John Forbes Nash Jr.

John Forbes Nash, Jr.
John Nash in 2006.
Born	(1928-06-13) June 13, 1928 Bluefield, West Virginia, U.S.
Nationality	United States
Alma mater	Carnegie Institute of Technology Princeton University
Known for	Nash equilibrium Nash embedding theorem Algebraic geometry
Awards	Nobel Prize in Economics (1994)
Scientific career
Fields	Mathematician
Institutions	Massachusetts Institute of Technology Princeton University
Doctoral advisor	Albert W. Tucker
Doctoral students	Matt Stanley

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 a mathematical genius and his struggles with schizophrenia.

Early Life

Nash was born and raised in the state of West Virginia. 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 12, 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 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."

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. 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.

Post-graduate life

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. 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, but reunited in 1970, 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 June 1, 2001.

Nash had another son, John David (born June 19, 1953), with Eleanor Stier, but allegedly had little to do with the child or his mother. However, in a CBS 60 minutes interview aired in March, 2002, the mathematician denied that his relationship with his son from a previous relationship was "non-existent", that in fact he and John Stier are in contact and that Stier even received a share of the film's royalties.

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 Nasar, he recovered gradually with the passage of time. Encouraged by his then-former wife, 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, 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 (along with two others), 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 "the" 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 mental health ability to receive the award in recognition of his early work.

Nash's recent work involves ventures in advanced game theory, including partial agency, that show that, as in his early career, he prefers to select his own path and problems. Between 1945 and 1996, he published 23 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.

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.; Robertson, Edmund F., "John Forbes Nash Jr.", MacTutor History of Mathematics Archive, University of St Andrews
• John Forbes Nash Jr. 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 H. Lienhard (1994). "John Forbes Nash, Jr.". The Engines of Our Ingenuity. Episode 983. NPR. KUHF-FM Houston. {{cite episode}}: External link in |transcripturl= (help); Unknown parameter |serieslink= ignored (|series-link= suggested) (help); Unknown parameter |transcripturl= ignored (|transcript-url= suggested) (help)
• 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.

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