John Nash Dies

John Forbes Nash, Jr. (June 13, 1928 – May 23, 2015) was 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 economics, computing, evolutionary biology, artificil 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.  In 2015, he was awarded the Abel Prize (along with Louis Nirenberg) for his work on nonlinear partial differential equations.

In 1959, Nash began showing clear signs of mental illness, and spent several years at psychiatric hospitals being treated for paranoid schizophrenia.  After 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s.  His struggles with his illness and his recovery became the basis for Sylvia Nasar's biography A Beautiful Mind as well as a feature film [of the same name] starring Russell Crowe.

On May 23, 2015, Nash and his wife were killed in an automobile accident in New Jersey.

Youth

Nash was born on June 13, 1928, in Bluefield, West Virginia, United States. His father, also named John Forbes Nash, 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 was baptized in the Episcopal Church directly opposite the Martin house on Tazewell Street.  He had a younger sister, Martha, who was born on 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 the Carnegie Institute of Technology (CIT; now Carnegie Mellon University) with a full scholarship, the George Westinghouse Scholarship, and initially majored in chemicak engineering.  He switched to chemistry, and eventually to mathematics. After graduating in 1948 with a B.S. degree and an M.S. degree, both in mathematics, he accepted a scholarship to Princeton University, where he pursued graduate studies in mathematics.

Nash's adviser and former CIT professor Richard 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, later known as the Nash equilibrium.

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 the Nash equilibrium. A crucial concept in non-cooperative games, it won Nash the Nobel Memorial Prize in Economic Sciences in 1994.

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

• Nash, JF (1950). “Equilibreum Points in N-person Games”.  Proceedings of the National Academy of Sciences 36 (36): 48–9. doi:10.1073/pnas.36.1.48 PMC 1063129l  PMID 16588946.  MR 0041701.
• "The Bargaining Problem". Econometrica (18): 155–62. 1950.  MR0035977.
• Nash, J. (1951). "Non-cooperative Games". Annals of Mathematics 54 (54): 286–95. doi:10.2307/1969529. JSTOR 1969529. 
• "Two-person Cooperative Games". Econometrica (21): 128–40. 1953. MR 0053471.

          Other mathematics

Nash did groundbreaking work in the area of real algebraic geometry:

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

His work in mathematics includes the Nash embedding theorem, which shows that every 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.

Personal life

In 1951, Nash was hired by the Massachusetts Institute of Technology (MIT) as a C. L. 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 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.

In 1954, while in his 20s, Nash was arrested for indecent exposure in an entrapment 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.

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 MIT, 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 tenured 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 MIT 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. 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, and remarried in 2001.

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 involved ventures in advanced game theory, including partial agency, which show that, as in his early career, he preferred 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 views in evolutionary psychology 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.  On May 19, 2015, he and Louis Nirenberg were presented with the 2015 Abel Prize by King Harald V of Norway at a ceremony in Oslo.

Death

On May 23, 2015, Nash and his wife Alicia were killed in an automobile accident on the New Jersey Turnpike near Monroe Township.  The driver of the taxi they were riding in lost control as he tried to overtake another vehicle and struck a guard rail; the couple were thrown out of the car.  A police spokesman declined to comment on media reports that they were not wearing seat belts.

Russell Crowe, who played Nash in the film version of A Beautiful Mind, took to Twitter to pay tribute.

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.

Sylvia Nasar’s biography of Nash, A Beautiful Mind, was published in 1998.  A film by the same name was released in 2001, directed by Ron Howard with Russell Crowe playing Nash.

http://en.wikipedia.org/wiki/John_Forbes_Nash,_Jr.