# John Nash The American mathematician whose **1950 PhD dissertation at Princeton established the foundational equilibrium concept of modern game theory** — the Nash Equilibrium. Nash (1928–2015) was awarded the 1994 Nobel Prize in Economics (shared with John Harsanyi and Reinhard Selten) and the 2015 Abel Prize (mathematics' highest honor, shared with Louis Nirenberg). His personal struggle with paranoid schizophrenia and eventual partial recovery were the subject of the 2001 film *A Beautiful Mind* (loosely based on Sylvia Nasar's 1998 biography). ## Career and contribution **Background.** Carnegie Institute of Technology (BS/MS 1948), Princeton (PhD 1950) at age 22. His dissertation was 28 pages long; it established Nash Equilibrium and the existence proof that every finite game has at least one equilibrium (potentially in mixed strategies). The brevity and consequence of the dissertation became legendary. **Mathematical career.** Beyond game theory, Nash made fundamental contributions to differential geometry (Nash embedding theorems, 1956), partial differential equations, and other areas of pure mathematics. The Abel Prize (2015) recognized his work in partial differential equations rather than game theory. **Mental illness.** Nash was diagnosed with paranoid schizophrenia in 1959. He spent much of the 1960s and 1970s hospitalized or otherwise outside academic productivity. Substantial partial recovery began in the late 1970s; by the 1990s he was largely functional and the Nobel committee was willing to award him the 1994 prize despite his then-stable mental state. **Death.** Killed (with his wife Alicia) in a New Jersey Turnpike taxi accident, May 23, 2015. ## KB significance **The foundational concept of strategic interaction analysis.** Nash Equilibrium is the basic vocabulary of contemporary game theory, which is foundational to economics, political science, biology, and military strategy. The framework is hugely useful and frequently misapplied — actual political situations often have Nash equilibria that are bad for everyone but stable because no individual can unilaterally improve. ## See also - [[Nash Equilibrium]] — the eponymous concept - [[Prisoners Dilemma]] — canonical game-theoretic application - [[John von Neumann]] — Nash's predecessor in establishing game theory