John Forbes Nash Jr. (born June 13, 1928) is a mathematician who worked in game theory and differential geometry. He shared the 1994 Nobel Prize for economics with two other game theorists, Reinhard Selten and John Harsanyi.
After a promising start to his mathematical career, Nash began to suffer from schizophrenia around his 30th year, an illness from which he has only recovered some 25 years later.
John Nash was born in Bluefield, West Virginia as son of John Nash Sr. and Virginia Martin. His father was an electrotechnician; his mother a language teacher. As a young boy he spent much time reading books and experimenting in his room, which he had converted into a laboratory.
From June 1945-June 1948 Nash studied at the Carnegie Institute of Technology in Pittsburgh, intending to become a technical engineer like his father. Instead, he developed a deep love for mathematics and a lifelong interest in subjects such as number theory, Diophantine equations, quantum mechanics and relativity theory. He loved solving problems.
At Carnegie he became interested in the 'negotiation problem', which John von Neumann had left unsolved in his book The Theory of Games and Economic Behavior (1928). He participated in the game theory group there.
From Pittsburgh he went to Princeton University where he worked on his equilibrium theory. He received a Ph.D. in 1950 with the dissertation Non-cooperative games. The thesis contained the definition and properties of what would later be called the Nash equilibrium; 44 years later, it would earn him the Nobel prize. His studies on this subject led to three articles, the first entitled 'Equilibrium Points in N-person Games', published in the Proceedings of the National Academy of Sciences (USA) (1950), and the others in Econometrica about The Bargaining Problem (April 1950) and 'Two-person Cooperative Games' (January 1953). The only official economic lessons he followed were a series about international trade.
In the summer of 1950 he worked at the RAND Corporation in Santa Monica, California, where he returned for shorter periods in 1952 and 1954. From 1950-1951 he taught calculus courses at Princeton, studied and managed to stay out of military service. During this time, he proved the Nash embedding theorem, an important result in differential geometry about manifolds. In 1951-1952 he became science assistant at MIT in Cambridge, Massachusetts.
At MIT, he met Alicia Lopez-Harrison de Lardé, a math student from El Salvador, whom he married in February 1957. Their son, John Charles Martin (b. May 20, 1959), remained nameless for a year because Alicia, having just committed Nash to a mental hospital, felt that he should have a say in what to name the baby. As was his parents, John became a mathematician, but, like his father, he was diagnosed a paranoid schizophrenic. Nash had another son, John David (b. June 19, 1953), by Eleanor Stier, but refused to have anything to do with them. An admitted bisexual, he carried on intimate relationships with men during this period.
Although she divorced him in 1963, Alicia took him back in 1970. But, according to Sylvia Nasar's biography of Nash, Alicia referred to him as her "boarder," and they lived "like two distantly related individuals under one roof" until he won the Nobel Prize in 1994, then they renewed their relationship. They remarried on June 1, 2001.
In 1958 John Nash began to show the first signs of his mental illness. He became paranoid and was admitted into the McLean Hospital, April-May 1959, where he was diagnosed with 'paranoid schizophrenia'. After a problematic stay in Paris and Geneva, Nash returned to Princeton in 1960. He remained in and out of mental hospitals until 1970, and held a research position at Brandeis University from 1965-1967. Illustrative is the 30-year publication gap between 1966 and 1996 of any scientific work. In 1978 he was awarded the John Von Neumann Theory Prize for his invention of non-cooperative equilibriums, now called Nash equilibria.
Nash's mental health improved very slowly. His interest in mathematical problems gradually returned, and with it the ability to think logically. He also became interested in computer programming. The 1990s brought a return of his genius, though it lived in a still feeble mind. In 1994 he received the Nobel Prize in Economics as a result of his game theory work at Princeton as a graduate student. He is still hoping to score substantial scientific results.
Between 1945 and 1996 John Nash published a total of 23 scientific studies, plus an autobiographical essay, 'Les Prix Nobel' (1994)  (http://www.nobel.se/economics/laureates/1994/nash-autobio.html), first published in Sweden.
A film titled A Beautiful Mind, released in December 2001 and directed by Ron Howard, dramatically portrayed some events of Nash's life. It is (loosely) based on the biography of the same title, written by Sylvia Nasar (1999) and received four Oscars in 2002. A deleted scene from A Beautiful Mind reveals that Nash (re)invented the board game known as Hex or (at Princeton) "Nash" or "John", as it was often played on hexagonal bathroom floor tiles. A Beautiful Mind has been criticized for its inaccurate portrayal of John Nash's life and schizophrenia. The PBS documentary A Brilliant Madness attempts to portray his life more accurately.