Photo of John Griggs Thompson

John Griggs Thompson

  • National Medal of Science
  • Mathematics And Computer Science

For his profound and lasting contributions to the mathematical sciences, providing fundamental advances for the study of finite simple groups, the inverse Galois problem and connections between group theory and number theory.

John Griggs thompson defines group theory

At 26 years old, John Griggs Thompson used his doctoral thesis to solve a problem that had puzzled mathematicians for nearly double the time he’d been alive.

The achievement, touted in the New York Times, concerned Frobenius’ conjecture, a function of group theory.

Group theory studies structures called “groups,” a central factor in abstract algebra. Following Thompson’s discovery, the field rose to prominence and saw rapid progress in problem-solving, including the classification of finite simple groups.

A finite group is built from a collection of finite simple groups like a Rubik’s cube that can be manipulated into three rows of smaller cubes.

Thompson’s theory of finite groups laid the foundation for their classification, determining that non-elementary simple groups contain an even number of elements – a proof that filled 250 pages.

In addition, Thompson concluded that all finite simple groups belong to standard families, except for 26 sporadic groups that stand alone.