John G. Thompson

fl. 1932, Ottawa, Kansas, United States

AlgebraFields Medal 1970Wolf Prize in Mathematics 1992Abel Prize 2008

American mathematician who, with the Feit–Thompson theorem and the classification of minimal simple groups, laid the foundations of the classification of finite simple groups; Fields Medal 1970, Wolf Prize 1992, Abel Prize 2008.

John Griggs Thompson was born in Ottawa, Kansas, and studied at Yale University before taking his PhD at the University of Chicago in 1959 under Saunders Mac Lane. His thesis already contained a breakthrough: a proof that groups admitting a fixed-point-free automorphism of prime order are nilpotent, settling a conjecture attributed to Frobenius and introducing techniques that would pervade finite group theory.

In 1962–1963 Thompson and Walter Feit proved that every finite group of odd order is solvable, filling an entire issue of the Pacific Journal of Mathematics. The theorem confirmed a conjecture going back to Burnside and supplied both the methods — local analysis of subgroups and their normalizers — and the ambition that drove the classification of finite simple groups, completed in the early 1980s. Thompson's own classification of the minimal simple groups, and his work on the sporadic groups (including the Fischer–Griess monster's early theory), placed him at the center of that enterprise.

Thompson moved from Chicago to the University of Cambridge in 1970 as Rouse Ball Professor, later joining the University of Florida. He received the Fields Medal in 1970, the Wolf Prize in 1992 jointly with Lennart Carleson, and the Abel Prize in 2008 jointly with Jacques Tits, for achievements that shaped modern algebra.

Workplaces: University of Chicago, University of Cambridge, University of Florida

United States

Award-winning work

Fields Medal 1970Awarded for his fundamental contributions to the theory of finite groups. In his 1959 doctoral thesis Thompson proved that every group with a fixed-point-free automorphism of prime order is nilpotent, resolving a conjecture of Frobenius. With Walter Feit he proved the Feit–Thompson theorem (1963): every finite group of odd order is solvable, a 255-page proof that opened the era of the classification of finite simple groups. He then classified the minimal simple groups — those whose proper subgroups are all solvable — introducing local group-theoretic methods that became standard in finite group theory.

Contributions, linked to the library

Library topicGroup theoryProved the solvability of finite groups of odd order and classified minimal simple groups, launching the classification of finite simple groups.