John Forbes Nash Jr.

John Forbes Nash, Jr.
John Nash at a symposium of game theory at the University of Cologne, Germany (2006)
Born	(1928-06-13) June 13, 1928 Bluefield, West Virginia, USA
Nationality	American
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	Mathematics, Economics
Institutions	Massachusetts Institute of Technology Princeton University
Doctoral advisor	Albert W. Tucker

John Forbes Nash, Jr. (born June 13, 1928), is an American mathematician and economist 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 Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.

Nash is also the subject of the Hollywood movie, A Beautiful Mind, which was nominated for eight Oscars (winning four), and was based on the biography of the same name about him, his mathematical genius and his struggle with schizophrenia.

Early life

Nash was born and raised in Bluefield, West Virginia. He was born to electrical engineer John Forbes Nash and his wife Margaret Virginia Martin, an English and Latin teacher. On November 16, 1930 his sister Martha Nash was born. 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 carried out scientific experiments in his room. At a young age, he already preferred to work 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, wrote about him that "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 at Bluefield 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 Carnegie Tech.

Nash also created two popular games: Hex in 1947 (independently created first in 1942 by Piet Hein), and So Long Sucker in 1950 with M. Hausner and Lloyd S. Shapley.

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

In 1948, while applying to Princeton’s mathematics department, Nash's advisor and former Carnegie Tech professor, R.J. Duffin, wrote a letter of recommendation consisting of a single sentence: "This man is a genius." 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 the mathematics department at 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 (Nash equilibrium). 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 four 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
• "Non-cooperative Games", Annals of Mathematics 54 (1951), 286–295.

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 afterward, 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 received the "honoris causa" degree in Economics by the University of Naples Federico II on 19th March 2003.

Schizophrenia

He began to show signs of extreme paranoia and his wife later described his behavior as becoming increasingly erratic, stating that he began speaking of characters who were putting him in danger. Nash mailed letters to foreign embassies in Washington, D.C. declaring that he was establishing a world government.

He was involuntarily admitted into the McLean Hospital, April–May 1959, where he was diagnosed with paranoid schizophrenia and mild clinical depression. Upon his release, Nash resigned from MIT, withdrew his pension, and went to Europe, unsuccessfully seeking political asylum in France and Eastern Germany. He tried to renounce his U.S. citizenship. After a problematic stay in Paris and Geneva, Nash was arrested by the French police and deported back to the United States on the request of the U.S. government.

In 1961 he was involuntarily hospitalized into the Trenton State Hospital. He was in and out of mental hospitals until 1970, being given insulin shock therapy and antipsychotic medications, usually as a result of being involuntarily committed.

Although prescribed antipsychotic medication, Nash has said he never really took it. For some periods he was forced to or voluntarily complied under the pressure, but after 1970 he was never committed to the hospital again and never took antipsychotic medication again. The film "A Beautiful Mind" fabricated him later taking the then new atypical antipsychotics, which Nash attributes to the screenwriter (whose mother, he notes, was a psychiatrist) not wanting to incite people to stop taking their medication. Others, however, have questioned whether the fabrication obscured a key question as to whether recovery from problems like Nash's can actually be hindered by such drugs and Nash has said they are over-rated and the adverse effects are not given enough consideration once someone is considered mentally ill. According to his biographer Nasar, Nash 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. Alicia also said that for Nash "it's just a question of living a quiet life".

Nash dates the start of what he terms "mental disturbances" to the early months of 1959 when his wife was pregnant. He has described a process of change "from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'" including seeing himself as a messenger or having a special function in some way, and with supporters and opponents and hidden schemers, and a feeling of being persecuted, and looking for signs representing divine revelation. Nash has suggested his delusional thinking was related to his unhappiness, and his striving to feel important and be recognized, and to his characteristic way of thinking such that "I wouldn't have had good scientific ideas if I had thought more normally." He has said that "If I felt completely pressureless I don't think I would have gone in this pattern". He does not see a categorical distinction between terms such as schizophrenia and bipolar disorder. Nash reports that he did not hear voices at first, only some years later around 1964, until later engaging in a process of rejecting them. Nash reports that he was always taken to hospital against his will, and only temporarily renounced his "dream-like delusional hypotheses" after being in hospital long enough to decide to superficially conform and behave normally or experience "enforced rationality". Only gradually on his own did he "intellectually reject" some of the "delusionally influenced" and "politically-oriented" thinking as a waste of effort. However, by 1995 he felt that although "thinking rationally again in the style that is characteristic of scientists", it was not entirely a matter of joy as he felt more limited.

Recognition and later career

In Princeton 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.

In 1978, Nash was awarded the John von Neumann Theory Prize for his discovery of non-cooperative equilibria, now called Nash equilibria. He won the Leroy P. Steele Prize in 1999.

In 1994, he received the Nobel Memorial Prize in Economic Sciences (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 has suggested hypotheses on mental disorder. He has compared not thinking in an acceptable manner, or being "insane" and not fitting into a usual social function, to being "on strike" from an economic point of view. He has advanced evolutionary psychology views about the value of human diversity and the potential benefits of apparently non-standard behaviors or roles.

Nash has also developed work on the role of money in society. In the context that people can be so controlled and motivated by money that they may not be able to reason rationally about it, he has criticized interest groups that promote quasi-doctrines based on Keynesian economics that permit manipulative short-term inflation and debt tactics that ultimately undermine currencies. He has suggested a global "industrial consumption price index" system that would support the development of more "ideal money" that people could trust, rather than more unstable "bad money". He notes that some of his thinking parallels economist and political philosopher Friedrich Hayek's thinking regarding money and a nontypical viewpoint of the function of the authorities.

Personal life

In 2002, aspects of Nash's personal life were brought to international attention when "mudslinging" ensued over screenwriter Akiva Goldsman's semifictional interpretation of Sylvia Nasar's biography of Nash's life in A Beautiful Mind in relation to the film of the same name. The movie A Beautiful Mind, nominated for eight Oscars, credits Goldsman under "written by" rather than "screenplay by" from the Writer's Guild as Goldsman's "omissions are glaring and peculiar, specifically Nash's homosexual experiences, his extramarital sexual activities, his racial attitudes and anti-Semitic remarks." Nash later claimed any anti-Semitic remarks must have been made while he was delirious.

In the mid-1950s Nash was arrested in a Santa Monica restroom on a morals charge related to a homosexual encounter and "subsequently lost his post at the RAND Corporation along with his security clearance." According to Nasar, "After this traumatic series of career-threatening events, he decided to marry."

Nasar stated about the film that the filmmakers had "invented a narrative that, while far from a literal telling, is true to the spirit of Nash's story." Others suggested that the material was "conveniently left out of the movie in order to make Nash more sympathetic," possibly in an effort to more fully focus on the "debilitating longevity" of living with paranoid-schizophrenia on a day-to-day basis.

New York Times critic A. O. Scott pointed to a different perspective. Scott wrote of the Oscar scandal and the artistic choices made in the omissions as well as choices, such as casting actors, that have to be made that "the cold war in A Beautiful Mind in which the paranoia and uncertainty of McCarthy-era academic life is reduced to spy-movie clichés" smoothed over "and made palatable and familiar" a "difficult passage in American history." Thus the cold war's effects on Nash's life and career were left unexplored. Goldsman won the Oscar for "Best Adapted Screenplay". The film also won Best Picture, Best Director (Ron Howard) and Best Supporting Actress (Jennifer Connelly).

External links

• Autobiography at the Nobel Prize website
• Nash's home page at Princeton
• IDEAS/RePEc
• 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.
• video: Ariel Rubinstein's Lecture: "John Nash, Beautiful Mind and Game Theory"
• Lecture of John Forbes Nash at the Nobel Laureate Meeting in Lindau, Germany, 2005
• Nash Equilibrium 2002 article in Slate magazine by Robin Wright, speculating on links between Nash's theoretical work and his delusions
• Video, enclosed in a book, of the meeting with Ennio De Giorgi, Trento, Italy, 1996

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