# John Forbes Nash

### Learn more about John Forbes Nash

Born | June 13 1928 (age 88) Bluefield, West Virginia, USA <tr><th>Residence</th><td>Image:Flag of the United States.svg USA</td></tr><tr><th>Nationality</th><td>Image:Flag of the United States.svg American</td></tr><tr><th>Field</th><td>Mathematician</td></tr><tr><th>Institution</th><td>Princeton University</td></tr><tr><th>Alma Mater</th><td>Carnegie Institute of Technology</br> Princeton University</td></tr><tr><th>Academic Advisor</th><td>Albert W. Tucker</td></tr><tr><th>Known for</th><td>Nash equilibrium</br>Nash embedding theorem</br>Algebraic geometry</td></tr><tr><th>Notable Prizes</th><td>Nobel Prize in Economics (1994)</td></tr> |
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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 Bank of Sweden Prize in Economic Sciences (also called the 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 schizophrenia.

## Contents |

## [edit] Childhood

On June 13, 1928, John Forbes Nash was born in the small Appalachian city of Bluefield, West Virginia, the son of John Nash Sr., an electrical engineer and graduate of Texas A&M University, and Virginia Martin, a teacher.

He was an avid reader of Compton's Picture Encyclopedia, Life Magazine, and Time magazine. Later he had a job at the Bluefield Daily Telegraph.

At age 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 practical jokes and intellectual superiority, believing their dances and sports to be a distraction from his experiments and studies. Martha, his younger 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."

In his autobiography, Nash notes that it was E.T. Bell's book Men of Mathematics in particular the essay on Fermat that first sparked an interest for him in mathematics.

During war time, when other boys his age wanted to be soldiers, he was inventing secret codes.

## [edit] Education and early career

He attended classes at Bluefield College while still in high school.

He later attended the Carnegie Institute of Technology (currently named Carnegie Mellon University) in Pittsburgh, Pennsylvania on a Westinghouse scholarship, where he studied first engineering and later chemistry before switching to mathematics. He received both his bachelor's degree and his master's degree in 1948 while at Carnegie Mellon. After graduation, Nash took a summer job in White Oak, Maryland working on a Navy research project being run by Clifford Ambrose Truesdell.

From White Oak he went to Princeton University in Princeton, New Jersey, 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 algebraic geometry:

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

His most famous work in pure mathematics was the Nash embedding theorem, which showed that any abstract Riemannian manifold can be isometrically realized as a submanifold of Euclidean space. He also made contributions to the theory of nonlinear parabolic partial differential equations.

## [edit] 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 admitted Nash to a mental hospital in 1959 for 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 later diagnosed with schizophrenia. Nash had another son, John David (b. June 19 1953), with Eleanor Stier, but had little to do with the child or his mother.

## [edit] 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 1998 biography of Nash, *A Beautiful Mind*. The couple renewed their relationship after Nash won the Nobel Prize in Economics in 1994. They remarried on June 1, 2001.

## [edit] Schizophrenia

Nash began to show signs of schizophrenia in 1958. However, all throughout his years at Princeton (1945-1949) he believed he had a roommate while records show he lived by himself. He became paranoid and was committed into the McLean Hospital, April-May 1959, where he was diagnosed with paranoid schizophrenia and mild depression with 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, being given insulin shock therapy and antipsychotic medications, usually as a result of being committed rather than by his choice. From 1970, by his choice, he never took antipsychotic medication again. According to his biographer Sylvia Nasar, he recovered gradually with the passage of time. Encouraged by Alicia, Nash worked in a communitarian setting where his eccentricities were accepted.

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.

## [edit] Recognition

In 1978 Nash was awarded the John Von Neumann Theory Prize for his invention of non-cooperative equilibria, now called Nash equilibria. He won the Leroy P Steele Prize in 1999.

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. In the late 1980s, Nash had begun to use electronic mail to gradually link with working mathematicians who realized that he was "John Nash" and that 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.

Nash's 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.

Nash is still at Princeton, where he holds an appointment in mathematics.

Between 1945 and 1996, Nash published 23 scientific studies.

## [edit] Games

Nash also created two popular games: Hex, (independently created first in 1942 by Piet Hein); and So Long Sucker, in 1964 with M. Hausner and Lloyd S. Shapley.

## [edit] *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 Sylvia Nasar's biography of the same name, 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 room 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 was 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:

- Little 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. However Nash's work on manifold embedding, which must rank among his most characteristic work, is referred to in at least one scene.
- 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.
- The film has Nash saying at the time of his Nobel acceptance speech in 1994 "I take the newer medications", when in fact Nash didn't take any medication from 1970 onwards, something Nasar's biography highlights.

- A deleted scene from
*A Beautiful Mind*reveals (in an inaccurate manner) that Nash independently invented the board game Hex.

## [edit] See also

## [edit] External links

- [1] 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 - O'Connor, John J., and Edmund F. Robertson. "John Forbes Nash".
*MacTutor History of Mathematics archive*. - John Forbes Nash at the Mathematics Genealogy Project
- PBS documentary
- John Nash speaks out about alleged
- John Nash Forum
- A Beautiful Mind
- No. 983: John Forbes Nash, Jr.
- Department of Economics - News
- John F. Nash presented in Freedom section
- John Nash and "A Beautiful Mind"
- Penn State's The 2003-2004 John M. Chemerda Lectures in Science: Dr. John F. Nash, Jr.

**Nobel Memorial Prize in Economic Sciences: Laureates (1976-2000)**

1976: Friedman |
1977: Ohlin, Meade |
1978: Simon |
1979: Schultz, Lewis |
1980: Klein |
1981: Tobin |
1982: Stigler |
1983: Debreu |
1984: Stone |
1985: Modigliani |
1986: Buchanan |
1987: Solow |
1988: Allais |
1989: Haavelmo |
1990: Markowitz, Miller, Sharpe |
1991: Coase |
1992: Becker |
1993: Fogel, North |
1994: Harsanyi, |

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Categories: 1928 births | Living people | American mathematicians | 20th century mathematicians | John von Neumann Theory Prize winners | Princeton University | People from West Virginia | Nobel laureates in Economics | People with schizophrenia | Game theorists | Board game designers | Massachusetts Institute of Technology alumni | Carnegie Mellon University alumni | Members and associates of the US National Academy of Sciences | Fellows of the Econometric Society | Fellows of the Econometric Society elected in 1990 | Erdős number 4