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John Forbes Nash, Jr. (born June 13, 1928) is an American mathematician who
works in game theory, differential geometry, and partial differential equations. 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.
 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. 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.
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 (now the Intel Science
Talent Search), 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 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 prestigious John F. 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.
At the Massachusetts Institute of Technology, 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, 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. 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.
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.
Nash is currently a Senior Research Mathematician at Princeton.
Source : Some of the information on this page came
from a Wikipedia article and is licensed under the GNU Documentation
License. ©2008 www.geneticmatrix.com.
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John
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