# John Forbes Nash

**John Forbes Nash Jr.** (born June 13, 1928) is an American mathematician who works 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.

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, which was written under the supervision of Albert W. Tucker, 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 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 *Nash's Embedding Theorem*.."Two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic." [1]

## Contents

## Personal life

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. By the time he was about twelve years old he was showing great interest in carrying out scientific experiments in his room at home.

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".

At Massachusetts Institute of Technology, 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. 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. Sylvia Nasar, Nash's biographer, cites evidence that Nash was bisexual. However, John and Alicia denied such on 60 Minutes in 2002.

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 Bank of Sweden Prize in Economic Sciences in 1994, when they renewed their relationship. They remarried on June 1, 2001.

### Schizophrenia

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 shock therapy.

Some of his treatments may have worsened his condition because his doctors did not realize the centrality of work and community to curing mental illness, and the most successful "treatment" seems to have been administrative decisions at Princeton's mathematics department and computer center to allow Nash to use university facilities for his researches during this period, although the researches were initially delusional.

In student and on-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.

However, encouraged by his wife Alicia, Nash persisted in working in a communitarian setting where his eccentricities were unremarked and developed, among other interests, an interest in the calculation of exact values of large numbers, researches which drove him to Princeton's Information Centers, where he developed computer programs (of high quality) for his work. Here he had more contact with Princetonians and also, in the late 1980s, 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 was 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 some very interesting ventures in advanced game theory including partial agency which show that as in early career, he prefers to select his own path and problems.

## Career

He currently holds an appointment in mathematics at Princeton. While cautious with people he does not know, insiders cite a dry sense of humor.

His wife Alicia would divorce him some time after his illness manifested itself. She took him back after he won the Nobel prize, and remarried him, immediately after the filming of A Beautiful Mind, the Hollywood treatment of his life.

### 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 genius game theory work at Princeton as a graduate student.

Between 1945 and 1996, Nash published a total of twenty-three scientific studies.

*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 the biography of the same title by Sylvia Nasar (1999), 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 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 while at Rand and his second family in Boston — although his son from Boston plays a bit part in the movie, as a nurse manhandling Nash in the hospital.
- Nash joined Wheeler's lab at MIT after gaining his PhD from Princeton — however, there is no such lab at MIT. He was actually 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 unfortunately portrayed only 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 that Nash independently invented the board game Hex.

## See also

## External links

- Extensive John Nash Biography
- Autobiography at the Nobel Prize website
- Nash's home page at Princeton
- John Forbes Nash Jr Information
- 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
- John Nash speaks out about alleged bisexuality

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