Lie Groups, Representations and Discrete Mathematics

The classification of finite simple groups is widely acknowledged to be one of the major results in modern mathematics. The successful completion of its proof was announced in the early 1980's by Daniel Gorenstein. The original proof occupied somewhere around 15,000 journal pages spread across more than 500 separate articles written by more than 100 mathematicians. Shortly thereafter, a "revision" project has been started (the GLS-project), whose goal was to produce a new unified correct proof of the Classification Theorem possibly of shorter length. The strategy of the proof differs from the original one. In this talk we will try to outline the "Generation 2"-proof of the Classification, and discuss a specific part of it.