John Forbes Nash

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.

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 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 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 Carnegie Mellon.

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

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.
 * "The Bargaining Problem", Econometrica 18 (1950), 155–162.
 * "Two-person Cooperative Games", Econometrica 21 (1953), 128–140.

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


 * "Real algebraic manifolds", Annals of Mathematics 56 (1952), 405–421. 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.

Family life
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. John Martin became a mathematician and, like his father, was later diagnosed with schizophrenia.

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 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.

A Beautiful Mind
The film A Beautiful Mind, released in 2001, directed by Ron Howard, starred Russell Crowe as Nash and Jennifer Connelly as his wife, was inspired by Nash's life and received four Academy Awards, including Best Picture. It is loosely based on Sylvia Nasar's biography, also called A Beautiful Mind, 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. This assumes that the prettiest girl has no decision making role, however one might argue that the fact that she was initially snubbed may lead her to remove herself from the game.) 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 &mdash; although his son from Boston plays a 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 around the time of his Nobel prize 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 that Nash independently invented the board game Hex.
 * Nash's work in game theory did not "disprove" Adam Smith's Invisible Hand as was suggested in the film.