John Forbes Nash Jr. (born June 13, 1928) is an American mathematician who works in game theory and differential geometry. 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 mental illness.
Birth and Youth
On June 13, 1928, John Forbes 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. It was quite apparent at a young age that he didn't like working with other people, preferring to do things alone. At school, he wasn't accepted socially by his peers. He felt recreational events enjoyed by his peers, such as dances, sports and other things of the sort to be a distraction from his experiments and studies. John Nash realized that he was much smarter than any of his classmates, giving him a feeling of high superiority over them.
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".
Education
The winner of a Westinghouse scholarship, he attended the Carnegie Institute of Technology, where he received both his bachelor's degree and his master's degree in 1948. 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:
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 embedding theorem.."Two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic." [1]
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. 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 Martin became a mathematician and, like his father, was diagnosed with paranoid schizophrenia. Nash had another son, John David (b. June 19, 1953), by Eleanor Stier, but unfortunately had little to do with them.
Divorce
Although the couple divorced in 1963, they reunited in 1970; the relationship was not romantic, but instead resembled that of two unrelated "roommates" sharing the same house. 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"; Nasar cites evidence that Nash was bisexual, though John and Alicia denied such on 60 Minutes in 2002. [2] When Nash won the Bank of Sweden Prize in Economic Sciences in 1994, however, the couple renewed their relationship and remarried on June 1, 2001.
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.
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.
Encouraged by his wife Alicia, Nash persisted in working in a communitarian setting where his eccentricities were unremarked. In this environment, he developed an interest (among others) in the calculation of exact values of large numbers - researches which impelled him to Princeton's Information Centers where he developed computer programs (of high quality). Here, he had more contact with Princetonians, which helped Nash to further cope with his mental illness.
In the late 1980s, Nash 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 were 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 his early career, he prefers to select his own path and problems (though he continues to work in a communal setting to assist in managing his illness).
Nash is still at Princeton, where he holds an appointment in mathematics. While cautious with people he does not know, insiders cite the senior faculty member as having a dry sense of humor.
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 game theory work at Princeton as a graduate student.
Between 1945 and 1996, Nash published a total of twenty-three scientific studies.
Games
Nash also created two popular games, but it often escapes notice that he was the one who created them. Hex was created in 1942 with Piet Hein, and So Long Sucker was created in 1964 with M. Hausner and Lloyd S. Shapley. Both games demonstrate what Nash worked on for years: the concept that in a game, one must win and everyone else must lose. (See Nash equilibrium.)
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 bar game described in the movie was not a Nash equilibrium as 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:
- 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 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.
A deleted scene from A Beautiful Mind reveals (in an inaccurate manner) that Nash independently invented the board game Hex.
Books by Nash
- Essays on Game Theory, by Nash, John F published by Edward Elgar in December 1996 ISBN 1858984262
See also
External links
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