01 · A life in mathematics
The person behind the work
John Thompson was born in Ottawa, Kansas, in 1932 and became a central architect of finite group theory. His 1970 Fields Medal recognised results on finite simple groups, including the odd-order theorem proved with Walter Feit and his classification of minimal simple groups. Cambridge records list him as a visiting professor from 1968 to 1970, before his later Rouse Ball chair; this is more precise for the award period than the IMU’s Chicago label. His work helped organise the algebraic building blocks that underlie finite symmetry.
The contribution, explained
A finite group records a collection of reversible symmetries and how they combine. Simple groups have no nontrivial proper normal subgroup, making them fundamental building blocks. Feit and Thompson proved that every finite group of odd order is solvable. Consequently a nonabelian finite simple group must have even order; the odd-order simple groups are cyclic groups of prime order. The result imposes an unexpectedly strong restriction using only the number of elements. Its lengthy proof combined local subgroup analysis with character theory and became a landmark in the classification programme.
Why it matters
The odd-order theorem and Thompson’s further subgroup analysis supplied decisive tools and structural restrictions for the study and eventual classification of finite simple groups.