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Person: Nash, John Forbes

John Nash was an American mathematician who won the Nobel Prize for Economics for his work in game theory. He achieved fame through the film A Beautiful Mind.

Mathematical Profile (Excerpt):

• However while the others played together Johnny played by himself with toy airplanes and matchbox cars.
• Johnny's teachers at school certainly did not recognise his genius, and it would appear that he gave them little reason to realise that he had extraordinary talents.
• They were more conscious of his lack of social skills and, because of this, labelled him as backward.
• Although it is easy to be wise after the event, it now would appear that he was extremely bored at school.
• By the time he was about twelve years old he was showing great interest in carrying out scientific experiments in his room at home.
• It is fairly clear that he learnt more at home than he did at school.
• His parents encouraged him to take part in social activities and he did not refuse, but sports, dances, visits to relatives and similar events he treated as tedious distractions from his books and experiments.
• Nash first showed an interest in mathematics when he was about 14 years old.
• He tried, and succeeded, in proving for himself results due to Fermat which Bell stated in his book.
• The excitement that Nash found here was in contrast to the mathematics that he studied at school which failed to interest him.
• He entered Bluefield College in 1941 and there he took mathematics courses as well as science courses, in particular studying chemistry, which was a favourite topic.
• He began to show abilities in mathematics, particularly in problem solving, but still with hardly any friends and behaving in a somewhat eccentric manner, this only added to his fellow pupils view of him as peculiar.
• He did not consider a career in mathematics at this time, however, which is not surprising since it was an unusual profession.
• Nash won a scholarship in the George Westinghouse Competition and was accepted by the Carnegie Institute of Technology (now Carnegie-Mellon University) which he entered in June 1945 with the intention of taking a degree in chemical engineering.
• There he came in contact with John Synge who had recently been appointed as Head of the Mathematics Department and taught the relativity course.
• Synge and the other mathematics professors quickly recognised Nash's remarkable mathematical talents and persuaded him to become a mathematics specialist.
• They realised that he had the talent to become a professional mathematician and strongly encouraged him.
• Nash quickly aspired to great things in mathematics.
• He took the William Lowell Putnam Mathematics Competition twice but, although he did well, he did not make the top five.
• It was a failure in Nash's eyes and one which he took badly.
• The Putnam Mathematics Competition was not the only thing going badly for Nash.
• Although his mathematics professors heaped praise on him, his fellow students found him a very strange person.
• He behaved oddly, playing a single chord on a piano over and over, leaving a melting ice cream cone melting on top of his cast-off clothing, walking on his roommate's sleeping body to turn off the light.
• He showed homosexual tendencies, climbing into bed with the other boys who reacted by making fun of the fact that he was attracted to boys and humiliated him.
• They played cruel pranks on him and he reacted by asking his fellow students to challenge him with mathematics problems.
• He ended up doing the homework of many of the students.
• Nash received a BA and an MA in mathematics in 1948.
• He felt that Harvard was the leading university and so he wanted to go there, but on the other hand their offer to him was less generous than that of Princeton.
• Nash felt that Princeton were keen that he went there while he felt that his lack of success in the Putnam Mathematics Competition meant that Harvard were less enthusiastic.
• He took a while to make his decision, while he was encouraged by Synge and his other professors to accept Princeton.
• When Lefschetz offered him the most prestigious Fellowship that Princeton had, Nash made his decision to study there.
• In September 1948 Nash entered Princeton where he showed an interest in a broad range of pure mathematics: topology, algebraic geometry, game theory and logic were among his interests but he seems to have avoided attending lectures.
• Usually those who decide not to learn through lectures turn to books but this appears not to be so for Nash, who decided not to learn mathematics "second-hand" but rather to develop topics himself.
• In many ways this approach was successful for it did contribute to him developing into one of the most original of mathematicians who would attack a problem in a totally novel way.
• In 1949, while studying for his doctorate, he wrote a paper which 45 years later was to win a Nobel prize for economics.
• During this period Nash established the mathematical principles of game theory.
• Whether we are analysing candidates' election strategies, the causes of war, agenda manipulation in legislatures, or the actions of interest groups, predictions about events reduce to a search for and description of equilibria.
• However, my most vivid memory of this time is of the many games which were played in the common room.
• The game "Nash" was almost identical to Hex which had been invented independently by Piet Hein in Denmark.
• If he was in a room with twenty people, and they were talking, if you asked an observer who struck you as odd it would have been Nash.
• Nash was totally spooky.
• he'd take a lot of time answering a question.
• If he thought the question was foolish he wouldn't answer at all.
• It was a mixture of pride and something else.
• He was so isolated but there really was underneath it all a warmth and appreciation of people.
• A lot of us would discount what Nash said.
• You didn't feel comfortable with the person.
• He went to see Einstein not long after he arrived in Princeton and told him about an idea he had regarding gravity.
• After explaining complicated mathematics to Einstein for about an hour, Einstein advised him to go and learn more physics.
• In 1950 Nash received his doctorate from Princeton with a thesis entitled Non-cooperative Games.
• In the summer of that year he worked for the RAND Corporation where his work on game theory made him a leading expert on the Cold War conflict which dominated RAND's work.
• He worked there from time to time over the next few years as the Corporation tried to apply game theory to military and diplomatic strategy.
• Back at Princeton in the autumn of 1950 he began to work seriously on pure mathematical problems.
• It might seem that someone who had just introduced ideas which would, one day, be considered worthy of a Nobel Prize would have no problems finding an academic post.
• However, Nash's work was not seen at the time to be of outstanding importance and he saw that he needed to make his mark in other ways.
• We should also note that it was not really a move towards pure mathematics for he had always considered himself a pure mathematician.
• He had already obtained results on manifolds and algebraic varieties before writing his thesis on game theory.
• His famous theorem, that any compact real manifold is diffeomorphic to a component of a real-algebraic variety, was thought of by Nash as a possible result to fall back on if his work on game theory was not considered suitable for a doctoral thesis.
• So that might have been an anticipation of mental problems.
• In 1952 Nash published Real Algebraic Manifolds in the Annals of Mathematics.
• The most important result in this paper is that two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic.
• Although publication of this paper on manifolds established him as a leading mathematician, not everyone at Princeton was prepared to see him join the Faculty there.
• This was nothing to do with his mathematical ability which everyone accepted as outstanding, but rather some mathematicians such as Artin felt that they could not have Nash as a colleague due to his aggressive personality.
• Martin is appointing John Nash to an Assistant Professorship (not the Nash at Illinois, the one out of Princeton by Steenrod) and I'm pretty annoyed at that.
• He also makes a damned fool of himself in various ways contrary to this philosophy.
• He recently heard of the unsolved problem about imbedding a Riemannian manifold isometrically in Euclidean space, felt that this was his sort of thing, provided the problem were sufficiently worthwhile to justify his efforts; so he proceeded to write to everyone in the math society to check on that, was told that it probably was, and proceeded to announce that he had solved it, modulo details, and told Mackey he would like to talk about it at the Harvard colloquium.
• So it is generally conceded he is getting nowhere and making an even bigger ass of himself than he has been previously supposed by those with less insight than myself.
• But we've got him and saved ourselves the possibility of having gotten a real mathematician.
• Ambrose, the author of this letter, and Nash had rubbed each other the wrong way for a while.
• They had played silly pranks on each other and Ambrose seems not to have been able to ignore Nash's digs in the way others had learned to do.
• From 1952 Nash had taught at the Massachusetts Institute of Technology but his teaching was unusual (and unpopular with students) and his examining methods were highly unorthodox.
• His research on the theory of real algebraic varieties, Riemannian geometry, parabolic and elliptic equations was, however, extremely deep and significant in the development of all these topics.
• Nash continued to develop this work in the paper The imbedding problem for Riemannian manifolds published in 1956.
• This paper contains his famous deep implicit function theorem.
• After this Nash worked on ideas that would appear in his paper Continuity of solutions of parabolic and elliptic equations which was published in the American Journal of Mathematics in 1958.
• Nash, however, was very disappointed when he discovered that E De Giorgi had proved similar results by completely different methods.
• The outstanding results which Nash had obtained in the course of a few years put him into contention for a 1958 Fields Medal but since his work on parabolic and elliptic equations was still unpublished when the Committee made their decisions he did not make it.
• One imagines that the Committee would have expected him to be a leading contender, perhaps even a virtual certainty, for a 1962 Fields Medal but mental illness destroyed his career long before those decisions were made.
• During his time at MIT Nash began to have personal problems with his life which were in addition to the social difficulties he had always suffered.
• He met Eleanor Stier and they had a son, John David Stier, who was born on 19 June 1953.
• Eleanor was a shy girl, lacking confidence, a little afraid of men, did not want to be involved.
• She found in Nash someone who was even less experienced than she was and found that attractive.
• Nash did not want to marry Eleanor although she tried hard to persuade him.
• In the summer of 1954, while working for RAND, Nash was arrested in a police operation to trap homosexuals.
• He was dismissed from RAND.
• One of Nash's students at MIT, Alicia Larde, became friendly with him and by the summer of 1955 they were seeing each other regularly.
• He also had a special friendship with a male graduate student at this time: Jack Bricker.
• Eleanor found out about Alicia in the spring of 1956 when she came to Nash's house and found him in bed with Alicia.
• At a New Year's Party Nash appeared at midnight dressed only with a nappy and a sash with "1959" written on it.
• He spent most of the evening curled up, like the baby he was dressed as, on his wife's lap.
• One student immediately dropped the course! Nash asked a graduate student to take over his course and vanished for a couple of weeks.
• When he returned he walked into the common room with a copy of the New York Times saying that it contained encrypted messages from outer space that were meant only for him.
• For a few days people thought he was playing an elaborate private joke.
• Norbert Wiener was one of the first to recognize that Nash's extreme eccentricities and personality problems were actually symptoms of a medical disorder.
• Upon his release, Nash abruptly resigned from MIT, withdrew his pension, and went to Europe, where he intended to renounce his US citizenship.
• She then had Nash deported - back to the United States.
• After their return, the two settled in Princeton where Alicia took a job.
• Nash's illness continued, transforming him into a frightening figure.
• He spent most of his time hanging around on the Princeton campus, talking about himself in the third person as Johann von Nassau, writing nonsensical postcards and making phone calls to former colleagues.
• A long sad episode followed which included periods of hospital treatment, temporary recovery, then further treatment.
• Alicia divorced Nash in 1962.
• Nash spent a while with Eleanor and John David.
• In 1970 Alicia tried to help him taking him in as a boarder, but he appeared to be lost to the world, removed from ordinary society, although he spent much of his time in the Mathematics Department at Princeton.
• Slowly over many years Nash recovered.
• the staff at my university, the Massachusetts Institute of Technology, and later all of Boston were behaving strangely towards me.
• Despite spending periods in hospital because of his mental condition, his mathematical work continued to have success after success.
• In the 1990s Nash made a recovery from the schizophrenia from which he had suffered since 1959.
• His ability to produce mathematics of the highest quality did not totally leave him.
• Nash was awarded (jointly with Harsanyi and Selten) the 1994 Nobel Prize in Economic Science for his work on game theory.
• for a seminal contribution to research.
• striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.

Born 13 June 1928, Bluefield, West Virginia, USA. Died 23 May 2015, New Jersey, USA.

View full biography at MacTutor

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Prize Abel, Origin Usa, Prize Nobel

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@J-J-O'Connor

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive