John Forbes Nash Jr.

John Forbes Nash Jr. (June 13, 1928 – May 23, 2015) was an American mathematician whose work reshaped game theory, real algebraic geometry, differential geometry, and partial differential equations. Born in Bluefield, West Virginia, to an electrical engineer father and a former schoolteacher mother, Nash showed early mathematical promise. He attended the Carnegie Institute of Technology on a scholarship, initially studying chemical engineering before switching to chemistry and finally mathematics, earning both bachelor’s and master’s degrees in 1948. He then accepted a fellowship at Princeton University, where his graduate advisor Richard Duffin had described him as a mathematical genius. At Princeton, Nash developed the Nash equilibrium and the Nash bargaining solution, central concepts in game theory, and earned his PhD in 1950 with a 28-page dissertation on noncooperative games. In the 1950s, he proved the Nash embedding theorems by solving nonlinear partial differential equations in Riemannian geometry, work that introduced a preliminary form of the Nash–Moser theorem and later earned the Leroy P. Steele Prize for Seminal Contribution to Research. Independently, Ennio De Giorgi and Nash developed methods that led to the De Giorgi–Nash theorem on the smoothness of solutions to elliptic and parabolic equations, resolving Hilbert’s nineteenth problem. In 1959, Nash began exhibiting signs of schizophrenia and spent years in psychiatric hospitals. His condition gradually improved after 1970, allowing him to return to academic work by the mid-1980s. He shared the 1994 Nobel Prize in Economics with John Harsanyi and Reinhard Selten, and in 2015 he and Louis Nirenberg received the Abel Prize for contributions to partial differential equations. Nash’s life inspired Sylvia Nasar’s 1998 biography *A Beautiful Mind* and the subsequent 2001 film. Declassified 1950s letters also show he anticipated modern cryptography concepts.