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发信人: StephenKing (金博士), 信区: StephenKing
标 题: 不系安全带，John Nash今天车祸死了
发信站: BBS 未名空间站 (Sun May 24 11:17:59 2015, 美东)
John Forbes Nash, Jr.
Born June 13, 1928
Bluefield, West Virginia, U.S.
Died May 23, 2015 (aged 86) [1]
Residence United States
Nationality American
Fields
Mathematics
Economics
Institutions
Massachusetts Institute of Technology
Princeton University
Alma mater
Princeton University
Carnegie Institute of Technology (now part of Carnegie Mellon University)
Doctoral advisor Albert W. Tucker
Known for
Nash equilibrium
Nash embedding theorem
Nash functions
Nash–Moser theorem
Notable awards
John von Neumann Theory Prize (1978)
Nobel Memorial Prize in Economic Sciences (1994)
Abel Prize (2015)
Spouse Alicia Lopez-Harrison de Lardé (m. 1957–1963) (divorced); (m.
2001–2015) (their deaths)
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,
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. In 2015, he
was awarded the Abel Prize (along with Louis Nirenberg) for his work on
nonlinear partial differential equations.
Nash is the subject of Sylvia Nasar's biography A Beautiful Mind, and the
film based on it, which focuses on Nash's mathematical genius and his
schizophrenia.[2][3][4]
Contents
1 Youth
1.1 Education
2 Major contributions
2.1 Game theory
2.2 Other mathematics
3 Personal life
4 Mental illness
5 Recognition and later career
6 Death
7 Representation in culture
8 Awards
9 See also
10 References
11 Bibliography
12 Documentaries and video interviews
13 External links
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.[5] 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 chemical 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.[5]
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."[6] 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.[7] Nash also considered Princeton more
favorably because of its location closer to his family in Bluefield.[5] 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.[8][9] 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). "Equilibrium Points in N-person Games". Proceedings of
the National Academy of Sciences 36 (36): 48–9. doi:10.1073/pnas.36.1.48.
PMC 1063129. PMID 16588946. MR 0031701.
"The Bargaining Problem". Econometrica (18): 155–62. 1950. MR 0035977.
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.
In her book 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 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.[5]
In 2011, the National Security Agency declassified letters written by Nash
in the 1950s, in which he had proposed a new encryption–decryption machine.
[10] The letters show that Nash had anticipated many concepts of modern
cryptography, which are based on computational hardness.[11]
Personal life
In 1951, Nash was hired by the Massachusetts Institute of Technology (MIT)
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.[12] 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.[13]
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.[14]
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.[5] They married in
February 1957 at a Roman Catholic ceremony, although Nash was an atheist.[15
][16]
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[5] 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, and has also suffered from paranoid schizophrenia.[
17]
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.[17] 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.
Nash was a longtime resident of West Windsor Township, New Jersey.[18]
Mental illness
Nash in November 2006 at a game theory conference in Cologne, Germany
Nash began to show signs of paranoia,[when?] 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.[19][20] 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 realized that something was wrong.[21]
He was admitted to the McLean Hospital, April–May 1959, where he was
diagnosed with paranoid schizophrenia. The clinical diagnosis 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 present – particularly
auditory and perceptional disturbances, a lack of motivation for life, and
mild clinical depression.[22]
In 1961, Nash was admitted to the New Jersey State Hospital at Trenton.[
citation needed] Over the next nine years, he spent periods in psychiatric
hospitals, where, aside from receiving antipsychotic medications, he was
administered insulin shock therapy.[22][23][24]
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.[25] Robert Whitaker wrote an article suggesting that
recovery from problems like Nash's can be hindered by such drugs.[26]
Nash has said the psychotropic drugs are overrated and that the adverse
effects are not given enough consideration once someone is deemed mentally
ill.[27][28][29] 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".[20]
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'"[30] 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.[31] 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".[32] He does not see a categorical
distinction between terms such as schizophrenia and bipolar disorder.[33]
Nash reports that he did not hear voices until around 1964, and later
engaged in a process of consciously rejecting them.[34] 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 – 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.[30][35]
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
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.[5]
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.[citation needed]
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 views in evolutionary psychology about the value of human
diversity and the potential benefits of apparently nonstandard behaviors or
roles.[36]
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.[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 on March 19, 2003,[39] 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.[40]
Death
On May 23, 2015, Nash and his wife Alicia were killed in an automobile
accident on the New Jersey Turnpike. The driver of a taxi they were riding
lost control of the vehicle and struck a guard rail, throwing the couple
from the car.[41]
Representation in culture
At Princeton, campus legend Nash became known as "The Phantom of Fine Hall"[
42] (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.[43]
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.
Awards
1994 – Nobel Memorial Prize for Economics
2010 – Double Helix Medal[44]
2015 – Abel Prize[45]
See also
Hex (board game)
List of Nobel laureates
References
http://www.nydailynews.com/news/crime/john-nash-86-dies-car-acc
"Oscar race scrutinizes movies based on true stories". USA Today. March 6,
2002. Retrieved January 22, 2008.
"List of Oscar Winners". USA Today. March 25, 2002. Retrieved August 30,
2008.
Yuhas, Daisy. "Throughout History, Defining Schizophrenia Has Remained A
Challenge (Timeline)". Scientific American Mind. Retrieved March 2, 2013.
"John F. Nash, Jr. – Autobiography". Nobel Foundation. 1994. Retrieved
February 5, 2011.
Kuhn W, Harold and Nasar, Sylvia (ed.). "The Essential John Nash" (PDF).
Princeton University Press. pp. Introduction, xi. Retrieved April 17, 2008.
Nasar (2011), pp. 46–7.
Nash, John F. (May 1950) Non-Cooperative Games, PhD Thesis, Princeton
University.
Osborne, MJ (2004). An Introduction to Game Theory. Oxford, ENG: Oxford
University Press. p. 23. ISBN 0195128958.
"2012 Press Release – National Cryptologic Museum Opens New Exhibit on Dr.
John Nash". National Security Agency. Retrieved February 25, 2012.
"John Nash's Letter to the NSA ; Turing's Invisible Hand". Retrieved
February 25, 2012.
Goldstein, Scott (April 10, 2005) Eleanor Stier, 84; Brookline nurse had son
with Nobel laureate mathematician John F. Nash Jr., Boston.com News.
Sutherland, John (March 18, 2002) "Beautiful mind, lousy character", The
Guardian, March 18, 2002.
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."
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."
Nasar (2011), p. 212: "Nash, by then an atheist, balked at a Catholic
ceremony. He would have been happy to get married in city hall."
David Goodstein, 'Mathematics to Madness, and Back', The New York Times,
June 11, 1998
"John Forbes Nash May Lose N.J. Home". Associated Press. March 14, 2002.
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."
Nasar (2011), p. 251.
Nasar, Sylvia (November 13, 1994). "The Lost Years of a Nobel Laureate". The
New York Times. mirror1 mirror2
Sabbagh, Karl (2003). Dr. Riemann's Zeros. London: Atlantic Books. pp. 87–
88. ISBN 1-84354-100-9.
Nasar (2011), p. 32.
Ebert, Roger (2002). Roger Ebert's Movie Yearbook 2003. Andrews McMeel
Publishing. ISBN 978-0-7407-2691-0. Retrieved July 10, 2008.
Beam, Alex (2001). Gracefully Insane: The Rise and Fall of America's Premier
Mental Hospital. PublicAffairs. ISBN 978-1-58648-161-2. Retrieved July 10,
2008.
Greihsel, Marika (September 1, 2004) Interview with John Nash. Nobel
Foundation.
Whitaker, R. (March 4, 2002) "Mind drugs may hinder recovery". USA Today.
Nash, John "PBS Interview: Medication". 2002.
Nash, John "PBS Interview: Paths to Recovery". 2002.
Nash, John "PBS Interview: How does Recovery Happen?" 2002.
Nash, John (1995) "Autobiography" from Les Prix Nobel. The Nobel Prizes 1994
, Editor Tore Frängsmyr, [Nobel Foundation], Stockholm, 1952,
Nash, John "PBS Interview: Delusional Thinking". 2002.
Nash, John "PBS Interview: The Downward Spiral" 2002.
Nash, John (April 10, 2005) "Glimpsing inside a beautiful mind". Interview
by Shane Hegarty. Schizophrenia.com.
Nash, John "PBS Interview: Hearing voices". 2002.
Nash, John "John Nash: My experience with mental illness". PBS Interview,
2002.
Neubauer, David (June 1, 2007). "John Nash and a Beautiful Mind on Strike".
Yahoo! Health. Archived from the original on April 21, 2008.
Nash, John (2002). "Ideal Money". Southern Economic Journal 69 (1): 4–11.
doi:10.2307/1061553. JSTOR 1061553.
Zuckerman, Julia (April 27, 2005) "Nobel winner Nash critiques economic
theory". The Brown Daily Herald.
Capua, Patrizia (March 19, 2003). "Napoli, laurea a Nash il 'genio dei
numeri'" (in Italian). la Repubblica.it.
List of Fellows of the American Mathematical Society, retrieved February 24,
2013.
Ma, Myles (2015-05-23). "Famed 'A Beautiful Mind' mathematician John Nash,
wife killed in taxi crash, police say". NJ.com. Retrieved 2015-05-23.
Kwon, Ha Kyung (December 10, 2010). "Nash GS ’50: ‘The Phantom of Fine
Hall'". The Daily Princetonian. Retrieved May 6, 2014.
Nasar, Sylvia (November 3, 1994). "The Lost Years of a Nobel Laureate". The
New York Times. Retrieved May 6, 2014.
"John F. Nash, Jr. 2010 Honoree". Retrieved July 16, 2014.
"Nash receives Abel Prize for revered work in mathematics". Retrieved March
25, 2015.
发信人: StephenKing (金博士), 信区: StephenKing
标 题: 不系安全带，John Nash今天车祸死了
发信站: BBS 未名空间站 (Sun May 24 11:17:59 2015, 美东)
John Forbes Nash, Jr.
Born June 13, 1928
Bluefield, West Virginia, U.S.
Died May 23, 2015 (aged 86) [1]
Residence United States
Nationality American
Fields
Mathematics
Economics
Institutions
Massachusetts Institute of Technology
Princeton University
Alma mater
Princeton University
Carnegie Institute of Technology (now part of Carnegie Mellon University)
Doctoral advisor Albert W. Tucker
Known for
Nash equilibrium
Nash embedding theorem
Nash functions
Nash–Moser theorem
Notable awards
John von Neumann Theory Prize (1978)
Nobel Memorial Prize in Economic Sciences (1994)
Abel Prize (2015)
Spouse Alicia Lopez-Harrison de Lardé (m. 1957–1963) (divorced); (m.
2001–2015) (their deaths)
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,
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. In 2015, he
was awarded the Abel Prize (along with Louis Nirenberg) for his work on
nonlinear partial differential equations.
Nash is the subject of Sylvia Nasar's biography A Beautiful Mind, and the
film based on it, which focuses on Nash's mathematical genius and his
schizophrenia.[2][3][4]
Contents
1 Youth
1.1 Education
2 Major contributions
2.1 Game theory
2.2 Other mathematics
3 Personal life
4 Mental illness
5 Recognition and later career
6 Death
7 Representation in culture
8 Awards
9 See also
10 References
11 Bibliography
12 Documentaries and video interviews
13 External links
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.[5] 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 chemical 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.[5]
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."[6] 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.[7] Nash also considered Princeton more
favorably because of its location closer to his family in Bluefield.[5] 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.[8][9] 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). "Equilibrium Points in N-person Games". Proceedings of
the National Academy of Sciences 36 (36): 48–9. doi:10.1073/pnas.36.1.48.
PMC 1063129. PMID 16588946. MR 0031701.
"The Bargaining Problem". Econometrica (18): 155–62. 1950. MR 0035977.
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.
In her book 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 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.[5]
In 2011, the National Security Agency declassified letters written by Nash
in the 1950s, in which he had proposed a new encryption–decryption machine.
[10] The letters show that Nash had anticipated many concepts of modern
cryptography, which are based on computational hardness.[11]
Personal life
In 1951, Nash was hired by the Massachusetts Institute of Technology (MIT)
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.[12] 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.[13]
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.[14]
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.[5] They married in
February 1957 at a Roman Catholic ceremony, although Nash was an atheist.[15
][16]
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[5] 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, and has also suffered from paranoid schizophrenia.[
17]
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.[17] 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.
Nash was a longtime resident of West Windsor Township, New Jersey.[18]
Mental illness
Nash in November 2006 at a game theory conference in Cologne, Germany
Nash began to show signs of paranoia,[when?] 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.[19][20] 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 realized that something was wrong.[21]
He was admitted to the McLean Hospital, April–May 1959, where he was
diagnosed with paranoid schizophrenia. The clinical diagnosis 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 present – particularly
auditory and perceptional disturbances, a lack of motivation for life, and
mild clinical depression.[22]
In 1961, Nash was admitted to the New Jersey State Hospital at Trenton.[
citation needed] Over the next nine years, he spent periods in psychiatric
hospitals, where, aside from receiving antipsychotic medications, he was
administered insulin shock therapy.[22][23][24]
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.[25] Robert Whitaker wrote an article suggesting that
recovery from problems like Nash's can be hindered by such drugs.[26]
Nash has said the psychotropic drugs are overrated and that the adverse
effects are not given enough consideration once someone is deemed mentally
ill.[27][28][29] 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".[20]
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'"[30] 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.[31] 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".[32] He does not see a categorical
distinction between terms such as schizophrenia and bipolar disorder.[33]
Nash reports that he did not hear voices until around 1964, and later
engaged in a process of consciously rejecting them.[34] 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 – 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.[30][35]
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
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.[5]
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.[citation needed]
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 views in evolutionary psychology about the value of human
diversity and the potential benefits of apparently nonstandard behaviors or
roles.[36]
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.[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 on March 19, 2003,[39] 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.[40]
Death
On May 23, 2015, Nash and his wife Alicia were killed in an automobile
accident on the New Jersey Turnpike. The driver of a taxi they were riding
lost control of the vehicle and struck a guard rail, throwing the couple
from the car.[41]
Representation in culture
At Princeton, campus legend Nash became known as "The Phantom of Fine Hall"[
42] (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.[43]
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.
Awards
1994 – Nobel Memorial Prize for Economics
2010 – Double Helix Medal[44]
2015 – Abel Prize[45]
See also
Hex (board game)
List of Nobel laureates
References
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ceremony. He would have been happy to get married in city hall."
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June 11, 1998
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proposals to replace a nearby bridge."
Nasar (2011), p. 251.
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