “The Big Short.” Most of all, it reminds us that the perceived economic need for a mortgage, a bridge, or a derivative is a historical construct, and therefore, so is the economic necessity of the actuary, engineer, or quant who built it. Nothing about modern economic life is necessarily mathematical or not. Rather, at times of crisis or anxiety, Americans have turned to the democratic potential of mathematical calculation to resolve political debates over commercial authority and economic expertise. The necessity of the disinterested quant, opposite the greedy capitalist, remains a persistent feature of the national economy. The history also puts Americans’ modern anxiety about mathematical education and skill into greater context. It suggests that our hand-wringing over American children’s less than stellar performance in international standardized testing speaks not only to a fear that American workers will not be able to compete in a global marketplace, but that American children are fundamentally unable to be legitimate economic actors, and therefore, full citizens.12 The recent financial crisis 12 For an example that also covers a decent history of twentieth century math education, see Elizabeth Green, “Why Do Americans Stink at Math?” The New York Times Magazine, July 23, 2014. New efforts to combat “math 287 heightened this anxiety, and seems to have produced a new stage in the so-called “math wars.” But mathematical education has become a focus during times of economic and geopolitical anxiety in the past. The “new math” emerged in the 1960s to confront fears that America was losing out to the Soviet Union, economically and scientifically. Then it was overturned by the “back to basics” movement, which itself had roots in the struggling economy of the 1970s.13 From the founding of the nation to the Cold War to our anxious present, mathematics and mathematical education have been inextricably bound up with ideas about participatory democracy. And yet, in so many cases we persist in talking about mathematics as though it is beyond the comprehension of mere mortals. On the contrary, its history shows us that, like all forms of knowledge, mathematics has the social, political, and economic power that we allow it. That does not mean the decision to create a mathematical economy can be undone in a day; as this project shows, its erection took place over a long time, beginning with its deep foundations in the early republic. It simply means that the project of disentangling the various fields of mathematics from their applications and cultural valences is a necessary part of understanding the modern world. If we can begin to see David Li as a descendant of Loammi Baldwin and Elizur Wright, we can understand him not as a criminal or a martyr, but as another character in a long and constantly developing narrative, and maybe start to see the outlines of the next chapter. The historical relationship of democracy, science, and capitalism is vast and complex, and no single lens can illuminate it all. But mathematics occupies so much of our current cultural anxiety” are on the rise in educational theory and policy; see, for example, Valerie Strauss, “Stop telling kids you’re bad at math: You are spreading math anxiety like a virus” The Washington Post, April 25, 2016. 13 Christopher J. Phillips, The New Math: A Political History (Chicago: University of Chicago Press, 2014). 288 headspace about the relationship between education, economics, and expertise, that understanding its history is essential to understanding our present. So much political and economic power in the modern world is conferred by claims that certain ideas and processes are natural, inevitable, and ahistorical. History is a great weapon in undermining those claims. But to use it, we must commit to demystifying our most mysterious things. The idea that mathematics is beyond the abilities of ordinary mortals is a historical one, but it is also one in which we remain complicit by referring to it only in abstract generalizations and by shying away from its history. Historians should embrace the project of demystifying mathematics, and in doing so, shine a light on the institutions that it has allowed to move beyond the reach of public accountability and critique. 289 Bibliography Major Manuscript Collections American Philosophical Society, Philadelphia PA Archives, American Philosophical Society, 1743-1984 Miscellaneous Manuscripts Collection, 1668-1983 Robert M. (Robert Maskell) Patterson papers, 1775-1853 Baker Library, Harvard Business School, Boston MA Baldwin Family Business Papers, 1694-1887 Boston and Albany Railroad Co. Boston and Albany Railroad Co. Records, 1829-1916 Elizur and Walter Wright Business Papers, 1845-1916 George S. Roorbach Papers, 1909-1934 New England Mutual Life Insurance Company records, 1844-1999 Proprietors of the Locks and Canals on Merrimack River Records, 1792-1947 Boston Public Library, Boston MA Bentley, Harry C. (1877- ) Collection Columbia University Rare Books & Manuscripts, New York NY John Bates Clark Papers, 1848-1955 David M. Rubenstein Library, Duke University, Durham NC American Economic Association Records, 1886-2008 Harvard University Archives, Cambridge, MA Correspondence and Faculty Reports by John Farrar, Hollis Professor of Mathematics and Natural Philosophy, 1810-1831 Records of the Department of Economics, 1900-1969 Historical Society of Pennsylvania, Philadelphia PA Apprentices Library Company of Philadelphia Records, 1820-1948. 290 John Hay Library, Brown University, Providence, RI Bureau of Business Research records, 1919-1939 Massachusetts Historical Society, Boston MA Boston Society for the Diffusion of Useful Knowledge Papers, 1830-1843 New York Historical Society, New York NY Records of the American Institute of the City of New York for the Encouragement of Science and Invention, 1808-1983 New York Public Library, New York NY Joseph G. Swift Correspondence, 1809-1862 Phillips Library, Peabody Essex Museum, Salem MA Bowditch Family Papers Schlesinger Library, Harvard University, Cambridge MA Records of the Bureau of Vocational Information, 1908-1932 [digital collection] Online Databases & Journals America’s Historical Newspapers American Economic Association Quarterly Journal of the Institute of Actuaries Publications of the American Economic Association The American Annals of Education The American Economic Review The Common School Assistant The Common School Journal The Quarterly Journal of Economics 291 Printed Primary ---- “Discussions on Technical Education, at the Washington Meeting of the American Institute of Mining Engineers, February 22d and 23d, 1876, and at a Joint Meeting of the American Society of Civil Engineers, and the American Institute of Mining Engineers at Philadelphia, and June 19th and 20th, 1876.” Easton, PA: American Institute of Mining Engineers, 1876. ---- “Elements of Life Insurance: For the Use of Family Banks.” Boston: Wright & Potter, 1876. ---- “Reports of the Principal Engineer, of his Operations in the Year 1826: Summary Report. “The Eleventh, Twelfth, and Thirteenth Annual Reports of the Board of Public Works, to the General Assembly of Virginia.” Richmond, VA: Samuel Shepherd & Co, 1829. ----“Public Works of Pennsylvania. Cost, Revenue and Expenditure, up to November 30, 1853. Printed by Order of the Legislature.” Harrisburg, PA: A Boyd Hamilton, State Printer, 1854. ---- Manual of the Lancastrian System of Teaching Reading, Writing, Arithmetic, and Needle- Work, as Practiced in the Schools of the Free-School Society of New York. New York: Samuel Wood and Sons, 1820. Abbott, Joseph. Rollo’s Vacation. Boston: Weeks, Jordan, & Co., 1839. Adams, Julius W. Templeton’s Engineer, Millwright, and Mechanic’s Pocket Companion. New York: Appleton & Co, 1852. Babbage, Charles. Reflections on the Decline of Science in England: and On Some of Its Causes. London: B. Fellowes, 1830. Baldwin Jr., Loammi. Report on the Subject of Introducing Pure Water into the City of Boston. Boston: John H. Eastburn, 1834. ---- Thoughts on the Study of Political Economy: As Connected with the Population, Industry and Paper Currency of the United States. Cambridge: Hilliard and Metcalf, 1809. Becker, George. A Treatise on the Theory and Practice of Book-Keeping by Double Entry. 1847. Bridge, B. The Southern and Western Calculator: or, Elements of Arithmetic Adapted to the Currency of the United States. Philadelphia: Key and Mielke, 1831. Brooks, Edward. Methods of Teaching Mental Arithmetic. Philadelphia: Sower, & Co., 1860. Brunton, Robert. A Compendium of Mechanics, or Text Book for Engineers, Mill-Wrights, Machine-Makers, Founders, Smiths, &c. New York: Carvill, 1830. Bryant, H.B. and H.D. Stratton, Bryant & Stratton’s National Book-Keeping. New York: Ivison & Co., 1860. 292 Burritt, Elijah Hinsdale. Burritt’s Universal Multipliers for Computing Interest, Simple and Compound; Adapted to the Various Rates in the United States on a New Plan. New York: Henry C. Sleight, 1830. Byrne, Oliver. The Practical Model Calculator, for the Engineer, Mechanic, Machinist, Manufacturer of Engine-work, Naval Architect, Miner, and Millwright. Philadelphia: H.C. Baird, 1852. Cameron, A.S. “On the Necessity of a Bureau of Mechanics: A paper read before the Society of Engineers and Associates, October 28, 1869.” New York: Slater, 1869. Colburn, Warren. First Lessons in Arithmetic on the Plan of Pestazzoli with Some Improvements. Cummings, Hilliard & Company: Boston, 1825. Comer, George N. Book-Keeping Rationalized. Boston: Comer & Co., 1862. Crowfield, Christopher [Harriet Beecher Stowe], House and Home Papers. Boston: Ticknor and Fields, 1865. Davies, Charles. Intellectual Arithmetic, or An Analysis of the Science of Numbers, with Special Reference to Mental Training and Development. New York: A.S. Barnes, 1856. Day, Jeremiah. An Introduction to Algebra, Being the First Part of A Course of Mathematics, Adapted to the Method of Instruction in the American Colleges. New Haven: Howe & Deforest, 1814. De Tocqueville, Alexis. Democracy in America, Volume I, 3d American edition. New York: G. Adlard, 1839. Eaton, Amos. Art Without Science: or, Mensuration, Surveying and Engineering, Divested of the Speculative Principles and Technical Language of Mathematics. Second Edition. Albany: Wester and Skinners, 1830. Ellet Jr., Charles. An Essay on the Laws of Trade, in Reference to the Works of Internal Improvement in the United States. New York: Augustus M. Kelley, 1966. ---- A Popular Exposition of the Incorrectness of the Tariffs of Toll in Use on the Public Improvements of the U.S. Philadelphia: Sherman & Co., 1839. Emerson, Joseph. Female Education, a Discourse, Delivered at the Dedication of the Seminary Hall, in Saugus, Jan. 15, 1822. Boston: Samuel T. Armstrong, 1822. Everett, Edward. An Address delivered as the introduction to the Franklin Lectures, in Boston, November 14, 1831. Boston: Gray and Bowen, 1832. Forsyth, C.H. Mathematical Theory of Life Insurance. New York: Wiley & Sons, 1924. 293 Gallatin, Albert. Report of the Secretary of the Treasury, on the subject of public roads and canals; made in pursuance of a resolution of the Senate, of March 2, 1807. Washington: R.C. Weightman, 1808. Green, Samuel. Daboll’s Schoolmaster’s Assistant. Utica: Gardner Tracy 1837. Greenleaf, Benjamin. The National Arithmetic, on the Inductive System; Combining the Analytic and Synthetic Methods, Together with the Canceling System; Forming a Complete Mercantile Arithmetic. Boston, 1850. Grimké, Thomas Smith. Oration on American Education, Delivered Before the Western Literary Institute and College of Professional Teachers, at their Fourth Annual Meeting, October, 1834. Cincinnati: Josiah Drake, 1835. Holbrook, Alfred. The Normal: or Methods of Teaching the Common Branches. New York: Barnes & Burr, 1860. Jones, Thomas. Paradoxes of Debit and Credit Demolished. New York: John Wiley, 1859. Kelt, Thomas. The Mechanics’ Text-Book and Engineer’s Practical Guide: Containing a Concise Treatise on the Nature and Application of Mechanical Forces. Boston: Phillips, Sampson and Company, 1853. Macaulay, T.B. “The Actuarial Society of America,” Journal of the Institute of Actuaries (1886- 1994), Vol. 29, No. 6 (January, 1892). Marshall, Alfred. The Principles of Economics, 9th ed. London: Macmillan for the Royal Economic Society, 1961. Massachusetts General Court, “Act to Incorporate the Spot Pond Aqueduct Company” Boston: Massachusetts General Court, 1843. Mayhew, Ira. A Practical System of Bookkeeping. Boston: Bazin & Ellsworth, 1861. ---- Standard Book-Keeping for Business Colleges, Commercial Departments, the Counting- Room, and Self Instruction. Chicago: Buckbee & Co., 1888. McAlpine, William J. “Modern Engineering. A Lecture, Delivered at the American Institute in New York.” New York: D. Van Nostrand, 1874. New York Mutual, Considerations on Life Insurance: By a Lady. New York: Mutual Life Insurance Company, 1855. Palmer, Joseph H. A Treatise on Practical Book-Keeping and Business Transactions. New York: Pratt Woodford & Co, 1852. 294 Parke, Uriah. The Farmers’ and Mechanics’ Practical Arithmetic. Winchester, VA: Samuel H. Davis, 1822. Playfair, John. Dissertation Second: Exhibiting a General View of the Progress of Mathematical and Physical Science, since the Revival of Letters in Europe. Boston: Wells and Lilly, 1817. Robinson, James Jr., The American Arithmetick: In which the Science of Numbers is Theoretically Explained and Practically Applied. Boston: Lincoln & Edmands, 1825. Root, Erastus. An Introduction to Arithmetic for the Use of Common Schools. Norwich, CT: Thomas Hubbard, 1796. Ross, William P. The Accountant’s Own Book, and Business Man’s Manual. Philadelphia: Zieber & Co., 1848. Rowland, Henry A. “A Plea for Pure Science” Science, Vol. 2, No. 29 (Aug. 24, 1883): 242-250. Rugg, Harold O. and John R. Clark. Fundamentals of High School Mathematics: A Textbook Designed to Follow Arithmetic. Chicago: World Book Company, 1919. Smith, Roswell C. Practical and Mental Arithmetic on a New Plan. Philadelphia: Marshall Clarke & Co., 1833. Strickland, William. Reports on Canals, Railways, Roads, and Other Subjects, Made to ‘The Pennsylvania Society for the Promotion of Internal Improvement. Philadelphia: H.C. Carey & I. Lea, 1826. Theodore Lyman Jr., “Communication to the City Council, on the subject of introducing water into the City.” Boston: J. H. Eastburn Press, 1834. Todhunter, I[saac]. The Conflict of Studies and Other Essays on Subjects Connected with Education. London: MacMillan, 1873. Van Amringe, J.H. A Plain Exposition of the Theory and Practice of Life Assurance. New York: Charles A. Kittle, 1874. Verplanck, Gulian. A Lecture, Introductory to the Course of Scientific Lectures before The Mechanics’ Institute of the City of New York. New York: G.P. Scott & Co, 1833. Wade, John E. The Merchants & Mechanics’ Commercial Arithmetic; or, Instantaneous Method of Computing Numbers. New York: Russell Brothers, 1872. Walker, Francis A. “Arithmetic in Primary and Grammar Schools. Remarks of Mr. Walker, April 12, 1887.” Boston: Damrell & Upham, 1887. 295 Webber, Samuel. Mathematics, Compiled from the Best Authors, and Intended to be the Text Book of the Course of Private Lectures on These Sciences in the University of Cambridge. Second Edition. Cambridge: William Hilliard, 1808. Wharton, Joseph. Is A College Education Advantageous to a Business Man? Philadelphia, 1890. White, E.E. et al. Bryant and Stratton’s Commercial Arithmetic, in Two Parts. New York: Oakley and Mason, 1865. Wing, Halsey R. Essay on the Moral and Intellectual Effects of Studying the Mathematical and Physical Sciences; and on the Application of these Sciences to the Arts. Albany: Young Men’s Association, 1834. Workman, Benjamin. The American Accountant; or, Schoolmasters New Assistant. Philadelphia: Printed for William Young, 1793. Wright, Frances. An Address to the Industrious Classes; a Sketch of a National System of Education. New York: Free Enquirer, 1830. Secondary Sources Adelstein, Richard. “Mind and Hand: Economics and Engineering at the Massachusetts Institute of Technology” in William J. Barber, et al. (eds.), Breaking the Academic Mould: Economists and American Higher Learning in the Nineteenth Century (Middletown: Wesleyan University Press, 1988). Alexander, Amir. “The Skeleton in the Closet: Should Historians of Science Care about the History of Mathematics?” Isis, Vol. 102, No. 3 (September 2011): 475-480. ---- Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice. Palo Alto: Stanford University Press, 2002. Allen, Robert Loring. Irving Fisher: A Biography. Cambridge: Blackwell, 1993. Ashworth, William J. “Memory, Efficiency, and Symbolic Analysis: Charles Babbage, John Herschel, and the Industrial Mind” Isis, 87 (1996): 629-53 Bailyn, Bernard. Education in the Forming of American Society. New York: Random House, 1960. Balogh, Brian. A Government Out of Sight: The Mystery of National Authority in Nineteenth- Century America. New York: Cambridge University Press, 2009. Bates, Ralph S. Scientific Societies in the United States, 3d ed. Cambridge: MIT Press, 2003. 296 Becher, Harvey W. “Radicals, Whigs, and Conservatives: The Middle and Lower Classes in the Analytical Revolution at Cambridge in the Age of Aristocracy,” British Journal for the History of Science, 28 (1995): 405-26. Becher, Harvey W. “Radicals, Whigs, and Conservatives: The Middle and Lower Classes in the Analytical Revolution at Cambridge in the Age of Aristocracy,” British Journal for the History of Science, 28 (1995): 405-26. Bedini, Silvio A. Thinkers and Tinkers: Early American Men of Science. New York: Charles Scribner's Sons, 1975. Belhose, Bruno. “The École Polytechnique and Mathematics in Nineteenth-Century France” Changing Images in Mathematics: From the French Revolution to the New Millennium, ed. Umberto Bottazini and Amy Dahan Dalmedio. New York: Routledge, 2001. Bensel, Richard Franklin. Yankee Leviathan: The Origins of Central State Authority in America, 1859–1877. Cambridge, UK: Cambridge University Press, 1990. Bernard, Richard and Maris Vionovskis. “The Female School Teacher in Ante-Bellum Massachusetts,” Journal of Social History (10) (1977): 332-45 Berry, Daina Ramey. The Price for their Pound of Flesh: The Value of the Enslaved from Womb to Grave in the Building of a Nation. New York: Beacon Press, 2017. Blake, John B. “Lemuel Shattuck and the Boston Water Supply” Bulletin of the History of Medicine, Vol. 29, No 6., Nov-Dec (1955). Bouk, Dan. How Our Days Became Numbered: Risk and the Rise of the Statistical Individual. Chicago: University of Chicago Press, 2015. ---- “Review: Tocqueville’s Ghost” Historical Studies in the Natural Sciences, Vol. 42, No. 4 (September 2012): 329-339. ---- “The Science of Difference: Developing Tools for Discrimination in the American Life Insurance Industry, 1830—1930” Enterprise & Society, Vol. 12, No. 4 (December 2011). Boyer, Carl C. and Uta C. Merzbach. A History of Mathematics. New York: Wiley, 1989. Breslau, Daniel. “Economics Invents the Economy: Mathematics, Statistics, and Models in the Work of Irving Fisher and Wesley Mitchell” Theory and Society, Vol. 32, No. 3 (Jun., 2003): 379-411. Buck, Peter. “People Who Counted: Political Arithmetic in the Eighteenth Century” Isis, Vol. 73, No. 1 (Mar., 1982): 28-45. ---- “Seventeenth-Century Political Arithmetic: Civil Strife and Vital Statistics” Isis, Vol. 68, No. 1 (Mar., 1977): 67-84. 297 Bühlmann, Hans. “The Actuary: The Role and Limitations of the Profession since the Mid-19th Century” ASTIN Bulletin, 27 (2), 1997. Cain, Louis P. “Raising and Watering a City: Ellis Sylvester Chesbrough and Chicago's First Sanitation System” Technology and Culture, Vol. 13, No. 3 (Jul., 1972): 353-372. Cajori, Florian. The Teaching and History of Mathematics in the United States. Washington: Government Printing Office, 1890. Carnes, Mark C. Secret Ritual and Manhood in Victorian America. New Haven: Yale University Press, 1991. Carruthers, Bruce G. and Wendy Nelson Espeland. “Accounting for Rationality: Double-Entry Bookkeeping and the Rhetoric of Economic Rationality” American Journal of Sociology, Vol. 97, No. 1 (Jul., 1991): 31-69. Chandler, Alfred D. The Visible Hand: The Managerial Revolution in America. Knopf: New York, 1977. Clawson, Mary Ann. Constructing Brotherhood: Class, Gender, and Fraternalism. Princeton: Princeton University Press, 1989. Clements, M. A. Ken and Nerida F. Ellerton, Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics. New York: Springer, 2015. Coase, Ronald. “The Nature of the Firm” Economica 4:16 (1937): 386-405. Cohen, Lara Langer. The Fabrication of American Literature: Fraudulence and Antebellum Print Culture. Philadelphia: University of Pennsylvania Press, 2011. Cohen, Patricia Cline. A Calculating People: The Spread of Numeracy in Early America. Chicago: University of Chicago Press, 1982. Collison Black, R.D. et al, The Marginal Revolution in Economics: Interpretation and Evaluation. Durham: Duke University Press, 1973. Conevery Bolton Valencius et. al., “Science in Early America: Print Culture and the Sciences of Territoriality” Journal of the Early Republic, Volume 36, Number 1 (Spring 2016): 73-123. Conkin, Paul K. Prophets of Prosperity: America’s First Political Economists. Bloomington: Indiana UP, 1980. Cook, Harold J. Matters of Exchange: Commerce, Medicine, and Science in the Dutch Golden Age. New Haven: Yale University Press, 2007. Cook, James C. The Arts of Deception: Playing with Fraud in the Age of Barnum. Cambridge: Harvard University Press, 2001. 298 Cronon, William. Nature’s Metropolis: Chicago and the Great West. New York: Norton, 1991. Daston, Lorraine. “Enlightenment Calculations” Critical Inquiry, Vol. 21, No. 1 (Autumn, 1994), pp. 182-202. ---- Classical Probability in the Enlightenment. Princeton: Princeton University Press, 1988. Davenport, Stewart. Friends of the Unrighteous Mammon: Northern Christians and Market Capitalism, 1815-1860. Chicago: University of Chicago Press, 2008. Davis, Natalie Zemon. “Sixteenth-Century French Arithmetics on the Business Life” Journal of the History of Ideas Vol. 21, No. 1 (Jan. - Mar., 1960). Dear, Peter “From Truth to Disinterestedness in the Seventeenth Century” Social Studies of Science Vol. 22, No. 4 (Nov., 1992): 619-631. ---- “Miracles, Experiments, and the Ordinary Course of Nature” Isis, 81:4 (1990): 663-683. Dorn, Charles. For the Common Good: A New History of Higher Education in America. Ithaca: Cornell University, 2017. Dudley, Charlotte W. “Jared Mansfield: United States Surveyor General” Ohio History, 85 (1998): 231–246. Edwards, Laura. The People and Their Peace: Legal Culture and the Transformation of Inequality in the Post-Revolutionary South. Chapel Hill: UNC Press, 2009. Emery, George. A Young Man's Benefit: The Independent Order of Odd Fellows and Sickness Insurance in the United States and Canada, 1860-1929. Montreal: McGill-Queen’s University Press, 1999. Espeland, Nelson and Mitchell L. Stevens, “A Sociology of Quantification,” European Journal of Sociology 49, no. 3 (2008): 401-436. Farber, Hannah. “Nobody Panic: The Emerging Worlds of Economics and History in America” Enterprise & Society, 16: 686-695. Faust, Drew. This Republic of Suffering: Death and the American Civil War. New York: Vintage Books, 2009. Feingold, Mordechai. “Mathematicians and Naturalists: Newton in the Royal Society.” Jed Z. Buchwald and I. Bernard Cohen (eds.), Isaac Newton’s Natural Philosophy. Cambridge: MIT Press, 2004. Fiss, Andrew “Professing Mathematics: Science and Education in Nineteenth-Century America” PhD Dissertation, Indiana University, 2011. 299 Frängsmyr, Tore, J.L Heilbron, and Robin E. Rider, eds., The Quantifying Spirit in the 18th Century. Berkeley: University of California Press, 1990. Fredrickson, George M. The Inner Civil War: Northern Intellectuals and the Crisis of the Union. New York: Harpers & Row, 1965. Friedman, Walter A. Fortune Tellers: The Story of America’s First Economic Forecasters. Princeton University Press: Princeton, 2014. Furstenberg, Francois. In the Name of the Father: Washington’s Legacy, Slavery, and the Making of a Nation. New York: Penguin Random House, 2007. Geiger, Roger L. To Advance Knowledge: The Growth of American Research Universities, 1900- 1940. New York: Oxford University Press, 1986. Gigerenzer, Gerd et al. (eds.), The Empire of Chance: How Probability Changed Science and Everyday Life. Cambridge, UK: Cambridge University Press, 1989. Goldin, Claudia. Understanding the Gender Gap: An Economic History of American Women. New York: Oxford University Press, 1992. Goodheart, Lawrence B. Abolitionist, Actuary, Atheist: Elizur Wright and the Reform Impulse. Kent, OH: Kent State University Press, 1990. Goodrich, Carter “Internal Improvements Reconsidered,” Journal of Economic History, 30 (June 1970), 289-311. GPO, The Centennial of the United States Military Academy at West Point, New York, 1802- 1902: Volume I, Addresses and Histories. Washington: Government Printing Office, 1904. Grabiner, Judith V. The Origins of Cauchy’s Rigorous Calculus. Cambridge: MIT Press, 1981. Greenberg, Amy. Manifest Manhood and the Antebellum American Empire. Cambridge: Cambridge University Press, 2005. Greene, John C. American Science in the Age of Jefferson. Ames, IA: Iowa State University Press, 1984. ---- “Science, Learning, and Utility: Patterns of Organization in the Early American Republic.” Alexandra Oleson and Sandra C. Brown, The Pursuit of Knowledge in the Early American Republic. Baltimore: Johns Hopkins University Press, 1976. Hacking, Ian. “Biopower and the Avalanche of Printed Numbers,” Humanities in Society, 5, nos. 3 and 4 (1982): 279-295. ---- The Emergence of Probability: A Philosophical Study of Early Ideas About Probability, Induction and Statistical Inference. Cambridge, UK: Cambridge University Press, 1975. 300 Halttunen, Karen. Confidence Men and Painted Women: A Study of Middle-class Culture in America, 1830-1870. New Haven: Yale University Press, 1982. Haskell, Thomas L. The Emergence of Professional Social Science: The American Social Science Association and the Nineteenth-Century Crisis of Authority. Chicago: University of Illinois Press, 1977. Hindle, Brooke The Pursuit of Science in Revolutionary America, 1735-1789. Chapel Hill: University of North Carolina Press, 1956. Horwitz, Morton J. The Transformation of American Law, 1780-1860. Cambridge: Harvard University Press, 1977. Hounshell, David A. “On the Discipline of the History of American Technology” The Journal of American History Vol. 67, No. 4 (Mar., 1981): 854-865. Johnson, Ann. “Material Experiments: Environment and Engineering Institutions in the Early American Republic” Osiris, Vol. 24, No. 1, Science and National Identity (2009): 53-74. Johnson, Paul E. A Shopkeeper's Millennium: Society and Revivals in Rochester, New York, 1815-1837. New York: Hill and Wang, 1978. Johnson, Walter. Soul by Soul: Life Inside the Antebellum Slave Market. Cambridge: Harvard University Press, 2001. Jonsson, Fredrik Albritton. “Rival Ecologies of Global Commerce: Adam Smith and the Natural Historians” The American Historical Review, Vol. 115, No. 5 (December 2010): 1342-1363. Kafka, Ben. The Demon of Writing: Powers and Failures of Paperwork. New York: Zone Books, 2012. Kaufman, Jason. For the Common Good? American Civic Life and the Golden Age of Fraternity. New York: Oxford University Press, 2002. Kelley, Mary. Learning to Stand and Speak: Women, Education, and Public Life in America’s Republic. University of North Carolina Press: Chapel Hill, 2006. Khurana, Rakesh. From Higher Aims to Hired Hands: The Social Transformation of American Business Schools and the Unfulfilled Promise of Management as a Profession. Princeton: Princeton University Press, 2010. Kline, Morris. Mathematical Thought from Ancient to Modern Times. Oxford: Oxford University Press, 1990. Kuhn, Thomas “Mathematical vs. Experimental Traditions in the Development of Physical Science.” Journal of Interdisciplinary History, 7:1 (1976): 1-3. 301 ---- “Energy Conservation as an Example of Simultaneous Discovery.” Margaret Claggett (ed.), Critical Problems in the History of Science. Madison: University of Wisconsin Press, 1969. Kwolek-Folland, Angel. Engendering Business: Men and Women in the Corporate Office, 1870- 1930. Johns Hopkins University Press: Baltimore, 1994. Latour, Bruno. Pandora's Hope: Essays on the Reality of Science Studies. Cambridge: Harvard University Press, 1999. Lawson, John Lauritz. Internal Improvement: National Public Works and the Promise of Popular Government in the Early United States. Chapel Hill: UNC Press, 2001. Lepler, Jessica M. The Many Panics of 1837: People, Politics, and the Creation of a Transatlantic Financial Crisis. Cambridge, UK: Cambridge University Press, 2013. Lepore, Jill. A is for American: Letters and Other Characters in the Newly United States. New York: Vintage, 2002. Lerman, Nina E. “The Uses of Useful Knowledge: Science, Technology, and Social Boundaries in an Industrializing City,” Osiris 12 (1997): 39-59. Levy, Jonathan. Freaks of Fortune: The Emerging World of Capitalism and Risk in America. Chicago: University of Chicago Press, 2012. Lewis, Andrew J. Democracy of Facts: Natural History in the Early Republic. Philadelphia: University of Pennsylvania Press, 2011. Livingston, James. Pragmatism and the Political Economy of Cultural Revolution, 1850-1940. Chapel Hill: University of North Carolina Press, 1997. Loughran, Trish. The Republic in Print: Print Culture in the Age of U.S. Nation Building, 1770- 1870. New York: Columbia University Press, 2007. Lucier, Paul. “Commercial Interests and Scientific Disinterestedness: Consulting Geologists in Antebellum America,” Isis (1995): 245-267 ---- “The Professional and the Scientist in Nineteenth-Century America,” Isis (2009): 699-732. Luskey, Brian. On the Make: Clerks and the Quest for Capital in Nineteenth-Century America. New York: New York University Press, 2010. Lyons, Jonathan. The Society for Useful Knowledge: How Benjamin Franklin and Friends Brought the Enlightenment to America. New York: Bloomsbury Press, 2013. Maas, Harro. “Sorting Things Out: The Economist as an Armchair Observer.” Lorraine Daston and Elizabeth Lunbeck (eds.), Histories of Scientific Observation. Chicago: University of Chicago Press, 2011. 302 MacKenzie, Donald and Fabian Muniesa & Lucia Siu (eds.), Do Economists Make Markets? On the Performativity of Economics. Princeton: Princeton University Press, 2008. MacKenzie, Donald. An Engine, Not a Camera: How Financial Models Shape Markets. Cambridge: MIT Press, 2006. McCoy, Drew The Elusive Republic: Political Economy in Jeffersonian America. Chapel Hill: University of North Carolina Press, 1980. McGraw, Judith A. (ed.), Early American Technology: Making and Doing Things from the Colonial Era to 1850. Chapel Hill: University of North Carolina Press, 1994. Mihm, Stephen. A Nation of Counterfeiters: Capitalists, Con Men, and the Making of the United States. Cambridge: Harvard University Press, 2007. Miller, Peter. “Governing by Numbers: Why Calculative Practices Matter” Social Research, Vol. 68, No. 2, Numbers (Summer 2001): 379-396 Mirowski, Philip. More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics. Cambridge, UK: Cambridge University Press, 1989. Mitchell, Timothy “Fixing the Economy,” Cultural Studies, 12, 1 (1998): 82–101 Moorhead, E.J. Our Yesterdays: The History of the Actuarial Profession in North America, 1809-1979. Schaumburg, IL: Society of Actuaries, 1989. Morgan, Mary S. The History of Econometric Ideas. Cambridge, UK: Cambridge University Press, 1990. Moroney, Siobhan “Birth of a Canon: The Historiography of Early Republican Educational Thought” History of Education Quarterly Vol. 39, No. 4 (Winter, 1999): 476-491. Morrison, Jr., James Lunsford. “The United States Military Academy, 1833-1866: Years of Progress and Turmoil” PhD Dissertation. Department of Political Science, Columbia University, 1970. Murphy, Sharon Investing in Life: Insurance in Antebellum America. Baltimore: Johns Hopkins University Press, 2010. Nash, Margaret A. “Contested Identities: Nationalism, Regionalism, and Patriotism in Early American Textbooks” History of Education Quarterly Vol. 49, No. 4 (Nov 2009): 417-441. National Council of Teachers of Mathematics, A History of Mathematics Education in the United States and Canada. Washington, DC: NCTM, 1970. Neem, Johann N. Creating a Nation of Joiners: Democracy and Civil Society in Early National Massachusetts. Cambridge: Harvard University Press, 2008. 303 Nelson, Daniel. Frederick W. Taylor and the Rise of Scientific Management. Madison: University of Wisconsin Press, 1980. Nelson, Scott Reynolds. A Nation of Deadbeats: An Uncommon History of America’s Financial Disasters. Alfred Knopf: New York, 2012. Netz, Raviel. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge, UK: Cambridge University Press, 1999. Noble, David F. America By Design: Science, Technology, and the Rise of Corporate Capitalism. New York: Knopf, 1977. North, Douglass C. “Life Insurance and Investment Banking at the Time of the Armstrong Investigation of 1905-1906” The Journal of Economic History, Vol. 14, No. 3 (Summer, 1954): 209-228. Novak, William J. The People’s Welfare: Law and Regulation in Nineteenth-century America. Chapel Hill: University of North Carolina Press, 1996. O’Neill, Onora. A Question of Trust. Cambridge: Cambridge University Press, 2002. Ogle, Maureen. “Water Supply, Waste Disposal, and the Culture of Privatism in the Mid- Nineteenth-Century American City” Journal of Urban History 1999 25: 321. Oleson, Alexandra and Sanborn C. Brown, The Pursuit of Knowledge in the Early American Republic: American Scientific and Learned Societies from Colonial Times to the Civil War. Baltimore: Johns Hopkins University Press, 1976. Oz, Frankel. States of Inquiry: Social Investigations and Print Culture in Nineteenth-Century Britain and the United States. Baltimore: Johns Hopkins University Press, 2006. Pangle, Lorraine Smith and Thomas Pangle. The Learning of Liberty: The Educational Ideas of the American Founders. Lawrence: University of Kansas Press, 1993. Parshall, Karen and David Rowe. The Emergence of the American Mathematical Research Community, 1876-1900. Providence, RI: American Mathematical Society, 1994. Pasley, Jeffrey L. “The Tyranny of Printers”: Newspaper Politics in the Early American Republic. Charlottesville: University of Virginia Press, 2002. Peskin, Lawrence A. Manufacturing Revolution: The Intellectual Origins of Early American Industry. Baltimore: Johns Hopkins University Press, 2003. Phillips, Christopher J. “An Officer and a Scholar: West Point and the Invention of the Blackboard,” History of Education Quarterly Vol. 55, No. 1 (Feb. 2015): 82-108. 304 Phillips, Christopher J. The New Math: A Political History. Chicago: University of Chicago Press, 2015. Pietruska, Jamie. Looking Forward: Prediction and Uncertainty in Modern America. Chicago: University of Chicago Press, 2017. Porter, Theodore M. “Locating the Domain of Calculation” Journal of Cultural Economy, Vol. 1, No. 1 (March 2008). ---- “Objectivity and Authority: How French Engineers Reduced Public Utility to Numbers” Poetics Today, Vol. 12, No. 2, Disciplinarity (Summer, 1991): 245-265. ---- “Thin Description: Surface and Depth in Science and Science Studies” Osiris, Vol. 27, No. 1 (2012): 209-226. ---- The Rise of Statistical Thinking, 1820-1900. Princeton: Princeton University Press, 1986. ---- Trust in Numbers: The Pursuit of Objectivity in Science and Public Life. Princeton: Princeton University Press, 1996. Quintana, Ryan A. “Planners, Planters, and Slaves: Producing the State in Early National South Carolina” Journal of Southern History 81 (February 2015): 79–116. Ransom, Roger L. and Richard Sutch, “Tontine Insurance and the Armstrong Investigation: A Case of Stifled Innovation, 1868–1905” The Journal of Economic History Volume 47, Issue 2 (June 1987): 379-390. Rao, Gautham. “Review: Tamara Plakins Thornton, Nathaniel Bowditch and the Power of Numbers: How a Nineteenth-Century Man of Business, Science, and the Sea Changed American Life” The American Historical Review, Vol. 122, No. 3 (June 2017). Rawson, Michael, “The Nature of Water: Reform and the Antebellum Crusade for Municipal Water in Boston” Environmental History, Vol. 9, No. 3 (Jul., 2004): 411-435. Reynolds, Terry S. (ed.) The Engineer in America: A Historical Anthology from Technology and Culture. Chicago: University of Chicago Press, 1991. Richards, Joan. “Augustus De Morgan, the History of Mathematics, and the Foundations of Algebra” Isis, Vol. 78, No. 1 (Mar., 1987): 6-30. Richards, Joan. “Rigor and Clarity: Foundations of Mathematics in France and England, 1800- 1840,” Science in Context, 4 (1991): 297-319. Rider, Robin E. “Perspicuity and Neatness of Expression: Algebra Textbooks in the Early American Republic” in Apple et. al (eds.), Science in Print: Essays on the History of Science and the Culture of Print. Madison: University of Wisconsin Press, 2012. 305 Rodgers, Daniel T. Atlantic Crossings: Social Politics in a Progressive Age. Cambridge: Harvard University Press, 1998. Rosenthal, Caitlin C. “From Memory to Mastery: Accounting for Control in America, 1750- 1880,” Enterprise & Society (December 2013). ---- “Numbers for the Innumerate: Everyday Arithmetic and Atlantic Capitalism” Technology and Culture, Vol. 58, No. 2 (April 2017): 529-544. Ross, Dorothy. Origins of American Social Science. New York: Cambridge University Press, 1992. Rotella, Elyce J. From Home to Office: U.S. Women at Work, 1870-1930. Ann Arbor, MI: University of Michigan Research Press, 1981. Roy, William G. Socializing Capital: The Rise of the Large Industrial Corporation in America. Princeton: Princeton University Press, 1997. Rudolph, Frederick. The American College and University: A History, 2d ed. Athens, GA: University of Georgia Press, 1991. Ryan, Mary P. Civic Wars: Democracy and Public Life in the American City during the Nineteenth Century. Berkeley: University of California Press, 1997. Sandage, Scott A. Born Losers: A History of Failure in America. Cambridge: Harvard University Press, 2006. Schabas, Margaret. A World Ruled by Number: William Stanley Jevons and the Rise of Mathematical Economics. Princeton: Princeton University Press, 1990. ---- The Natural Origins of Economics. Chicago: University of Chicago Press, 2005. Schaffer, Simon. “Babbage’s Intelligence: Calculating Engines and the Factory System,” Critical Inquiry, Vol. 21, No. 1 (Autumn, 1994): 203-227. Schulten, Susan. Mapping the Nation: History and Cartography in Nineteenth-Century America. Chicago: University of Chicago Press, 2012. Scott, James C. Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed. New Haven: Yale University Press, 1998. Shade, William G. “The ‘Working Class’ and Educational Reform in Early America: The Case of Providence, Rhode Island” The Historian Vol. 39, No. 1 (November 1976): 1-23. Shalhope, Robert E. The Baltimore Bank Riot: Political Upheaval in Antebellum Maryland. Champaign, IL: University of Illinois Press, 2009. 306 Shallat, Todd. Structures in the Stream: Water, Science, and the Rise of the U.S. Army Corps of Engineers. University of Texas Press, 1994. Shapin, Steven and Simon Schaffer. Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life. Princeton: Princeton University Press, 1985. Shapin, Steven. A Social History of Truth: Civility and Science in Seventeenth-Century England. University of Chicago Press, 1994. ---- “Of Gods and Kings: Natural Philosophy and Politics in the Leibniz-Clarke Disputes.” Isis, Vol. 72, No. 2 (Jun., 1981), pp. 187-215 ---- The Scientific Life: A Moral History of a Late Modern Vocation. Chicago: University of Chicago Press, 2008. Sinclair, Bruce. Philadelphia's Philosopher Mechanics: A History of the Franklin Institute, 1824–1865. Baltimore: Johns Hopkins University Press, 1974. Sklansky, Jeffrey P. The Soul’s Economy: Market Society and Selfhood in American Thought, 1820-1920. Chapel Hill: University of North Carolina Press, 2002. Sklar, Martin J. The Corporate Reconstruction of American Capitalism, 1890-1916. Cambridge, UK: Cambridge University Press, 1988. Slobodian, Quinn. “How to See the World Economy: Statistics, Maps, and Schumpeter's Camera in the First Age of Globalization” Journal of Global History, Vol. 10 (2015): 307-332. Slotten, Hugh R. Patronage, Practice, and the Culture of American Science: Alexander Dallas Bache and the U. S. Coast Survey. Cambridge: Cambridge University Press, 1994. Smallwood, Stephanie E. Saltwater Slavery: A Middle Passage from Africa to American Diaspora. Cambridge: Harvard University Press, 2008. Smith, Carl. City Water, City Life: Water and the Infrastructure of Ideas in Urbanizing Philadelphia, Boston, and Chicago. Chicago: University of Chicago Press, 2013. Soll, Jacob. The Reckoning: Financial Accountability and the Rise and Fall of Nations. 1st ed. New York: Basic Books, 2014. Spary, Emma. “Political, Natural and Bodily Economies.” N. Jardine, J.A. Secord, and E.C. Spary (eds.) Cultures of Natural History. Cambridge: Cambridge University Press, 1996. Steinberg, Theodore. Nature Incorporated: Industrialization and the Waters of New England. Amherst: University of Massachusetts Press, 1994. Stevens, Edward W., Jr., The Grammar of the Machine: Technical Literacy and Early Industrial Expansion in the United States. New Haven: Yale University Press, 1995. 307 Stinchcombe, Arthur L. “Reason and Rationality” Sociological Theory, Vol. 4, No. 2 (Autumn, 1986): 151-166. Stone, Sharon Hartman. Beyond the Typewriter: Gender, Class, and the Origins of Modern American Office Work, 1900-1930. Urbana, IL: University of Illinois Press, 1992. Thelin, John R. A History of American Higher Education, 2d ed. Baltimore: Johns Hopkins University Press, 2013. Thompson, E. P. “Time, Work-Discipline, and Industrial Capitalism” Past & Present, no. 38 (1967): 56-97. Thornton, Tamara Plakins. “‘A Great Machine’ or a ‘Beast of Prey’: A Boston Corporation and Its Rural Debtors in an Age of Capitalist Transformation” Journal of the Early Republic, Vol. 27, No. 4 (Winter, 2007), pp. 567-597. ---- Nathaniel Bowditch and the Power of Numbers: How a Nineteenth-Century Man of Business, Science, and the Sea Changed American Life. Chapel Hill: University of North Carolina Press, 2016. Veysey, Laurence R. The Emergence of the American University. Chicago: University of Chicago Press, 1965. Volk, Kyle. “The Perils of ‘Pure Democracy’: Minority Rights, Liquor Politics, and Popular Sovereignty in Antebellum America” Journal of the Early Republic Vol. 29, No. 4 (Winter, 2009): 641-679. Waldstreicher, David. In the Midst of Perpetual Fetes: The Making of American Nationalism, 1776-1820. Chapel Hill: University of North Carolina Press, 1997. Watkinson, James. “Useful Knowledge? Concepts, Values, and Access in American Education, 1776-1840” History of Education Quarterly Vol. 30, No. 3 (Autumn, 1990): 351-370. Watson, Harry L. Liberty and Power: The Politics of Jacksonian America. New York: Hill and Wang, 1990. Way, Peter. Common Labor: Workers and the Digging of North American Canals, 1780-1860. Baltimore: Johns Hopkins University Press, 1997. Weber, Max. The Protestant Ethic and the Spirit of Capitalism, trans. Talcott Parsons. New York: Scriberns, 1958. Welke, Barbara Young. Recasting American Liberty: Gender, Race, Law, and the Railroad Revolution, 1865-1920. New York: Cambridge University Press, 2001. Whaples, Robert and David Buffum, “Fraternalism, Paternalism, the Family, and the Market: Insurance a Century Ago” Social Science History, Vol. 15, No. 1 (Spring, 1991). 308 Wilentz, Sean. Chants Democratic: New York City and the Rise of the American Working Class, 1788-1850. New York: Oxford University Press, 1984. Wise, M. Norton (ed.), The Values of Precision. Princeton: Princeton University Press, 1997. Wolff, Megan J. “The Myth of The Actuary: Life Insurance and Frederick L. Hoffman's Race Traits and Tendencies of the American Negro” Public Health Rep, Vol. 121 No. 1 (2006 Jan- Feb): 84–91 Wood, Gordon. “The Enemy Is Us: Democratic Capitalism in the Early Republic” Journal of the Early Republic, Vol. 16, No. 2 (Summer, 1996): 293-308 Wyatt-Brown, Bertram. Lewis Tappan and the Evangelical War against Slavery. Baton Rouge, LA: LSU Press, 1997. Yates, JoAnne. Control Through Communication: The Rise of System in American Management. Baltimore: Johns Hopkins University Press, 1989. Yonay, Yuval P. The Struggle Over the Soul of Economics: Institutionalist and Neoclassical Economists in America Between the Wars. Princeton: Princeton University Press 1998. Zakim, Michael and Gary Kornblith. Capitalism Takes Command: The Social Transformation of Nineteenth-Century America. Chicago: University of Chicago Press, 2012. Zakim, Michael. “Inventing Industrial Statistics” Theoretical Inquiries in Law Vol. 11, No. 1 (Jan. 2010): 283-318. Zelizer, Viviana A. R. Morals and Markets: The Development of Life Insurance in the United States. New York: Columbia University Press, 1979. 309