Big mathematics – reflections on the history of the Classification of Finite Simple Groups, 1950s to 1980s

Abstract

The Classification of Finite Simple Groups (CFSG) 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 the CFSG/pure mathematics. We consider the CFSG as (possibly) the first instant of what we tentatively call “big mathematics” in our project. In this article we report on work in progress, first sketching out our project and then explaining what we mean by “big mathematics.”