History of Modern Mathematics: A Conversation

September 20, 2024 at the Institute for Advanced Study and by Zoom. 

11:00am (ET) Introduction   Karen H Parshall (University of Virginia) and Sonja Brentjes (Wuppertal)

11:05am (ET) Big Mathematics? The Classification of Finite Simple Groups, 1950s – 1980    Volker Remmert (BU Wuppertal) and Rebecca Waldecker (MLU Halle-Wittenberg)

12:15pm (ET) History of modern mathematics – how and why? (a panel discussion)    Alma Steingart (Columbia University, moderator); Helmut Hofer (IAS), Volker Remmert, Rebecca Waldecker, Akshay Venkatesh (IAS) 

Talk abstract: The Classification of Finite Simple Groups (CFSG), also known as the enormous theorem, is a highlight of 20^th-century mathematics, both with respect to its mathematical content and to the complex process of proving the result. From a historical perspective, it offers an excellent opportunity to focus on more general developments in the history of 20^th-century mathematics, such as changing perceptions of what a mathematical proof is, the character and the many contexts of mathematics as an intergenerational and international collaborative enterprise, and the impact of Cold War research policies on CFSG/pure mathematics. We consider the CFSG as (possibly) the first instant of what we tentatively call big mathematics in this project. The existing proof of the CFSG is estimated to be spread on somewhere between 10.000 and 15.000 journal pages in ca. 500 separate articles written by more than 100 mathematicians. The unprecedented nature of this enterprise from the 1950s until the 1980s is quite tangible: the extraordinarily large number of mathematicians involved internationally (working as a team), the difficulty and complexity of the problem, the use of computers within the proof, the effect of the Cold War on CFSG/pure mathematics (e.g. via new funding possibilities by both civil and military agencies). The history of CFSG has to be studied as a key example of the impact of politics on research in pure mathematics in the Cold War, namely via new possibilities of funding research in general and of mathematical research in particular, a largely unexplored territory, but crucial for CFSG. The historical analysis will be guided by three themes: suitability of big mathematics as an analytical concept, the role of self-historicization in CFSG, and the changing nature of proof in mathematics in the second half of the 20^th century.

About the panel discussion:    There is much opportunity for collaboration between mathematicians and historians to examine together the recent history of mathematics.  The practice of mathematics has changed greatly over the course of the twentieth century, and even more rapidly in recent years with the rise of computing and the internet. A deeper understanding of how cultural, intellectual, political, and social factors have interacted with and shaped the recent evolution of the discipline would be valuable both as intellectual history, and to inform the way mathematicians themselves think about their subject and anticipate to its future.  This panel looked at the difficulties and possibilities of such collaborative historical work.