Conditional Inequalities: American Pure and Applied Mathematics, 1940-1975 by ARCHNWA J 7 - *1 ~ ~ T N :' 11 I Alma Steingart Bachelor of Arts Columbia University, 2006 LBRA R ES Submitted to the Program in Science, Technology, and Society in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in History, Anthropology, and Science, Technology and Society at the Massachusetts Institute of Technology September 2013 ©2013 Alma Steingart. All Rights Reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature of Author: History, Anthropology, and ScieAce, Technology and Society / August 22, 2013 Certified by: David Kaiser Germeshausen Professor of the History of Science, STS Director, Program in Science, Technology, and Society Senior Lecturer, Department of Physics Thesis Supervisor Certified by: Christopher Capozzola U Associate Professor, History Thesis Committee Member Certified by: / Joan L. Richards / Professor, History Brown University Thesis Committee Member Accepted by: Heather Paxson Associate Professor, Anthropology Director of Graduate Studies, History, Anthropology, and STS Accepted by: _ David Kaiser Germeshausen Professor of the History of Science, STS Director, Program in Science, Technology, and Society Senior Lecturer, Department of Physics Conditional Inequalities American Pure and Applied Mathematics, 1940 -1975 By Alma Steingart Submitted to the Program in History, Anthropology, and Science, Technology, and Society in Partial Fulfillment of the Requirements of the Degree of Doctor of Philosophy in History, Anthropology, and Science, Technology and Society Abstract This study investigates the status of mathematical knowledge in mid-century America. It is motivated by questions such as: when did mathematical theories become applicable to a wide range of fields from medicine to the social science? How did this change occur? I ask after the implications of this transformation for the development of mathematics as an academic discipline and how it affected what it meant to be a mathematician. How did mathematicians understand the relation between abstractions and generalizations on the one hand and their manifestation in concrete problems on the other? Mathematics in Cold War America was caught between the sciences and the humanities. This dissertation tracks the ways this tension between the two shaped the development of professional identities, pedagogical regimes, and the epistemological commitments of the American mathematical community in the postwar period. Focusing on the constructed division between pure and applied mathematics, it therefore investigates the relationship of scientific ideas to academic and governmental institutions, showing how the two are mutually inclusive. Examining the disciplinary formation of postwar mathematics, I show how ideas about what mathematics is and what it should be crystallized in institutional contexts, and how in turn these institutions reshaped those ideas. Tuning in to the ways different groups of mathematicians strove to make sense of the transformations in their fields and the way they struggled to implement their ideological convictions into specific research agendas and training programs sheds light on the co-construction of mathematics, the discipline, and mathematics as a body of knowledge. The relation between pure and applied mathematics and between mathematics and the rest of the sciences were disciplinary concerns as much as they were philosophical musings. As the reconfiguration of the mathematical field during the second half of the twentieth century shows, the dynamic relation between the natural and the human sciences reveals as much about institutions, practices, and nations as it does about epistemological commitments. Thesis Supervisor: David Kaiser Title: Germeshausen Professor of the History of Science, STS Director, Program in Science, Technology, and Society 3 4 To Ruti, The first Dr. Steingart in the family 5 6 Table of Contents T itle ..................................................................................................... 1 Abstract ............................................................................................. 3 Table of Contents................................................................................ 7 Acknowledgments................................................................................9 Abbreviations-................................................................13 Introduction. The Logic of Mathematics..................................................... 15 Chapter 1. If and Only If ....................................................................... 39 Mathematicians at War Chapter 2. Necessary But Not Sufficient .................................................. 95 Mathematics and the Defense Establishment Chapter 3. Neither-Nor ......................................................................... 147 Making the Applied Mathematician Chapter 4. A Well-Ordered Set ............................................................... 201 The Growth of the Mathematical Sciences Chapter 5. Q. E. D. ............................................................................... 263 Mathematicians and the Job Market Crisis Epilogue. A Matter of Justification ........................................................... 307 Bibliography ...................................................................................... 317 7 8 ACKNOWLEDGMENTS Even in mathematics, sometimes the sum is greater than its parts. This is undoubtedly true when it comes to the incredible support I have received from mentors, colleagues, friends, and family over the past six years. Academic writing, I can now attest with absolute certainty, is not a solitary pursuit. My committee has challenged me to think more critically, creatively, and broadly. This project would not have been possible without my committee's abundant help. First and foremost, I am deeply grateful to my academic advisor, David Kaiser, who made me feel like a colleague and a friend from day one. Dave's diamond-sharp intellect, his bottomless generosity and kindness, and his perpetual good humor have guided me along the way. Writing this dissertation has been a far more rewarding and enjoyable enterprise for having him as my advisor. He is thoughtful in every sense of the term and he has taught me to be a scholar. Joan Richards has shared her vast knowledge of and passion for the history of mathematics with me. She has pushed me to write more clearly and offered much needed moral support. Despite the rickety commuter rail, I cherish my trips to Providence to no end. Christopher Capozzola made me question whether I chose the right specialization - delving with him into the world of American history as he inculcated me into the historian's craft has been a true pleasure. The HASTS graduate program at MIT has been a wonderful environment in which to develop my ideas and I take great pride in counting myself among its members. I greatly benefited from the support, sage advice, and intellectual acumen of a host of faculty. Michael Fischer, Stefan Helmreich, Vincent Lepinay, Heather Paxson, Harriet Ritvo, and Susan Silbey have made my time at MIT both rich and rewarding. I thank them for that. In numerous workshops, practice talks, seminars, and less formal gatherings the graduate student community of HASTS taught me the true meaning of interdisciplinarity and collegiality. That we were always able to come together across our diverse interests is a testimony to the program's success. I extend special thanks to Marie Burks, Tom Schilling, David Singerman, and Benjamin Wilson. The rotating crew of 098 - Michael Rossi, Lisa Messeri, Rebecca Woods, and Emily Wanderer - were not only my invaluable interlocutors but also great friends. I wrote much of this dissertation while in residence at the Max Planck Institute for the History of Science in Berlin, Germany. My gratitude goes to Lorraine Daston for inviting me to take part in the vibrant intellectual community that is Department II. The history of science has never appeared as lively and alluring as it did during my year in Berlin. Etienne Benson organized the predoctoral seminar at the MPIWG where I had the pleasure to present my work. I am indebted to many visitors and permanent members of the department for helpful comments, stimulating conversations, and academic mentorship: Joao Rangel de Almeida, Elena Aronova, Dan Bouk, Jeremiah James, Elaine Leong, Christine von Oertzen, Dominique Pestre, David Sepkoski, Elena Serrano, Skiili Sigurdsson, Dora Vargha, and Annette Vogt. I especially thank Yulia Frumer, Courtney Fullilove, Megan McNamee, Kathleen Vongsathorn, and Oriana Walker for their infallible encouragement through the final stages of writing this dissertation. Somehow they made sure I never felt alone. 9 Stephanie Dick, Moon Duchin, and Christopher Phillips shared with me their interest in mathematics, its history and historiography. I attended and presented my work in the annual Physics Phunday on several occasions. I thank Michael Gordin, Peter Galison, and participating graduate students for generously reading my work, offering feedback, and sharing their research with me. I presented a chapter of this dissertation before members of Cornell University's STS Department. Stephen Hilgartner, Ronald Kline, Michael Lynch,