John Forbes Nash
John Forbes Nash Jr. (born June 13, 1928) is a mathematician who worked in game theory and differential geometry. He shared the 1994 Bank of Sweden Prize in Economic Sciences 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 recovered some thirty years later.
From June 1945-June 1948 Nash studied at the Carnegie Institute of Technology in Pittsburgh, intending to become a engineer like his father. Instead, he developed a deep love for mathematics and what became 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 (1944). He participated in the game theory group there. His theory, now called as the Nash Equilibrium is a corollary to the minimax theorem stated earlier by John Von Neumann in 1928.
From Pittsburgh he went to Princeton University where he worked on his equilibrium theory. He received a Ph.D. in 1950 with a dissertation on non-cooperative games. The thesis contained the definition and properties of what would later be called the Nash equilibrium. His studies on this subject led to three articles:
- 'Equilibrium Points in N-person Games', published in the Proceedings of the National Academy of Sciences (USA) (1950);
- The Bargaining Problem (April 1950) in Econometrica, and
- Two-person Cooperative Games (January 1953), also in Econometrica.
John Nash was born in the small Appalachian town of Bluefield, West Virginia, the son of John Nash Sr., an electrical engineer, and Virginia Martin, a teacher. As a young boy he spent much time reading books and experimenting in his room, which he had converted into a laboratory.
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. 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 were 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, Nash carried on intimate relationships with men during this period.
Although she divorced him in 1963, Alicia took him back in 1970. 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, when they renewed their relationship. They remarried on June 1, 2001.
In 1958, 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, undergoing various treatments including insulin (a.k.a. hypoglycemic) coma therapy.
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. He is still hoping to score substantial scientific results.
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.
He currently holds honorary appointment in mathematics at Princeton.
In 1994 he received the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel as a result of his game theory work at Princeton as a graduate student.
Movie inspired by Nash's life
A film titled A Beautiful Mind, released in 2001 and directed by Ron Howard, was inspired by Nash's life; it received four Academy Awards, including Best Picture. The film is loosely based on the biography of the same title, written by Sylvia Nasar (1999).
- Autobiography at the Nobel Prize website
- Nash's home page at Princeton
- Nash FAQ from Princeton's Mudd Library, including a copy of his dissertation in PDF format
- Beautiful mind, unconventional matter, a 2001 Daily Princetonian interview
- MacTutor biography of Nash
- PBS documentary