Big Mathematics? The Classification of Finite Simple Groups, 1950s to 1980.

• Applicants: Professor Dr. Volker Remmert; Professorin Dr. Rebecca Anne Hedwig Waldecker
• Subject Area: History of Science ; Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 528127386

The Classification of Finite Simple Groups (CFSG), also known as the enormous theorem, is a highlight of 20th-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 20th-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, the roles that trust and consensus play within this 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 (a concept to be critically discussed within the framework of the 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 repercussions for the mathematical community, the effect of the Cold War on CFSG/pure mathematics (e.g. via new funding possibilities by both civil and military agencies). Our overall long-term goal is to thoroughly analyze the history of the CFSG and use it as a magnifying glass allowing to draw general conclusions not only about the history of mathematics and the mathematical community in the context of the Cold War. In particular 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 20th century.

• DFG Programme: Research Grants