The Feit–Thompson theorem established that all nonabelian finite simple groups possess an even order, a significant development in the study of finite group theory. This 1963 breakthrough, co-authored with Walter Feit, required an entire issue of the Pacific Journal of Mathematics to present its comprehensive proof and remains a cornerstone of modern algebraic research.
Academic Foundation
Born in 1932 in Ottawa, John G. Thompson pursued his early education at Ottawa High School. He completed his undergraduate studies at Yale University in 1955 before earning a Doctor of Philosophy from the University of Chicago, where he studied from 1955 to 1959 under the supervision of Saunders Mac Lane. His doctoral thesis achieved prominence by resolving the long-standing problem concerning the nilpotency of Frobenius kernels.
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Thompson’s career includes significant advances in the classification of finite simple groups. Beyond the Feit–Thompson theorem, his scholarly output introduced numerous analytical tools, including the Thompson factorization, the Thompson order formula, the Thompson subgroup, the Thompson transitivity theorem, and the Thompson uniqueness theorem. He further contributed to the inverse Galois problem, developing criteria to determine if finite groups function as Galois groups, which included applications regarding the monster simple group.
Institutional Appointments
Following his doctoral work, Thompson held positions at several institutions. He served at Harvard University from 1959 to 1962 and at the University of Chicago between 1962 and 1968. He was appointed the Rouse Ball Professor of Mathematics at the University of Cambridge, a position he held from 1971 until 1993. Later, he joined the faculty at the University of Florida in 1993.
Distinctions and Memberships
Thompson has received numerous international awards for his work. He was awarded the Fields Medal in 1970, the Senior Berwick Prize in 1982, and the Sylvester Medal in 1985. In 1992, he received the Wolf Prize in Mathematics, followed by the National Medal of Science in 2000 and the Abel Prize in 2008. He is a member of the Royal Society, the National Academy of Sciences, the Accademia Nazionale dei Lincei, the American Academy of Arts and Sciences, and the Norwegian Academy of Science and Letters.
Fast facts
- Born: 1932, Ottawa
- Citizenship: United States
- Fields of work: Mathematics, group theory
- Fields Medal recipient: 1970
- Abel Prize recipient: 2008
- Notable work: Feit–Thompson theorem
- Academic degree: Doctor of Philosophy
Questions readers ask
What is the Feit–Thompson theorem?
It is a mathematical result proving that all nonabelian finite simple groups are of even order.
Which major awards has John G. Thompson received?
He has received the Fields Medal, the Wolf Prize, the Abel Prize, the National Medal of Science, the Senior Berwick Prize, and the Sylvester Medal.
Achievements
- Fields medal — 1970
- Fellow of the Royal Society — 1979
- Abel Prize — 2008
- National Medal of Science — 2000
- De Morgan Medal — 2013
- Notable work: Feit–Thompson theorem
- Notable work: Feit–Thompson conjecture
- Notable work: Thompson uniqueness theorem
- Notable work: Thompson transitivity theorem
- Held posts at Harvard University, University of Chicago and University of Cambridge
