As a graduate student in the Princeton University Department of Mathematics, Nash introduced a number of concepts (including the Nash equilibrium and the Nash bargaining solution), which are now considered central to game theory and its applications in various sciences. In the 1950s, Nash discovered and proved the Nash embedding theorems by solving a system of nonlinear partial differential equations arising in Riemannian geometry. This work, also introducing a preliminary form of the Nash–Moser theorem, was later recognized by the American Mathematical Society with the Leroy P. Steele Prize for Seminal Contribution to Research. Ennio De Giorgi and Nash found, with separate methods, a body of results paving the way for a systematic understanding of elliptic and parabolic partial differential equations. Their De Giorgi–Nash theorem on the smoothness of solutions of such equations resolved Hilbert's nineteenth problem on regularity in the calculus of variations, which had been a well-known open problem for almost 60 years.
Life and Career
In 1959, Nash began showing signs of mental illness and spent several years at psychiatric hospitals being treated for schizophrenia. After 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s.
Nash's life was the subject of Sylvia Nasar's 1998 biographical book A Beautiful Mind, and his struggles with his illness and his recovery became the basis for a 2001 film of the same name directed by Ron Howard, in which Nash was portrayed by Russell Crowe.
Key Facts
- Born: June 13, 1928 in Bluefield, West Virginia, U.S.
- Died: 2015
- Field: Mathematics
Legacy and Impact
The influence of John Forbes Nash Jr. extends far beyond his own lifetime. He fundamentally shaped the foundations of modern mathematics, and his theorems and mathematical frameworks remain foundational to this day.
Though he passed away in 2015, his ideas continue to be studied, debated, and built upon by scholars and practitioners worldwide.
John Forbes Nash Jr. remains one of the most celebrated minds to emerge from United States, a testament to the rich intellectual heritage of the region.
Notable Geniuses from United States
United States has produced many remarkable minds. Alongside John Forbes Nash Jr.:
View all geniuses from United States →
Discover more brilliant minds in Mathematics
Explore Mathematics GeniusesRelated Articles
Explore More
Read the full profile of John Forbes Nash Jr.
View John Forbes Nash Jr.'s Profile →