John Forbes Nash, Jr.

John Forbes Nash, Jr. (born June 13, 1928) is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the factors that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Serving as a Senior Research Mathematician at Princeton University during the latter part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.

Nash is the subject of the 2001 Hollywood movie A Beautiful Mind. The film, loosely based on the biography of the same name, focuses on Nash's mathematical genius and also his schizophrenia.

§Youth

Nash was born on June 13, 1928, in Bluefield, West Virginia, United States. His father, after whom he is named, was an electrical engineer for the Appalachian Electric Power Company. His mother, born Margaret Virginia Martin and known as Virginia, had been a schoolteacher before she married. He had a younger sister, Martha, born November 16, 1930.

§Education

Nash attended kindergarten and public school. His parents and grandparents provided books and encyclopedias that he learned from. Nash's grandmother played piano at home, and Nash had positive memories of listening to her when he visited. Nash's parents pursued opportunities to supplement their son's education, and arranged for him to take advanced mathematics courses at a local community college during his final year of high school. Nash attended Carnegie Institute of Technology (now Carnegie Mellon University) with a full scholarship, the George Westinghouse Scholarship, and initially majored in Chemical Engineering. He switched to Chemistry, and eventually to Mathematics. After graduating in 1948 with a B.S. degree in Mathematics and a M.S. degree in Mathematics, he accepted a scholarship to Princeton University where he pursued graduate studies in mathematics.

Nash's adviser and former Carnegie Tech professor R. J. Duffin wrote a letter of recommendation for graduate school consisting of a single sentence: "This man is a genius." Nash was accepted by Harvard University, but the chairman of the mathematics department of Princeton, Solomon Lefschetz, offered him the John S. Kennedy fellowship, which was enough to convince Nash that Princeton valued him more. Nash also considered Princeton more favorably because of its location closer to his family in Bluefield. He went to Princeton where he worked on his equilibrium theory.

§Major contributions

§Game theory

Nash earned a Ph.D. degree in 1950 with a 28-page dissertation on non-cooperative games. The thesis, which was written under the supervision of doctoral advisor Albert W. Tucker, contained the definition and properties of what would later be called the "Nash equilibrium". It is a crucial concept in non-cooperative games, and it won Nash the Nobel prize in economics in 1994.

Nash's major publications relating to this concept are in the following papers:

1. Nash, JF (1950). "Equilibrium Points in N-person Games". Proceedings of the National Academy of Sciences 36 (36): 48â€"9. doi:10.1073/pnas.36.1.48. PMC 1063129. PMID 16588946. , MR 0031701.
2. "The Bargaining Problem". Econometrica (18): 155â€"62. 1950. . MR 0035977.
3. Nash, J. (1951). "Non-cooperative Games". Annals of Mathematics 54 (54): 286â€"95. doi:10.2307/1969529. JSTOR 1969529. .
4. "Two-person Cooperative Games". Econometrica (21): 128â€"40. 1953. , MR 0053471.

§Mathematics

Nash did ground-breaking work in the area of real algebraic geometry:

• "Real algebraic manifolds". Annals of Mathematics (56): 405â€"21. 1952. , MR 0050928. See "Proc. Internat. Congr. Math". AMS. 1952. pp. 516â€"17. .

His work in mathematics includes the Nash embedding theorem, which shows that any abstract Riemannian manifold can be isometrically realized as a submanifold of Euclidean space. He also made significant contributions to the theory of nonlinear parabolic partial differential equations and to singularity theory.

In her book A Beautiful Mind, author Sylvia Nasar explains that Nash was working on proving the Hilbert's nineteenth problem, a theorem involving elliptic partial differential equations when, in 1956, he suffered a severe disappointment. He learned that an Italian mathematician, Ennio de Giorgi, had published a proof just months before Nash achieved his proof. Each took different routes to get to their solutions. The two mathematicians met each other at the Courant Institute of Mathematical Sciences of New York University during the summer of 1956. It has been speculated that if only one had solved the problem, he would have been given the Fields Medal for the proof.

In 2011, the National Security Agency declassified letters written by Nash in the 1950s, in which he had proposed a new encryption-decryption machine. The letters show that Nash had anticipated many concepts of modern cryptography, which are based on computational hardness.

§Personal life

In 1951, Nash was hired by the Massachusetts Institute of Technology as a C. L. E. Moore Instructor in the mathematics faculty. About a year later Nash began a relationship in Massachusetts with Eleanor Stier, a nurse he met while she cared for him as a patient. They had a son, John David Stier, but Nash had left Stier when she told him of her pregnancy. The film based on Nash's life, A Beautiful Mind, was criticized during the run-up to the 2002 Oscars for omitting this aspect of his life. He was said to have abandoned her based on her social status, which he thought to have been beneath his.

Not long after breaking up with Eleanor he met Alicia Lopez-Harrison de Lardé (born January 1, 1933), a naturalized U.S. citizen from El Salvador. De Lardé graduated from M.I.T., having majored in physics. They married in February 1957 at a Roman Catholic ceremony, although Nash was an atheist.

In 1958 he was given a tenure position at MIT, but Nash had his first symptoms of mental illness in early 1959. Alicia was pregnant with their first child. He resigned his position as a member of the M.I.T. mathematics faculty in the spring of 1959 and Alicia had him admitted to the McLean Hospital for treatment of schizophrenia that year. Their son John Charles Martin Nash was born soon afterward. The boy was not named for a year because Alicia felt that her husband should have a say in the name. He also became a mathematician, as well as suffering from paranoid schizophrenia.

Due to the stress of dealing with his illness, Nash and de Lardé divorced in 1963. After his final hospital discharge in 1970, Nash lived in de Lardé's house as a boarder. This stability seemed to help him, and he learned how to consciously discard his paranoid delusions. He stopped taking psychiatric medication and was allowed by Princeton to audit classes. He continued to work on mathematics and eventually he was allowed to teach again. In the 1990s, Alicia and Nash resumed their relationship. They remarried in 2001.

In his 20s, Nash was arrested for indecent exposure in a police trap of homosexuals in Santa Monica, California. Although the charges were dropped, he was stripped of his top-secret security clearance and fired from RAND Corporation where he had spent a few summers as a consultant.

Nash has been a longtime resident of West Windsor Township, New Jersey.

§Mental illness

Nash began to show signs of extreme paranoia, and his wife later described his behavior as erratic. Nash seemed to believe that all men who wore red ties were part of a communist conspiracy against him. Nash mailed letters to embassies in Washington, D.C., declaring that they were establishing a government. Nash's psychological issues crossed into his professional life when he gave an American Mathematical Society lecture at Columbia University in 1959. Although ostensibly pertaining to a proof of the Riemann hypothesis, the lecture was incomprehensible. Colleagues in the audience immediately realised that something was wrong. ("Dr. Riemann's Zeros", Karl Sabbagh, Atlantic Books 2003).

He was admitted to the McLean Hospital, Aprilâ€"May 1959, where he was diagnosed with paranoid schizophrenia. The clinical picture is dominated by relatively stable, often paranoid, fixed beliefs that are either false, over-imaginative or unrealistic, usually accompanied by experiences of seemingly real perception of something not actually presentâ€"particularly auditory and perceptional disturbances, a lack of motivation for life, and mild clinical depression.

In 1961, Nash was admitted to the New Jersey State Hospital at Trenton. Over the next nine years, he spent periods in psychiatric hospitals, where, aside from receiving antipsychotic medications, he was administered insulin shock therapy.

Although he sometimes took prescribed medication, Nash later wrote that he only ever did so under pressure. After 1970, he was never committed to a hospital again, and he refused any further medication. According to Nash, the film A Beautiful Mind inaccurately implied that he was taking the new atypical antipsychotics during this period. He attributed the depiction to the screenwriter (whose mother, he notes, was a psychiatrist), who was worried about the film encouraging people with the disorder to stop taking their medication. R. Whitaker wrote an article suggesting that recovery from problems like Nash's can be hindered by such drugs.

Nash has said the psychotropic drugs are overrated and that the adverse effects are not given enough consideration once someone is deemed mentally ill. According to Sylvia Nasar, author of the book A Beautiful Mind, on which the movie was based, Nash recovered gradually with the passage of time. Encouraged by his then former wife, de Lardé, Nash worked in a communitarian setting where his eccentricities were accepted. De Lardé said of 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, saying, "I wouldn't have had good scientific ideas if I had thought more normally." He has also said, "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 until around 1964, and later engaged in a process of consciously rejecting them. He reports that he was always taken to hospitals against his will. He only temporarily renounced his "dream-like delusional hypotheses" after being in a hospital long enough to decide to superficially conform â€" to behave normally or to 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, although he was "thinking rationally again in the style that is characteristic of scientists," he says he also felt more limited.

Writing in 1994, Nash stated:

"I spent times of the order of five to eight months in hospitals in New Jersey, always on an involuntary basis and always attempting a legal argument for release. And it did happen that when I had been long enough hospitalized that I would finally renounce my delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances and return to mathematical research. In these interludes of, as it were, enforced rationality, I did succeed in doing some respectable mathematical research. Thus there came about the research for "Le problème de Cauchy pour les équations différentielles d'un fluide général"; the idea that Prof. Hironaka called 'the Nash blowing-up transformation'; and those of 'Arc Structure of Singularities' and 'Analyticity of Solutions of Implicit Function Problems with Analytic Data'.

"But after my return to the dream-like delusional hypotheses in the later 60's I became a person of delusionally influenced thinking but of relatively moderate behavior and thus tended to avoid hospitalization and the direct attention of psychiatrists.

"Thus further time passed. Then gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically oriented thinking as essentially a hopeless waste of intellectual effort. So at the present time I seem to be thinking rationally again in the style that is characteristic of scientists."

§Recognition and later career

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 John Harsanyi and Reinhard Selten) as a result of his game theory work as a Princeton graduate student. In the late 1980s, Nash had begun to use email 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.

As of 2011 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 23 scientific studies.

Nash has suggested hypotheses on mental illness. 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 nonstandard behaviors or roles.

Nash has developed work on the role of money in society. Within the framing theorem 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.

Nash received an honorary degree, Doctor of Science and Technology, from Carnegie Mellon University in 1999, an honorary degree in economics from the University of Naples Federico II on March 19, 2003, an honorary doctorate in economics from the University of Antwerp in April 2007, and was keynote speaker at a conference on Game Theory. He has also been a prolific guest speaker at a number of world-class events, such as the Warwick Economics Summit in 2005 held at the University of Warwick. In 2012 he was elected as a fellow of the American Mathematical Society.

§Representation in culture

At Princeton, campus legend Nash became known as "The Phantom of Fine Hall" (Princeton's mathematics center), a shadowy figure who would scribble arcane equations on blackboards in the middle of the night. He is referred to in a novel set at Princeton, The Mind-Body Problem, 1998, by Rebecca Goldstein.

Nasar's biography of Nash, A Beautiful Mind, was published in 1998. A film by the same name was released in 2001; it changed or omitted certain events for the sake of its storyline.

§Awards

• 1994 - Nobel Memorial Prize for Economics
• 2010 - Double Helix Medal

§See also

• Game theory
• Hex (board game)
• List of Nobel laureates
• Nash equilibrium

§References

§Bibliography

• Acocella, Nicola and Di Bartolomeo, Giovanni (2006), ‘Tinbergen and Theil meet Nash: controllability in policy games’, in: ‘Economics Letters’, 90(2): 213-218.
• Acocella, Nicola and Di Bartolomeo, G. and Piacquadio, P.G. [2009], ‘Conflict of interest, (implicit) coalitions and Nash policy games’, in: ‘Economics Letters’, 105: 303-305.
• Nasar, Sylvia (2011). A Beautiful Mind. Simon and Schuster. ISBN 9781439126493. 

§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 (PDF)
• 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" â€" a PBS American Experience documentary
• John Nash speaks out about alleged omissions in film â€" Guardian Unlimited
• John H. Lienhard (1994). "John Forbes Nash, Jr.". The Engines of Our Ingenuity. Episode 983. NPR. KUHF-FM Houston.
• "John F. Nash by Lao Long"
• video: Ariel Rubinstein's Lecture: "John Nash, Beautiful Mind and Game Theory"
• "Nash Equilibrium" 2002 Slate article by Robert Wright, about Nash's work and world government
• Video, with book, of Nash's meeting with Ennio De Giorgi, Trento, Italy, 1996.
• NSA releases Nash Encryption Machine plans to National Cryptologic Museum for public viewing, 2012
• John F. Nash Jr. (1928â€" ). The Concise Encyclopedia of Economics. Library of Economics and Liberty (2nd ed.) (Liberty Fund). 2008. 
• "Aljazeera - One on One - Professor John Nash - 5 Dec 09 - Part 1" on YouTube
• "Aljazeera - One on One - Professor John Nash - 5 Dec 09 - Part 2" on YouTube

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