The Subjects of Modernism: Mathematics, Art, and the Politics of Value in Twentieth-Century United States by Clare Seungyoon Kim Bachelor of Arts Brown University, 2011 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 2019 © 2019 Clare Kim. 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: Signatureredacted History, Anthr and Sc'nce, Technology and Society Signature redacted- August 23, 2019 Certified by: David Kaiser Germeshausen Professor of the History of the History of Science, STS Professor, Department of Physics Thesis Supervisor Certified by: Sianature redacted Christopher Capozzola MASSACHUSETTS INSTITUTE OFTECHNOLOGY Professor of History C-) Thesis Committee Member OCT 032019 LIBRARIES 1 Signature redacted Certified by: Stefan Helmreich Elting E. Morison Professor of Anthropology Signature redacted Thesis Committee Member Accepted by: Tanalis Padilla Associate Professor, History Director of Graduate Studies, History, Anthropology, and STS Signature redacted Accepted by: Jennifer S. Light Professor of Science, Technology, and Society Professor of Urban Studies and Planning Department Head, Program in Science, Technology, & Society 2 The Subjects of Modernism Mathematics, Art, and the Politics of Value in Twentieth-Century United States By Clare Kim Submitted to the Program in History, Anthropology, and Science, Technology and Society on September 6, 2019 in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in History, Anthropology, and Science, Technology and Society. Abstract My dissertation illuminates the status of mathematical knowledge in relation to other intellectual domains and racialized social forms-particularly American Orientalism-in the twentieth-century United States. Observers and practitioners have long engaged in drawing relations between mathematics and the arts. Around the turn of the twentieth century, however, when mathematicians reconceived mathematics around notions of abstraction, formalism, and "made" theories bearing no necessary relationship to the empirical world, understandings of the relationship of mathematics to the arts changed. Historians of mathematics, mathematicians, and historians of art have since referred to these twentieth-century intellectual changes as a "modernist" transformation. They refer to mathematical modernism in terms of metaphors that reflect shared values of being autonomous, creative, and a form of self-expression. My dissertation recovers an alternative history that upends the assumption that mathematical modernism developed within pre-existing boundaries of its discipline. It tracks a series of collective efforts between mathematicians, artists, critics, and historians, to use and articulate a place for formally abstract and axiomatically derived mathematical techniques within humanistic and artistic inquiries. Drawing from archival and published sources across four main chapters, I trace four specific efforts that reflect changes and transformations in American higher education and academic institutions between the 1890s and the present. Chapter one chronicles mathematicians', historians', and art collectors' interpretations of Japanese and Chinese mathematical traditions between the 1890s and 1920s. It shows how their conclusions that the resulting "oriental mathematics" was universal but inferior to the current practices were informed by a racialized discourse, treating Japanese and Chinese math as symbols of exotic difference. Chapter two recounts and describes the production of a mathematical theory of aesthetic measure at Harvard University in the 1930s. It shows how the theory was part of a broader artistic movement to articulate a theory of pure design. Chapter three examines the valuation and nature of mathematics within the liberal arts setting at Black Mountain College in the 1940s and 50s. It recovers how rather than being essential to high art, mathematics was also critical to the resurgence of craft. The final chapter elucidates the contradictions in valuing mathematics as abstract, creative, and autonomous, by examining a copyright dispute between a mathematical origami designer and a conceptual artist in the 2000s. The resulting view of US mathematical modernism as embedded within broader intellectual domains illuminates a more nuanced view of changes in what has or has not counted as a mathematical subject. Thesis Supervisor: David Kaiser Title: Germeshausen Professor of the History of Science and Professor of Physics 3 4 For Rui, Eunice, and Irene 5 Table of Contents T itle ............................................................................................................. 1 A b stract.................................................................................................. .. 3 T able of C ontents........................................................................................ 6 A cknow ledgem ents..................................................................................... 8 A bbrev iation s.................................................................................................11 Introduction When Mathematics Was Modern...................................................................... 13 Chapter One Universal Subjects: The Problem of "Oriental"Mathematics.................................... 31 Chapter Two Introspective Subjects: Efficient Expression andBirkhoff's Theory ofAesthetic Measure.........50 Chapter Three Formal Subjects: Max Dehn and Black Mountain College........................................ 75 Chapter Four Creative Subjects: Mathematical Origami and the Limits of Creative Expression..............83 E p ilo g u e ...................................................................................................... 1 1 1 B ib lio grap h y ................................................................................................ 1 16 6 7 Acknowledgements Long in the making with many more rewrites and edits to follow, my work is indebted to the support and generosity of a range of interlocutors: mentors, students, colleagues, research staff, friends, and family. I will try to do justice in these acknowledgements and in my footnotes to the many people who have guided me along the way. My first and biggest thanks goes to my advisor, David Kaiser, whose wit and generosity knows no bounds. I am eternally grateful to Dave for his guidance and support, for his willingness to listen, and for helping me to ground the chaotic, ill-formed thoughts that crowded my mind. His patience and humor have meant more than I can say. To Chris Capozzola, who first introduced me to U.S. intellectual history, and who never fails to ask the questions that get me to think beyond the history of mathematics and STS: thankyou. I would not have been able to move this project in the direction that it did without your generosity. And to Stefan Helmreich, who never tires of my questions and continues to encourage my foray into new strands of literature: thankyou. His belief in this project from its inception made everything that came after possible. Entering MIT and HASTS six years ago, I was lucky enough to have learned alongside a wonderful group of individuals who were as warm and welcoming as MIT's tunnels during the bitter winter months. I especially would like to thank Beth Semel, Lauren Kapsalakis, and Grace Kim for being there in a pinch during the final weeks of writing this dissertation. For their friendship and intellectual wit, I thank Marc Aidinoff, Renee Blackburn, Marie Burks, Ashawari Chaudhuri, Nadia Christidi, Amah Edoh, Richard Fadok, Steven Gonzalez, Kit Heitzman, Shreeharsh Kelkar, Younhun Kim, Rijul Kocchar, Nicole Labruto, Alison Laurence, Crystal Lee, Jia-Hui Lee, Lan Li, Srujan Meesala, Lucas Mueller, Peter Oviatt, Canay Ozden-Schilling, Tom Ozden-Schilling, Luisa Reis Castro, Alex Reiss Sorokin, Hilary Robinson, Elena Sobrino, Alex Reiss Sorokin, Mitali Thakor, Theodora Vardouli, Claire Webb, Jamie Wong, and Peter Y. Zhang. Faculty at HASTS and MIT challenged my thinking in more ways than I could have ever thought. For their questions, humor, and support, I thank Dwai Banerjee, William Broadhead, William Deringer, Mike Fischer, Deborah Fitzgerald, Slava Gerovitch, Caley Horan, Jennifer Light, Anne McCants, Amy Moran-Thomas, Kenda Mutongi, Steven Ostrow, Heather Paxson, Jeffrey Ravel, Harriet Ritvo, Robin Scheffler, Susan Silbey, Emma Teng, Craig Wilder, Roz Williams, William Uricchio, and Yufei Zhao. More significantly, my graduate student life wouldn't have been as smooth as it was without the support of the people who helped make everything run. I am eternally grateful to Karen Gardner, Paree K Pinkney, Gus Zahariadis, Margo F. Collett, Mabel Chin, Megan Pepin, Kathleen Lopes, Ayn Cavicchi, Irene Hartford, Barbara Keller, and Amberly Steward, Financial support for this project came in the form of the NSF Doctoral Dissertation Research Improvement Grant, the German Historical Institute, and the Notre Dame Institute for Advanced Study Graduate Fellowship. I received enormously generous help from the brilliant staff and archivists at the MIT Libraries, Institute