John Forbes Nash

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John Forbes Nash Jr. (born June 13, 1928) is an American mathematician who works in game theory and differential geometry. He shared the 1994 Nobel prize in Economics with two other game theorists, Reinhard Selten and John Harsanyi. He is best known in popular culture as the subject of the Hollywood movie, A Beautiful Mind, about his mathematical genius and his struggles with mental illness.

1 Birth and youth
2 Education
3 Marriage
4 Divorce
5 Schizophrenia and recovery
6 Recognition
7 Games
8 A Beautiful Mind
9 Books by Nash
10 See also
11 External links

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Birth and youth

On June 13, 1928, John Forbes 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. At 12, he was carrying out scientific experiments in his room at home. It was quite apparent at a young age that he didn't like working with other people, preferring to do things alone. He returned the social rejection of his classmates with intellectual superiority, and he believed their dances and sports to be a distraction from experiments and studies. Martha, his sister, seems to have been a remarkably normal child while Johnny seemed different from other children. She wrote later in life, "Johnny was always different. [My parents] knew he was different. And they knew he was bright. He always wanted to do things his way. Mother insisted I do things for him, that I include him in my friendships. ... but I wasn't too keen on showing off my somewhat odd brother".

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Education

He attended the Carnegie Institute of Technology on a Westinghouse scholarship, and received both his bachelor's degree and his master's degree in 1948. From Pittsburgh he went to Princeton University where he worked on his equilibrium theory. He earned a Ph.D. in 1950 with a dissertation on non-cooperative games. The thesis, which was written under the supervision of Albert W. Tucker, contained the definition and properties of what would later be called the Nash equilibrium. These studies 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 also did important work in the area of manifolds (complex spatial structures):

"Real algebraic manifolds", (1952) Ann. Math. 56 (1952), 405–421. (See also Proc. Internat. Congr. Math., 1950, (AMS, 1952), pp. 516–517.)

This work led to the Nash embedding theorem: "Two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic." [1]

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Marriage

At the Massachusetts Institute of Technology, he met Alicia Lopez-Harrison de Lardé, a physics student from El Salvador, whom he married in February 1957. Alicia committed Nash to a mental hospital in 1959 for paranoid schizophrenia; their son John Charles Martin was born soon afterward but remained nameless for a year because she felt that John should have a say in the name. John Martin became a mathematician and, like his father, was diagnosed with paranoid schizophrenia. Nash had another son, John David (b. June 19, 1953), by Eleanor Stier, but had little to do with them.

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Divorce

The couple divorced in 1963 and reunited in 1970, but in a nonromantic relationship that resembled that of two unrelated housemates. Alicia referred to him as her "boarder" and said they lived "like two distantly related individuals under one roof," according to Sylvia Nasar's 1999 biography of Nash, "A Beautiful Mind." Nasar cites evidence that Nash was bisexual, which John and Alicia denied on 60 Minutes in 2002. [2] The couple renewed their relationship after Nash won the Bank of Sweden Prize in Economic Sciences in 1994. They remarried on June 1, 2001.

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Schizophrenia and recovery

Nash began to show the first signs of his mental illness in 1958. He became paranoid and was admitted into the McLean Hospital, April-May 1959, where he was diagnosed with paranoid schizophrenia and mild depression resulting in low self-esteem. 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 insulin shock therapy and other treatments.

In campus legend, Nash became "The Phantom of Fine Hall" (Fine Hall is Princeton's mathematics center), a shadowy figure who would scribble arcane equations on blackboards in the middle of the night. The legend appears in a work of fiction based on Princeton life, "The Mind-Body Problem", by Rebecca Goldstein.

Encouraged by Alicia, Nash worked in a communitarian setting where his eccentricities were unremarked. He developed an interest in calculating the exact values of large numbers, research that impelled him to Princeton's Information Centers where he developed computer programs. Here, he had more contact with Princetonians, which helped Nash to cope with his mental illness.

In the late 1980s, Nash began to use electronic mail to gradually link with working mathematicians who realized that he was "John Nash" and his new work had value. They formed part of the nucleus of a group that contacted the Bank of Sweden's Nobel award committee and were able to vouch for Nash's ability to receive the award in recognition of his early work.

The 1990s brought a return of his genius, and Nash has taken care to manage the symptoms of his mental illness. He is still hoping to score substantial scientific results. His recent work involves ventures in advanced game theory including partial agency which show that, as in his early career, he prefers to select his own path and problems (though he continues to work in a communal setting to assist in managing his illness).

Nash is still at Princeton, where he holds an appointment in mathematics. While cautious with people he does not know, he is said to have a dry sense of humor.

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Recognition

In 1978 Nash was awarded the John Von Neumann Theory Prize for his invention of non-cooperative equilibria, now called Nash equilibria.

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 as a Princeton graduate student.

Between 1945 and 1996, Nash published 23 scientific studies.

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Games

Nash also created two popular games: Hex, in 1942 with Piet Hein; and So Long Sucker, in 1964 with M. Hausner and Lloyd S. Shapley. Both games demonstrate what Nash worked on for years: the concept that in a game, one must win and everyone else must lose. (See Nash equilibrium.)

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A Beautiful Mind

The film A Beautiful Mind, released in 2001 and directed by Ron Howard, was inspired by Nash's life and received four Academy Awards, including Best Picture. It is loosely based on Nasar's biography, and has been criticized for its inaccurate portrayal of Nash's life and schizophrenia as well as for the over-simplified representation of the famous Nash equilibrium. (The bar game described in the movie was not a Nash equilibrium; the men looking for a date would have an incentive to deviate from their original choices if the prettiest girl weren't still available.) The PBS documentary A Brilliant Madness attempts to portray his life more accurately.

The film's major departures from Nash's life and the Nasar biography include:

No mention of Nash's numerous mathematical theorems, the originality and difficulty of which makes him one of the best pure mathematicians of the 20th century
No mention of Nash's sexual adventures at Rand, nor his second family in Boston — although his son from Boston plays a bit part in the movie, as a nurse who manhandles Nash in the hospital.
Nash is shown to join Wheeler's lab at MIT, but there is no such lab. He was appointed as C.L.E. Moore Instructor at MIT.
His preservation at Princeton is shown as exclusively the work of professors in the Mathematics department while in fact administrators, especially at Firestone Library and the Information Centers in later years, also played a role. They are portrayed as one library clerk who didn't get interoffice mail.
Nash's hallucinations were exclusively auditory, and not both visual and auditory as shown in the film. It is true that his handlers, both from faculty and administration, had to introduce him to assistants and strangers.

A deleted scene from A Beautiful Mind reveals (in an inaccurate manner) that Nash independently invented Hex.

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