John Thompson has made seminal contributions to the theory of finite groups. With Walter Feit he proved the long-standing conjecture that every group of odd order is soluble (or solvable), a result for which he received a Fields Medal in 1970. The recent revival of the theory of finite groups, and above all the exciting progress towards the determination of all finite simple groups, would have been impossible without his deep and original methods. His series of six very substantial papers, Nonsolvable Finite Groups all of whose Local Subgroups are Solvable, in the Bulletin of the American Mathematical Society and the Pacific Journal of Mathematics, in which he determines all ‘minimal’ finite simple groups, are particularly notable.
For profound achievements in algebra and in particular for shaping modern group theory.
Proved jointly with W. Feit that all non-cyclic finite simple groups have even order. The extension of this work by Thompson determined the minimal simple finite groups, that is, the simple finite groups whose proper subgroups are solvable.
For his fundamental contributions leading to the complete classification of all finite simple groups.
In the field of mathematics for his profound contributions to all aspects of finite group theory and connections with other branches of mathematics.