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John Forbes Nash Jr.

From Wikipedia, the free encyclopedia

John Forbes Nash Jr. (June 13, 1928 – May 23, 2015) was an American mathematician who made fundamental contributions to game theory, differential geometry, and the study of partial differential equations.[2][3] Nash's work has provided insight into the factors that govern chance and decision-making inside complex systems found in everyday life.

His theories are widely used in economics. Serving as a senior research mathematician at Princeton University during the later 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 also shared the Abel Prize with Louis Nirenberg for his work on nonlinear partial differential equations. John Nash was the only person to be awarded both the Nobel Memorial Prize in Economic Sciences and the Abel Prize.[citation needed]

In 1959, Nash began showing clear signs of mental illness, and spent several years at psychiatric hospitals being treated for schizophrenia. After 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s.[4] His struggles with his illness and his recovery became the basis for Sylvia Nasar's biographical book A Beautiful Mind in 1998, as well as a film of the same name directed by Ron Howard, in which Nash was portrayed by actor Russell Crowe.[5][6][7]

Early life and education

John Forbes Nash Jr. was born on June 13, 1928, in Bluefield, West Virginia. His father and namesake, John Forbes Nash Sr., was an electrical engineer for the Appalachian Electric Power Company. His mother, Margaret Virginia (née Martin) Nash, had been a schoolteacher before she was married. He was baptized in the Episcopal Church.[8] He had a younger sister, Martha (born November 16, 1930).[9]

Nash attended kindergarten and public school, and he learned from books provided by his parents and grandparents.[9] 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. He attended Carnegie Institute of Technology (which later became Carnegie Mellon University) through a full benefit of the George Westinghouse Scholarship, initially majoring in chemical engineering. He switched to a chemistry major and eventually, at the advice of his teacher John Lighton Synge, to mathematics. After graduating in 1948, with both a B.S. and M.S. in mathematics, Nash accepted a fellowship to Princeton University, where he pursued further graduate studies in mathematics and sciences .[9]

Nash's adviser and former Carnegie professor Richard Duffin wrote a letter of recommendation for Nash's entrance to Princeton stating, "He is a mathematical genius".[10][11] Nash was also accepted at Harvard University. However, the chairman of the mathematics department at Princeton, Solomon Lefschetz, offered him the John S. Kennedy fellowship, convincing Nash that Princeton valued him more.[12] Further, he considered Princeton more favorably because of its proximity to his family in Bluefield.[9] At Princeton, he began work on his equilibrium theory, later known as the Nash equilibrium.[13]

Major contributions

Nash in November 2006 at a game theory conference in Cologne, Germany
Nash in November 2006 at a game theory conference in Cologne, Germany

Game theory

Nash earned a PhD in 1950 with a 28-page dissertation on non-cooperative games.[14][15]

The thesis, 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.

Publications authored by Nash relating to the concept are in the following papers :

Other mathematics

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

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. Nash also made significant contributions to the theory of nonlinear parabolic partial differential equations, and to singularity theory.

Mikhail Leonidovich Gromov writes about Nash's work:

Nash was solving classical mathematical problems, difficult problems, something that nobody else was able to do, not even to imagine how to do it. ... But what Nash discovered in the course of his constructions of isometric embeddings is far from 'classical' – it is something that brings about a dramatic alteration of our understanding of the basic logic of analysis and differential geometry. Judging from the classical perspective, what Nash has achieved in his papers is as impossible as the story of his life ... [H]is work on isometric immersions ... opened a new world of mathematics that stretches in front of our eyes in yet unknown directions and still waits to be explored.[16]

John Milnor gives a list of 21 publications.[17]

In the Nash biography A Beautiful Mind, author Sylvia Nasar explains that Nash was working on proving 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. 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.[9]

In 2011, the National Security Agency declassified letters written by Nash in the 1950s, in which he had proposed a new encryption–decryption machine.[18] The letters show that Nash had anticipated many concepts of modern cryptography, which are based on computational hardness.[19]

Mental illness

Although Nash's mental illness first began to manifest in the form of paranoia, his wife later described his behavior as erratic. Nash thought that all men who wore red ties were part of a communist conspiracy against him. He mailed letters to embassies in Washington, D.C., declaring that they were establishing a government.[4][20] Nash's psychological issues crossed into his professional life when he gave an American Mathematical Society lecture at Columbia University in early 1959. Originally intended to present proof of the Riemann hypothesis, the lecture was incomprehensible. Colleagues in the audience immediately realized that something was wrong.[21]

In April 1959, Nash was admitted to McLean Hospital for one month. Based on his paranoid, persecutory delusions, hallucinations, and increasing asociality, he was diagnosed with schizophrenia.[22][23] In 1961, Nash was admitted to the New Jersey State Hospital at Trenton.[24] Over the next nine years, he spent intervals of time in psychiatric hospitals, where he received both antipsychotic medications and insulin shock therapy.[23][25]

Although he sometimes took prescribed medication, Nash later wrote that he did so only under pressure. According to Nash, the film A Beautiful Mind inaccurately implied he was taking atypical antipsychotics. He attributed the depiction to the screenwriter who was worried about the film encouraging people with mental illness to stop taking their medication.[26]

Nash did not take any medication after 1970, nor was he committed to a hospital ever again.[27] Nash recovered gradually.[28] Encouraged by his then former wife, de Lardé, Nash lived at home and spent his time in the Princeton mathematics department where his eccentricities were accepted even when his mental condition was poor. De Lardé credits his recovery to maintaining "a quiet life" with social support.[4]

Nash dated the start of what he termed "mental disturbances" to the early months of 1959, when his wife was pregnant. He 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'".[9] For Nash, this included seeing himself as a messenger or having a special function of some kind, of having supporters and opponents and hidden schemers, along with a feeling of being persecuted and searching for signs representing divine revelation.[29] Nash suggested his delusional thinking was related to his unhappiness, his desire to be recognized, and his characteristic way of thinking, saying, "I wouldn't have had good scientific ideas if I had thought more normally." He also said, "If I felt completely pressureless I don't think I would have gone in this pattern".[30]

Nash reported that he started hearing voices in 1964, then later engaged in a process of consciously rejecting them.[31] He only renounced his "dream-like delusional hypotheses" after a prolonged period of involuntary commitment in mental hospitals—"enforced rationality". Upon doing so, he was temporarily able to return to productive work as a mathematician. By the late 1960s, he relapsed.[32] Eventually, he "intellectually rejected" his "delusionally influenced" and "politically oriented" thinking as a waste of effort.[9] In 1995, he said that he didn't realize his full potential due to nearly 30 years of mental illness.[33]

Nash wrote in 1994:

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. [Heisuke] 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 60s 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.[9]

Recognition and later career

Nash pictured in 2011
Nash pictured in 2011

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) for his game theory work as a Princeton graduate student.[34] 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 and ability to receive the award.[35]

Nash's later 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 advanced views in evolutionary psychology about the potential benefits of apparently nonstandard behaviors or roles.[36]

Nash developed work on the role of money in society. He 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 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 noted that some of his thinking parallels that of economist and political philosopher Friedrich Hayek, regarding money and an atypical viewpoint of the function of authority.[37][38]

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 in 2003,[39] an honorary doctorate in economics from the University of Antwerp in 2007, an honorary doctorate of science from the City University of Hong Kong in 2011,[1] and was keynote speaker at a conference on game theory.[40] Nash also received honorary doctorates from two West Virginia colleges: the University of Charleston in 2003 and West Virginia University Tech in 2006. He was a prolific guest speaker at a number of events, such as the Warwick Economics Summit in 2005, at the University of Warwick.

Nash was elected to the American Philosophical Society in 2006[41] and became a fellow of the American Mathematical Society in 2012.[42]

On May 19, 2015, a few days before his death, Nash, along with Louis Nirenberg, was awarded the 2015 Abel Prize by King Harald V of Norway at a ceremony in Oslo.[43]

Personal life

In 1951, the Massachusetts Institute of Technology (MIT) hired Nash as a C. L. E. Moore instructor in the mathematics faculty. About a year later, Nash began a relationship with Eleanor Stier, a nurse he met while admitted as a patient. They had a son, John David Stier,[1] but Nash left Stier when she told him of her pregnancy.[44] 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.[45]

In Santa Monica, California, in 1954, while in his twenties, Nash was arrested for indecent exposure in a sting operation targeting gay men.[46] Although the charges were dropped, he was stripped of his top-secret security clearance and fired from RAND Corporation, where he had worked as a consultant.[47]

Not long after breaking up with Stier, Nash met Alicia Lardé Lopez-Harrison, a naturalized U.S. citizen from El Salvador. Lardé graduated from MIT, having majored in physics.[9] They married in February 1957. Although Nash was an atheist,[48] the ceremony was performed in an Episcopal church.[49] In 1958, Nash was appointed to a tenured position at MIT, and his first signs of mental illness soon became evident. He resigned his position at MIT in the spring of 1959.[9] His son, John Charles Martin Nash, was born a few months later. The child was not named for a year[1] because Alicia felt that Nash should have a say in choosing the name. Due to the stress of dealing with his illness, Nash and Lardé divorced in 1963. After his final hospital discharge in 1970, Nash lived in Lardé's house as a boarder. This stability seemed to help him, and he learned how to consciously discard his paranoid delusions.[50] Princeton allowed him to audit classes. He continued to work on mathematics and was eventually allowed to teach again. In the 1990s, Lardé and Nash resumed their relationship, remarrying in 2001. John Charles Martin Nash earned a PhD in mathematics from Rutgers University and was diagnosed with schizophrenia as an adult.[49]


On May 23, 2015, Nash and his wife died in a car accident on the New Jersey Turnpike near Exit 8A in Monroe Township, NJ. They were on their way home from Newark Airport after a visit to Norway, where Nash had received the Abel Prize, when their taxicab driver, Tarek Girgis, lost control of the vehicle and struck a guardrail. Both passengers were ejected from the car upon impact. State police revealed that it appeared neither passenger was wearing a seatbelt at the time of the crash.[51][52] At the time of his death, the 86-year-old Nash was a longtime resident of New Jersey. He was survived by two sons, John Charles Martin Nash, who lived with his parents at the time of their death, and elder child John Stier.[53]

Following his death, obituaries appeared in scientific and popular media throughout the world. In addition to their obituary for Nash,[54] The New York Times published an article containing quotes from Nash that had been assembled from media and other published sources. The quotes consisted of Nash's reflections on his life and achievements.[55]


At Princeton in the 1970s, Nash became known as "The Phantom of Fine Hall"[56] (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, 1983, by Rebecca Goldstein.[4]

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; it won four Academy Awards, including Best Picture.


Documentaries and video interviews


  1. ^ a b c d Suellentrop, Chris (December 21, 2001). "A Real Number". Slate. Archived from the original on January 4, 2014. Retrieved May 28, 2015. A Beautiful Mind's John Nash is nowhere near as complicated as the real one.
  2. ^ Goode, Erica (May 24, 2015). "John F. Nash Jr., Math Genius Defined by a 'Beautiful Mind,' Dies at 86". The New York Times.
  3. ^ "John F. Nash Jr. and Louis Nirenberg share the Abel Prize". Abel Prize. March 25, 2015.
  4. ^ a b c d Nasar, Sylvia (November 13, 1994). "The Lost Years of a Nobel Laureate". The New York Times. Princeton, New Jersey. Retrieved May 6, 2014.
  5. ^ "Oscar race scrutinizes movies based on true stories". USA Today. March 6, 2002. Retrieved January 22, 2008.
  6. ^ "Academy Award Winners". USA Today. March 25, 2002. Retrieved August 30, 2008.
  7. ^ Yuhas, Daisy. "Throughout History, Defining Schizophrenia Has Remained A Challenge (Timeline)". Scientific American Mind. Retrieved March 2, 2013.
  8. ^ Nasar, Sylvia (1998). "Chapter One". A Beautiful Mind. Simon & Schuster. ISBN 0-684-81906-6. Archived from the original on December 5, 2000.
  9. ^ a b c d e f g h i j Nash, John (1995) "John F. Nash Jr. – Biographical" from Les Prix Nobel. The Nobel Prizes 1994, Editor Tore Frängsmyr, [Nobel Foundation], Stockholm, 1952,
  10. ^ "Nash recommendation letter" (PDF). p. 23. Archived from the original (PDF) on June 7, 2017. Retrieved June 5, 2015.
  11. ^ Kuhn, Harold W.; Nasar, Sylvia (eds.). "The Essential John Nash" (PDF). Princeton University Press. pp. Introduction, xi. Retrieved April 17, 2008.
  12. ^ Nasar (2011), pp. 46–7.
  13. ^ Nasar (2002), pp. xvi–xix.
  14. ^ Nash, John F. (May 1950). "Non-Cooperative Games" (PDF). PhD thesis. Princeton University. Archived from the original (PDF) on April 20, 2015. Retrieved May 24, 2015.
  15. ^ Osborne, Martin J. (2004). An Introduction to Game Theory. Oxford, England: Oxford University Press. p. 23. ISBN 0-19-512895-8.
  16. ^ Nash, John Forbes Jr.; Rassias, M. Th. (2016). Open Problems in Mathematics. New York City: Springer Publishing. pp. xi–xiii.
  17. ^ Milnor, John (1998). "John Nash and 'A Beautiful Mind'" (PDF). Notices of the AMS. Providence, Rhode Island: American Mathematical Society. 25 (10): 1329–1332.
  18. ^ "2012 Press Release – National Cryptologic Museum Opens New Exhibit on Dr. John Nash". National Security Agency. Retrieved July 30, 2022.
  19. ^ "John Nash's Letter to the NSA; Turing's Invisible Hand". February 17, 2012. Retrieved February 25, 2012.
  20. ^ Nasar (2011), p. 251.
  21. ^ Sabbagh, Karl (2003). Dr. Riemann's Zeros. London, England: Atlantic Books. pp. 87–88. ISBN 1-84354-100-9.
  22. ^ "Brown University Didactic Readings: DSM-IV Schizophrenia (DSM-IV-TR #295.1–295.3, 295.90)" (PDF). Providence, Rhode Island: Brown University. pp. 1–11. Retrieved June 1, 2015.
  23. ^ a b Nasar (2011), p. 32.
  24. ^ O'Connor, John J.; Robertson, Edmund F., "John Forbes Nash Jr.", MacTutor History of Mathematics archive, University of St Andrews
  25. ^ Ebert, Roger (2002). Roger Ebert's Movie Yearbook 2003. Andrews McMeel Publishing. ISBN 978-0-7407-2691-0. Retrieved July 10, 2008.
  26. ^ Greihsel, Marika (September 1, 2004). "John F. Nash Jr. – Interview". Nobel Foundation. Retrieved November 3, 2018.
  27. ^ Nash, John Forbes (2002). "PBS Interview: Medication". PBS.
  28. ^ Nash, John "PBS Interview: How does Recovery Happen?" 2002.
  29. ^ Nash, John "PBS Interview: Delusional Thinking". 2002.
  30. ^ Nash, John "PBS Interview: The Downward Spiral" 2002.
  31. ^ Nash, John "PBS Interview: Hearing voices". 2002.
  32. ^ Nash, John "PBS Interview: Paths to Recovery". 2002.
  33. ^ Nash, John "John Nash: My experience with mental illness". PBS Interview, 2002.
  34. ^ Nasar (2002), p. xiii.
  35. ^ "The Work of John Nash in Game Theory" (PDF). Nobel Seminar. December 8, 1994. Archived from the original (PDF) on August 10, 2013. Retrieved May 29, 2015.
  36. ^ Neubauer, David (June 1, 2007). "John Nash and a Beautiful Mind on Strike". Yahoo! Health. Archived from the original on April 21, 2008.
  37. ^ Nash, John (2002). "Ideal Money". Southern Economic Journal. 69 (1): 4–11. doi:10.2307/1061553. JSTOR 1061553.
  38. ^ Zuckerman, Julia (April 27, 2005) "Nobel winner Nash critiques economic theory". The Brown Daily Herald. By JULIA ZUCKERMAN Wednesday, April 27, 2005
  39. ^ Capua, Patrizia (March 19, 2003). "Napoli, laurea a Nash il 'genio dei numeri'" (in Italian). la
  40. ^ "Nobel Laureate John Nash to Visit HK". Retrieved January 7, 2017.
  41. ^ "APS Member History". Retrieved May 25, 2021.
  42. ^ List of Fellows of the American Mathematical Society. Retrieved February 24, 2013.
  43. ^ "2015: Nash and Nirenberg". Retrieved August 2, 2022.{{cite web}}: CS1 maint: url-status (link)
  44. ^ Goldstein, Scott (April 10, 2005) Eleanor Stier, 84; Brookline nurse had son with Nobel laureate mathematician John F. Nash Jr., News.
  45. ^ Sutherland, John (March 18, 2002) "Beautiful mind, lousy character", The Guardian, March 18, 2002.
  46. ^ "John Nash, mathematician - obituary". The Telegraph. May 24, 2015. Archived from the original on January 11, 2022. Retrieved August 29, 2016.
  47. ^ Nasar, Sylvia (March 25, 2002). "The sum of a man". The Guardian. Retrieved July 9, 2012. Contrary to widespread references to Nash's "numerous homosexual liaisons", he was not gay. While he had several emotionally intense relationships with other men when he was in his early 20s, I never interviewed anyone who claimed, much less provided evidence, that Nash ever had sex with another man. Nash was arrested in a police trap in a public lavatory in Santa Monica in 1954, at the height of the McCarthy hysteria. The military think-tank where he was a consultant, stripped him of his top-secret security clearance and fired him ... The charge – indecent exposure – was dropped.
  48. ^ Nasar (2011), Chapter 17: Bad Boys, p. 143: "In this circle, Nash learned to make a virtue of necessity, styling himself self-consciously as a "free thinker." He announced that he was an atheist."
  49. ^ a b Livio, Susan K. (June 11, 2017). "Son of 'A Beautiful Mind' John Nash has one regret". NJ Advance Media. Retrieved June 17, 2020.
  50. ^ David Goodstein, 'Mathematics to Madness, and Back', The New York Times, June 11, 1998
  51. ^ Ma, Myles (May 23, 2015). "Famed 'A Beautiful Mind' mathematician John Nash, wife killed in taxi crash, police say". The Star-Ledger. Retrieved May 23, 2015.
  52. ^ "'Beautiful Mind' mathematician John Nash killed in crash". BBC News. Retrieved May 24, 2015.
  53. ^ "John Forbes Nash May Lose N.J. Home". Associated Press. March 14, 2002. Archived from the original on May 18, 2013. Retrieved February 22, 2011 – via HighBeam Research. West Windsor, N.J.: John Forbes Nash Jr., whose life is chronicled in the Oscar-nominated movie A Beautiful Mind, could lose his home if the township picks one of its proposals to replace a nearby bridge.
  54. ^ Goode, Erica (May 24, 2015). "John F. Nash Jr., Math Genius Defined by a 'Beautiful Mind,' Dies at 86". The New York Times. Retrieved May 24, 2015.
  55. ^ "The Wisdom of a Beautiful Mind". The New York Times. May 24, 2015. Retrieved May 25, 2015.
  56. ^ Kwon, Ha Kyung (December 10, 2010). "Nash GS '50: 'The Phantom of Fine Hall'". The Daily Princetonian. Archived from the original on May 6, 2014. Retrieved May 6, 2014.
  57. ^ Fellows: Alphabetical List, Institute for Operations Research and the Management Sciences, archived from the original on May 10, 2019, retrieved October 9, 2019
  58. ^ "John F. Nash Jr. 2010 Honoree". Archived from the original on October 17, 2014. Retrieved July 16, 2014.
  59. ^ "Nash receives Abel Prize for revered work in mathematics". Retrieved March 25, 2015.
  60. ^ "Archived copy". PBS. Archived from the original on February 18, 2017. Retrieved September 1, 2017.{{cite web}}: CS1 maint: archived copy as title (link)


External links

Preceded by Laureate of the Nobel Memorial Prize in Economics
Served alongside: John C. Harsanyi, Reinhard Selten
Succeeded by
This page was last edited on 5 August 2022, at 00:55
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