John Nash studied at the Carnegie Institute of Technology, now called Carnegie-Mellon University. He received a B.A. and an M.A. in mathematics in 1948. In 1950. he received his doctorate from Princeton with a thesis Non-cooperative Games. In 1949, while studying for his doctorate, he wrote a paper which 45 years later was to win a Nobel prize for economics. During this period Nash established the mathematical principles of game theory. He introduced the concept of a Nash equilibrium, perhaps the most important idea in noncooperative game theory.

He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well. He enjoyed playing the games of Go, Kriegspiel, and Hex.

From 1952, Nash taught at Massachusetts Institute of Technology. His work on the theory of real algebraic varieties, Riemannian geometry, parabolic and elliptic differential equations was extremely deep and significant in the development of all these topics.

In 1959, he resigned because he was suffering from schizophrenia. Despite spending many periods in the hospital, his mathematical work continued to have success after success. In 1974, Nash made a recovery.

Nash won the Nobel prize in Economics (jointly with Harsanyi and Selten) in 1994. In 1999 he was awarded the Leroy P. Steele Prize by the American Mathematical Society.

He was played by Russell Crowe in the film "A Beautiful Mind". He and his wife died in a car crash in 2015 while riding in a taxi.