The theorem with the longest proof (??)

Abstract

This talk begins with the theorem, probably due to J.-P.Serre, 'Each element g of a finite simple group $G$ is a commutator, that is can be written as $g=aba^{-1}b^{-1}$ for some $a$, $b$ in $G$'.  The proof needs the classification of finite simple groups (CFSG) and much lengthy representation theory as well.  All of this leads to a retrospect on some of my old work on modular representations.