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Making Mathematics American: Gender, Professionalization, and Abstraction During the Growth of Mathematics in the United States, 1890-1945

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Making Mathematics American: Gender, Professionalization, and Abstraction During the Growth of Mathematics in the United States, 1890-1945 MAKING MATHEMATICS AMERICAN: GENDER, PROFESSIONALIZATION, AND ABSTRACTION DURING THE GROWTH OF MATHEMATICS IN THE UNITED STATES, 1890-1945 A Dissertation Presented to the Faculty of the Graduate School of Cornell University In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Ellen MacPhee Abrams August 2020 © 2020 Ellen MacPhee Abrams MAKING MATHEMATICS AMERICAN: GENDER, PROFESSIONALIZATION, AND ABSTRACTION DURING THE GROWTH OF MATHEMATICS IN THE UNITED STATES, 1890-1945 Ellen MacPhee Abrams, Ph. D. Cornell University 2020 This dissertation tells the story of how mathematics was made American. Like other American sciences, mathematics in the United States shifted during the Progressive Era from practical and educational activities toward research. Unlike other American sciences, however, American mathematics grew conspicuously apart from physical reality. Taking their cue from prominent scholars in places like France and Germany, mathematicians in the United States began building and working to define abstract mathematical systems. By following their European counterparts into abstract, so-called “modern” fields of research, however, American mathematicians risked alienation in a nation known for its “Yankee ingenuity” and practical know-how. This dissertation argues that, while the growth of mathematics in the United States meant establishing societies, journals, and graduate programs, it also meant reconfiguring what counted as mathematical work, who counted as a mathematician, and how each was thought to contribute to American society. While early-twentieth-century Americans were working to build a mathematics community, prominent researchers in Europe were working to rebuild the foundations of mathematics itself. Foundational questions, in turn, led some to reconsider the epistemological status and meaning of mathematical knowledge, as well as its value and values. By exploring foundational studies in the United States alongside popular, administrative, and biographical sources, this dissertation analyzes the growth of American mathematics as a series of scientific and cultural negotiations. Specifically, it considers the role of abstract research in redefining both the relevance of mathematics and what it meant to be an American mathematician. By choosing to encode their professional identities in the ideals of modern abstractions, mathematicians in the United States forfeited access to traditional forms of masculinity that were associated with military or industrial applications. Instead, they marshalled other forms of manliness tied to nostalgic traditions of farm work, rugged individualism, and, eventually, professional exclusivity and prestige. Overall, this dissertation identifies three ways in which mathematics was made compatible with American ideals: through the well-worn narrative of the self-made man, in proximity to American Pragmatism, and by asserting both scientific support for and humanist critiques of modern industrial progress. BIOGRAPHICAL SKETCH Ellen Abrams grew up in Colorado Springs, Colorado. She graduated from Northwestern University with a B.S. in Mechanical Engineering in 2011. After working in industry and for a variety of non-profits, Ellen joined the Department of Science and Technology Studies (STS) at Cornell University. Her Ph.D. candidacy fields include the history of science, with a focus on the history of mathematics; the history of technology, with a focus on race and gender; and United States cultural history, with a focus on the Gilded Age and Progressive Era. As a graduate student, Ellen was awarded the British Society for the History of Mathematics Taylor and Francis Early Career Prize, a shared grand prize for the National Academy of Sciences/National Research Council World War I research competition, and the Sheila Jasanoff Prize for Academic Excellence in Science & Technology Studies. Her research has been supported by grants from the Consortium for the History of Science, Technology, and Medicine, the National Academy of Sciences, and the National Science Foundation. Ellen enjoys working with students and has held a variety of teaching positions, including as a Summer Session and Writing Instructor at Cornell, a College Math and Writing Instructor at the Auburn Correctional Facility, and a College Readiness and Writing Instructor at University Heights High School in the Bronx. She has also worked as a Teaching Assistant for a range of STS courses related to medicine, computing, and the environment. Following the completion of her Ph.D., Ellen will begin a Postdoctoral Fellowship at the Society for the Humanities at Cornell University. While continuing her research, she will also help mentor and support the inaugural cohort of undergraduate students in the Humanities Scholars Program. For my parents ACKNOWLEDGMENTS Many wonderful people were involved in the process of writing this dissertation. I am especially grateful to my advisor, Suman Seth, whose kindness and brilliance have formed the bedrock of my graduate training over the past six years. Suman patiently read multiple drafts of every chapter of this dissertation, not to mention term papers and grant applications. In doing so, he helped me find the ideas in my research that were especially interesting and exciting to me. Suman is a generous teacher and mentor, and I have learned more from him than I ever thought possible. During my first two years at Cornell, I was fortunate to take courses from both Ronald Kline and Aaron Sachs. Even more than is suggested by my footnotes, I have relied heavily on Ron’s expertise ever since. What is not captured by footnotes, however, is my appreciation for his consistently friendly encouragement. Likewise, Aaron Sachs has been an invaluable source of expertise and support. He has created the space for me to reimagine what it means to be an artful historian and writer. Since joining the Department of Science and Technology Studies, I have enjoyed being part of an impressive and wide-ranging STS community. I am grateful to all of the STS faculty, staff, and students, especially Lisa Lehner and Brian Clark. Outside of my department, I have benefitted greatly from the brilliant members of my Humanities Dissertation Writing Group: Molly Reed, Sean Cosgrove, Nick Myers, and Athan Geolas. Outside of Cornell, I have relied heavily on various members of the history of mathematics community, including Michael Barany, Stephanie Dick, Theodora Dryer, David Dunning, Andy Fiss, Emily Hamilton, Abram Kaplan, Clare Kim, Jemma Lorenat, Jenne O’Brien, Christopher Phillips, Brittany Shields, Tasha Schoenstein, Alma Steingart, and Julia Tomasson. I am also thankful for guidance from Peggy Kidwell, Karen Parshall, and Joan Richards, and I am honored to offer a sliver of my gratitude to them here. I would especially like to thank the staff, librarians, and archivists at the Cornell University Carl A. Kroch Library, the Brown University John Hay Library, the Columbia University Rare Book and Manuscript Collection, the University of Chicago Special Collections Research Center, the University of Texas at Austin Dolph Briscoe Center for American History, the Archives of the National Academy of Sciences, and the Library of Congress Manuscript Division. Research for this dissertation has been funded by the Cornell University Society for the Humanities, the Cornell University American Studies Program, the Consortium for the History of Science, Technology, and Medicine, the National Academy of Sciences, and National Science Foundation Doctoral Dissertation Research Improvement Grant No. 1753998. Over the past six years, my friends in New York City—Christie, Steph, Kathleen, and Grace— have kept me grounded, as have phone calls with my brother, Ben, and my best friend, Ellen (J.). I have looked up to my brother for as long as I can remember, and he has always looked out for me. Likewise, Ellen has stood by me through all sorts of madness—from preschool through grad school. Large portions of this dissertation were written during the COVID-19 pandemic. Under shelter- in-place orders, my partner, Jesse, kept me well fed and (more or less) sane. He also read a full draft (!) of this dissertation and has supported me all along. I am grateful for him every day. I was fortunate to grow up in a household full of books, food, fresh air, and activity. My parents, Mickey and Gene, worked hard to make that happen. To this day, I have never once doubted their love and support. I owe everything, including this dissertation, to them. TABLE OF CONTENTS Introduction ................................................................................................................................... 1 Chapter 1: “Indebted to No One” Grounding and Gendering the Self-Made Mathematician ............................................................ 36 Chapter 2: “The Evolutionary Character of All Life’s Processes” Postulating American Mathematics .............................................................................................. 65 Chapter 3: “My Dear Sir” and “My Dear George” Relevance and Rhetoric During World War I ............................................................................. 101 Chapter 4: “Logical Fate” and “Intellectual Freedom” Cassius Keyser and the Humanism of Mathematics ................................................................... 135 Conclusion ................................................................................................................................
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