John Griggs Thompson (born October 13, 1932) is an American mathematician at the University of Florida noted for his work in the field of finite groups.

[3] Thompson's doctoral thesis introduced new techniques and included the solution of a problem in finite group theory which had stood for around sixty years: the nilpotency of Frobenius kernels.

This work was recognised by the award of the 1965 Cole Prize in Algebra of the American Mathematical Society.

This work had some influence on later developments in the classification of finite simple groups, and was quoted in the citation by Richard Brauer for the award of Thompson's Fields Medal in 1970 (Proceedings of the International Congress of Mathematicians, Nice, France, 1970).

In 1982, he was awarded the Senior Berwick Prize of the London Mathematical Society, and, in 1988, he received the honorary degree of Doctor of Science from the University of Oxford.