History and context of the discovery of the modern sporadic simple groups

Abstract

The Classification Theorem for Finite Simple Groups (CFSG) is one of the biggest results in mathematics in the 20th and 21st centuries. Its statement is that every finite simple group is either cyclic of prime order, an alternating group of degree at least 5, a finite simple group of Lie type, or one of 26 sporadic simple groups. Despite the unprecedented scope of its proof in terms of manpower and length, the history of the CFSG has barely been touched by historians of science. This dissertation deals with the history and context of the discovery of the 21 sporadic simple groups that were first conjectured to exist between 1964 and 1975, approximately 100 years after Émile Mathieu had found the other five sporadic simple groups. The focus is on the genesis of the mathematical ideas that led to the discovery of and existence proofs for these groups, as well as on the networks of the discoverers.