John Forbes Nash Jr.

John Nash in 2006. John Nash in 2006.
Born	May 13 1928 (1928--) (age 79) Bluefield, West Virginia, U.S.
Residence	USA
Nationality	United States
Field	Mathematician
Institutions	Massachusetts Institute of Technology Princeton University
Alma mater	Carnegie Institute of Technology Princeton University
Academic advisor	Albert W. Tucker
Notable students	Matt Stanley
Known for	Nash equilibrium Nash embedding theorem Algebraic geometry
Notable prizes	Nobel Prize in Economics (1994)

John Forbes Nash, Jr. (born June 13 1928) is an American mathematician who works in game theory, differential geometry, and partial differential equations, serving as a Senior Research Mathematician at Princeton University. 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 schizophrenia.

Childhood

On June 13, 1928, John Forbes Nash was born in the Appalachian city of Bluefield, West Virginia, 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 Pictured Encyclopedia, Life Magazine, and Time magazine. Later he had a job at the Bluefield Daily Telegraph.

At the age of twelve, he was carrying out scientific experiments in his room. It was quite apparent at a young age that he did not 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 John 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." ^[1]

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 his interest in mathematics.

Education and early career

He attended classes at Bluefield College while still in high school. He later attended the Carnegie Institute of Technology (now Carnegie Mellon University) in Pittsburgh, Pennsylvania on a Westinghouse scholarship, where he studied first chemical engineering and later chemistry before switching to mathematics. He received both his bachelor's degree and his master's degree in 1948 while at the Carnegie Institute.

After graduation, Nash took a summer job in White Oak, Maryland working on a Navy research project being run by Clifford Truesdell.

Though accepted by Harvard University, which had been his first choice because of what he perceived to be the institution's greater prestige and superior mathematics faculty, he was aggressively pursued by then chairman of Princeton University, Solomon Lefschetz, whose offer of the John S. Kennedy fellowship was enough to convince him that Harvard valued him less.^[2] Thus, from White Oak he went to Princeton University, where he worked on his equilibrium theory. He earned a doctorate 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", Proceedings of the National Academy of Sciences 36 (1950), 48–49. MR0031701
• "The Bargaining Problem", Econometrica 18 (1950), 155–162. MR0035977
• "Two-person Cooperative Games", Econometrica 21 (1953), 128–140. MR0053471

Nash also did important work in the area of algebraic geometry:

• "Real algebraic manifolds", Annals of Mathematics 56 (1952), 405–421. MR0050928 See also Proc. Internat. Congr. Math. (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.

In 1951, Nash went to the Massachusetts Institute of Technology as a C. L. E. Moore Instructor in the mathematics faculty. There, he met Alicia López-Harrison de Lardé (born January 1, 1933), 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 Nash, was born soon afterwards, but remained nameless for a year because his mother felt that her husband should have a say in the name.

Nash and Lopez-Harrison de Lardé 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.

Nash had another son, John David (born June 19, 1953), with Eleanor Stier, but had little to do with the child or his mother.

Schizophrenia

Nash began to show signs of schizophrenia 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 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. After 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.

Recognition and later career

In 1978 John Forbes 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 Nobel Prize in Economics 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. Between 1945 and 1996, he published twenty-three scientific studies.

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.

References

External links

• 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
• Video of Dr. Sylvia Nasar narrating the story of John Nash at MIT
• Beautiful mind, unconventional matter, a 2001 Daily Princetonian interview
• O'Connor, John J; Edmund F. Robertson "John Forbes Nash". MacTutor History of Mathematics archive.  
• John Forbes Nash at the Mathematics Genealogy Project
• "A Brilliant Madness" - a PBS American Experience documentary
• John Nash speaks out about alleged omissions in film - Guardian Unlimited
• John Nash and "A Beautiful Mind" Written by John Milnor as a reaction to the book A Beautiful Mind – not the movie – and mostly focusing on his mathematical achievements.
• "John Forbes Nash, Jr.". John H. Lienhard. The Engines of Our Ingenuity. NPR. KUHF-FM Houston. 1994. No. 983. Transcript.
• Department of Economics - News
• John F. Nash presented in Freedom section
• Penn State's The 2003-2004 John M. Chemerda Lectures in Science: Dr. John F. Nash, Jr.

•  • [ e] Nobel Memorial Prize in Economics Laureates
Milton Friedman (1976) • Bertil Ohlin / James Meade (1977) • Herbert Simon (1978) • Theodore Schultz / William Arthur Lewis (1979) • Lawrence Klein (1980) • James Tobin (1981) • George Stigler (1982) • Grard Debreu (1983) • Richard Stone (1984) • Franco Modigliani (1985) • James M. Buchanan (1986) • Robert Solow (1987) • Maurice Allais (1988) • Trygve Haavelmo (1989) • Harry Markowitz / Merton Miller / William Forsyth Sharpe (1990) • Ronald Coase (1991) • Gary Becker (1992) • Robert Fogel / Douglass North (1993) • John Harsanyi / John Forbes Nash / Reinhard Selten (1994) • Robert Lucas, Jr. (1995) • James Mirrlees / William Vickrey (1996) • Robert C. Merton / Myron Scholes (1997) • Amartya Sen (1998) • Robert Mundell (1999) • James Heckman / Daniel McFadden (2000)

Persondata
NAME	Jr., John Forbes Nash
ALTERNATIVE NAMES
SHORT DESCRIPTION	Mathematician
DATE OF BIRTH	13 June, 1928
PLACE OF BIRTH	Bluefield, West Virginia, U.S.
DATE OF DEATH
PLACE OF DEATH