From Wikipedia, the free encyclopedia
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 forces 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
Hollywood movie
A Beautiful Mind. The film, loosely based on the
biography of the same name, focuses on Nash's mathematical genius and struggle with
paranoid schizophrenia.
[1][2]
In 2002,
PBS produced a documentary about Nash titled
A Brilliant Madness, which tells the story of a mathematical genius whose career was cut short by his descent into madness.
In his own words, he states,
- I later 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
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.[3]
Early life and career
Nash was born on June 13, 1928, in
Bluefield, West Virginia. 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. Both parents pursued
opportunities to supplement their son's education, providing him with
encyclopedias and even allowing him to take advanced mathematics courses
at a local college while still in high school. After attending
Carnegie Institute of Technology (now
Carnegie Mellon University)
and graduating in 1948 with bachelor's and master's degrees in
mathematics, he accepted a scholarship to Princeton University where he
pursued his graduate studies in Mathematics.
[3]
Post-graduate career
Nash's advisor and former Carnegie Tech professor
R.J. Duffin wrote a letter of recommendation consisting of a single sentence: "This man is a
genius."
[4] 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 Harvard valued him less.
[5] Thus he went to Princeton where he worked on his
equilibrium theory. He earned a
doctorate in 1950 with a 28-page
dissertation on non-cooperative games.
[6] The thesis, which was written under the supervision of
Albert W. Tucker, contained the definition and properties of what would later be called the "
Nash equilibrium". These studies led to four articles:
- 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, MR0031701.
- "The Bargaining Problem", Econometrica (18): 155–62, 1950. MR0035977.
- Nash, J. (1951), "Non-cooperative Games", Annals of Mathematics 54 (54): 286–95[7], JSTOR 1969529.
- "Two-person Cooperative Games", Econometrica (21): 128–40, 1953, MR0053471.
Nash did ground-breaking work in the area of real
algebraic geometry:
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 the book
A Beautiful Mind, author Sylvia Nasar explains that Nash was working on proving a
theorem
involving elliptic partial differential equations when, in 1956, he
suffered a severe disappointment when he learned of an Italian
mathematician,
Ennio de Giorgi,
who 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 of
them had solved the problem, he would have been given the
Fields Medal for the proof.
[3]
In 2011, the
National Security Agency declassified letters written by Nash in 1950s, in which he had proposed a new encryption-decryption machine.
[8] The letters show that Nash had anticipated many concepts of modern
cryptography, which are based on computational hardness.
[9]
Personal life
In 1951, Nash went to the
Massachusetts Institute of Technology
as a C. L. E. Moore Instructor in the mathematics faculty. There, he
met Alicia Lopez-Harrison de Lardé (born January 1, 1933), a
physics student from
El Salvador, whom he married in February 1957 at a Catholic ceremony, although Nash was an atheist.
[10] She admitted Nash to a
mental hospital in 1959 for
schizophrenia;
their son, John Charles Martin Nash, was born soon afterward, but
remained nameless for a year because his mother felt that her husband
should have a say in the name.
Nash and de Lardé divorced in 1963, though after his final hospital
discharge in 1970 Nash lived in de Lardé's house. They were remarried in
2001.
Nash has been a longtime resident of
West Windsor Township, New Jersey.
[11]
Mental illness
Schizophrenia
Nash began to show signs of extreme
paranoia
and his wife later described his behavior as erratic, as he began
speaking of characters like Charles Herman and William Parcher who were
putting him in danger. 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.
[12][13]
He was admitted to the
McLean Hospital, April–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 present — particularly auditory and perceptional
disturbances, a lack of motivation for life, and mild
clinical depression.
[14] Upon his release, Nash resigned from MIT, withdrew his
pension, and went to Europe, unsuccessfully seeking
political asylum in
France and
East Germany. He tried to renounce his U.S.
citizenship. After a problematic stay in Paris and
Geneva, he was arrested by the French police and deported back to the United States at the request of the
U.S. government.
In 1961, Nash was committed 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.
[14][15][16]
Although he sometimes took prescribed medication, Nash later wrote
that he only ever did so under pressure. After 1970, he was never
committed to the hospital again and he refused any 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
encouraging people with the disorder to stop taking their medication.
[17]
Others, however, have questioned whether the fabrication obscured a key
question as to whether recovery from problems like Nash's can actually
be hindered by such drugs,
[18] and Nash has said they are overrated and that the adverse effects are not given enough consideration once someone is deemed
mentally ill.
[19][20][21] 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".
[13]
Nash in November 2006 at a game theory conference in Cologne.
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'"
[22]
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.
[23]
Nash has suggested his delusional thinking was related to his
unhappiness and his striving to feel important and be recognized, and to
his characteristic way of thinking such that "I wouldn't have had good
scientific ideas if I had thought more normally." He has said, "If I
felt completely pressureless I don't think I would have gone in this
pattern".
[24] He does not see a categorical distinction between terms such as schizophrenia and
bipolar disorder.
[25] Nash reports that he did not hear voices until around 1964, later engaging in a process of rejecting them.
[26]
He reports that he was always taken to hospitals against his will, and
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.
[22][27]
Recognition and later career
At Princeton, campus legend Nash became "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. The legend
appears in a work of fiction based on Princeton life,
The Mind-Body Problem, by
Rebecca Goldstein.
In 1978, Nash was awarded the
John von Neumann Theory Prize for his discovery of non-cooperative equilibria, now called
Nash equilibria. He won the
Leroy P. Steele Prize in 1999.
In 1994, he received the
Nobel Memorial Prize in Economic Sciences (along with
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
evolutionary psychology views about the value of human diversity and the potential benefits of apparently nonstandard behaviors or roles.
[28]
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.
[29][30]
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,
[31] 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.
See also
Awards And Nominations
Double Helix Medal
References
- ^ "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.
- ^ a b c "John F. Nash, Jr. - Autobiography". Nobel Foundation. 1994. Retrieved February 5, 2011.
- ^ Kuhn W, Harold; Sylvia Nasar (eds.). "The Essential John Nash" (PDF). Princeton University Press. pp. Introduction, xi. Retrieved April 17, 2008.
- ^ Nasar, Sylvia (1998), A Beautiful Mind, Simon & Schuster, pp. 46–7.
- ^ Osborne, MJ (2004), An Introduction to Game Theory, Oxford, ENG: Oxford University Press, p. 23.
- ^ Non-Cooperative Games; Dissertetion for PhD, Princeton University http://www.policonomics.com/wp-content/uploads/Non-Cooperative-Games.pdf
- ^ "2012 Press Release - National Cryptologic Museum Opens New Exhibit on Dr. John Nash". National Security Agency. Retrieved 25 February 2012.
- ^ "John Nash's Letter to the NSA ; Turing's Invisible Hand". Retrieved 25 February 2012.
- ^ Sylvia Nasar (1999). A Beautiful Mind: A Biography of John Forbes Nash, Jr., Winner of the Nobel Prize in Economics, 1994. Simon and Schuster. ISBN 9780684853703. "Nash, by then an atheist, balked at a Catholic ceremony. He would have been happy to get married in city hall."
- ^ Staff. "John Forbes Nash May Lose N.J. Home", Associated Press,
March 14, 2002. Retrieved February 22, 2011. "West Windsor, N.J.: John
Forbes Nash, 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, A Beautiful Mind, p. 251.
- ^ a b Nasar, Sylvia (November 13, 1994). "The Lost Years of a Nobel Laureate". New York Times.
- ^ a b Nasar, A Beautiful Mind, 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
- ^ John Nash "Interview by Marika Greihsel". Nobel Foundation. September 1, 2004
- ^ Whitaker, R. (March 4, 2002) "Mind drugs may hinder recovery". USA Today.
- ^ John Nash "PBS Interview: Medication". 2002.
- ^ John Nash "PBS Interview: Paths to Recovery". 2002.
- ^ John Nash "PBS Interview: How does Recovery Happen?" 2002.
- ^ a b John Nash (1995) "Autobiography" from Les Prix Nobel. The Nobel Prizes 1994, Editor Tore Frängsmyr, [Nobel Foundation], Stockholm, 1952,
- ^ John Nash "PBS Interview: Delusional Thinking". 2002.
- ^ John Nash "PBS Interview: The Downward Spiral" 2002.
- ^ John Nash (April 10, 2005) "Glimpsing inside a beautiful mind". Interview by Shane Hegarty. Schizophrenia.com.
- ^ John Nash "PBS Interview: Hearing voices". 2002.
- ^ John Nash "PBS Interview: My experience with mental illness". 2002.
- ^ Neubauer, David (June 1, 2007). "John Nash and a Beautiful Mind on Strike". Yahoo Health. Archived from the original on 2008-04-21.
- ^ John Nash (2002) "Ideal Money" Southern Economic Journal, 69(1), p.4-11.
- ^ Zuckerman, Julia (April 27, 2005) "Nobel winner Nash critiques economic theory". The Brown Daily Herald.
- ^ Capua, Patrizia (19.3.2003). "Napoli, laurea a Nash il 'genio dei numeri'" (in Italian). la Repubblica.it.
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)
- Video of Dr. Sylvia Nasar narrating the story of John Nash at MIT
- O'Connor, John J.; Robertson, Edmund F., "John Forbes Nash, Jr.", MacTutor History of Mathematics archive, University of St Andrews.
- John Forbes Nash, Jr. at the Mathematics Genealogy Project
- "A Brilliant Madness" — a PBS American Experience documentary
- John Nash speaks out about alleged omissions in film — Guardian Unlimited
- "John Nash and 'A Beautiful Mind'" John Milnor responds to A Beautiful Mind (book), focusing on Nash's achievements.
- 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"
- Penn State's The 2003-2004 John M. Chemerda Lectures in Science: Dr. John F. Nash, Jr.
- video: Ariel Rubinstein's Lecture: "John Nash, Beautiful Mind and Game Theory"
- Lecture by John F. Nash at the Nobel Laureate Meeting in Lindau, Germany, 2005
- "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
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