JOHN FORBES NASH (1928- _____ ):
UNA BREVE BIOGRAFIA
John F Nash's father, also called John Forbes
Nash so we shall refer to him as John Nash Senior, was a native of Texas. John
Nash Senior was born in 1892 and had an unhappy childhood from which he escaped
when he studied electrical engineering at Texas Agricultural and Mechanical. After
military service in France during World War I, John Nash Senior lectured on
electrical engineering for a year at the University of Texas before joining the
Appalacian Power Company in Bluefield, West Virginia. John F Nash's mother,
Margaret Virginia Martin, was known as Virginia. She had a university
education, studying languages at the Martha Washington College and then at West
Virginia University. She was a school teacher for ten years before meeting John
Nash Senior, and the two were married on 6 September 1924.
Johnny Nash, as
he was called by his family, was born in Bluefield Sanatorium and baptised into
the Episcopal Church. He was
... a
singular little boy, solitary and introverted ...
but he was brought up in a loving family surrounded by close relations
who showed him much affection. After a couple of years Johnny had a sister when
Martha was born. He seems to have shown a lot of interest in books when he was
young but little interest in playing with other children. It was not because of
lack of children that Johnny behaved in this way, for Martha and her cousins
played the usual childhood games cutting patterns out of books, playing
hide-and-seek in the attic, playing football. However while the others played
together Johnny played by himself with toy airplanes and matchbox cars. His
mother responded by enthusiastically encouraging Johnny's education, both by
seeing that he got good schooling and also by teaching him herself. Johnny's
father responded by treating him like an adult, giving him science books when
other parents might give their children colouring books. 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. Martha seems to have been a remarkably normal child while Johnny seemed
different from other children. She wrote later in life
Johnny was
always different. [My parents] knew he was different. And they knew he was
bright. He always wanted to do thinks his way. Mother insisted I do things for
him, that I include him in my friendships. ... but I wasn't too keen on showing
off my somewhat odd brother.
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. Quite how he
came to read E T Bell's Men of mathematics
is unclear but certainly this book inspired him. 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 considered
a career in mathematics at this time, however, which is not surprising since it
was an unusual profession. Rather he assumed that he would study electrical
engineering and follow his father but he continued to conduct his own chemistry
experiments and was involved in making explosives which led to the death of one
of his fellow pupils.
Boredom and
simmering adolescent aggression led him to play pranks, occasionally ones with
a nasty edge.
He caricatured classmates he disliked with weird cartoons, enjoyed
torturing animals, and once tried to get his sister to sit in a chair he had
wired up with batteries. 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. Soon, however, his growing interest in
mathematics had him take courses on tensor calculus and relativity. 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. Physically he was strong
and this saved him from being bullied, but his fellow students took delight in
making fun of Nash who they saw as an awkward immature person displaying
childish tantrums. One of his fellow students wrote:
He was a
country boy unsophisticated even by our standards. He behaved oddly, playing a
single chord on a piano over and over, leaving a melting ice cream cone melting
on top of his castoff clothing, walking on his roommate's sleeping body to turn
off the light.
Another wrote:
He was
extremely lonely.
And a third
fellow student wrote:
We tormented
poor John. We were very unkind. We were obnoxious. We sensed he had a mental
problem.
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. By this time he had been accepted into the mathematics
programme at Harvard, Princeton, Chicago and Michigan. 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. P Ordeshook wrote:
The concept
of a Nash equilibrium n-tuple is perhaps the most important idea in
noncooperative 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. Put simply, equilibrium strategies are the things
that we predict about people.
Milnor, who was a fellow
student, describes Nash during his years at Princeton in :
He was
always full of mathematical ideas, not only on game theory, but in geometry and
topology as well. However, my most vivid memory of this time is of the many
games which were played in the common room. I was introduced to Go and
Kriegspiel, and also to an ingenious topological game which we called Nash in honor
of the inventor.
In fact the
game "Nash" was almost identical to Hex which had been invented
independently by Piet Hein in Denmark.
Here are three comments
from fellow students:
Nash was out
of the ordinary. 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. It
wasn't anything he consciously did. It was his bearing. His aloofness.
Nash was
totally spooky. He wouldn't look at you. he'd take a lot of time answering a
question. If he thought the question was foolish he wouldn't answer at all. He
had no affect. 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. ... I wouldn't want to listen. You didn't feel
comfortable with the person.
He had ideas and was very sure they were important. 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. Apparently a physicist did publish a similar idea some
years later. 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. He said
in a recent interview:
I developed
a very good idea in pure mathematics. I got what became Real Algebraic
Manifolds. I could have published that earlier, but it wasn't rushed to
publication. I took some time in writing it up. Somebody suggested that I was a
prodigy. Another time it was suggested that I should be called "bug
brains", because I had ideas, but they were sort of buggy or not perfectly
sound. So that might have been an anticipation of mental problems. I mean,
taking it at face value.
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. Halmos received the
following letter in early 1953 from Warren Ambrose relating to Nash :
There's no significant news from here, as always. 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. Nash is a childish bright guy who wants to be "basically
original," which I suppose is fine for those who have some basic
originality in them. 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 cheek on that, was told that it probably was, and proceeded to
announce that he had solved it, module details, and told Mackey he would like
to talk about it at the Harvard colloquium. Meanwhile he went to Levinson to inquire about a differential equation that intervened and Levinson says it is a system of
partial differential equations and if he could only [get] to the
essentially simpler analog of a single ordinary differential equation it would
be a damned good paper - and Nash had only the vaguest notions about the whole
thing. 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. He's a bright guy but conceited as Hell,
childish as Wiener, hasty as X,
obstreperous as Y, for arbitrary X and Y.
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. It had
been Ambrose who had said to Nash:
If you're so
good, why don't you solve the embedding theorem for manifolds.
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. His
paper C1isometric imbeddings was published in 1954 and Chern, in a review, noted
that it:-
... contains
some surprising results on the C1-isometric imbedding into an
Euclidean space of a Riemannian manifold with a positive definite C0-metric.
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 has 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 with
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. Colleagues said:
Nash was
always forming intense friendships with men that had a romantic quality. He was
very adolescent, always with the boys. He was very experimental - mostly he
just kissed.
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, didn't want to be
involved. She found in Nash someone who was even less experienced than she was
and found that attractive. :
Nash was
looking for emotional partners who were more interested in giving than
receiving, and Eleanor, was very much that sort.
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. Nash said to a
friend:
My perfect
little world is ruined, my perfect little world is ruined.
Alicia didn't seem too upset at discovering that Nash had a child with
Eleanor and deduced that since the affair had been going on for three years,
Nash was probably not serious about her. In 1956 Nash's parents found out about
his continuing affair with Eleanor and about his son John David Stier. The
shock may have contributed to the death of Nash's father soon after but even if
it did not Nash may have blamed himself. In February of 1957 Nash married
Alicia; by the autumn of 1958 she was pregnant but, a couple of months later
near the end of 1958, Nash's mental state became very disturbed. 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. Some described his
behaviour as stranger than usual. On 4 January he was back at the university
and started to teach his game theory course. His opening comments to the class
were:-
The question
occurs to me. Why are you here?
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. After months of bizarre behaviour,
Alicia had her husband involuntarily hospitalised at McLean Hospital, a private
psychiatric hospital outside of Boston. Upon his release, Nash abruptly
resigned from M.I.T., withdrew his pension, and went to Europe, where he
intended to renounce his U.S. citizenship. Alicia left her newborn son with her
mother, and followed the ill Nash. 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. They
stoically listened to his endless discussions of numerology and world political
affairs. Her husband's worsening condition depressed Alicia more and more. In
January 1961 the despondent Alicia, John's mother, and his sister Martha made
the difficult decision to commit him to Trenton State Hospital in New Jersey
where he endured insulin-coma therapy, an aggressive and risky treatment, five
days a week for a month and a half. 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. The book is highly recommended for
its moving account of Nash's mental sufferings. Slowly over many years Nash
recovered. He delivered a paper at the tenth World Congress of Psychiatry in
1996 describing his illness; it is reported in . He was described in 1958 as
the:-
... most
promising young mathematician in the world ...
but he soon
began to feel that:
... the
staff at my university, the Massachusetts Institute of Technology, and later
all of Boston were behaving strangely towards me. ... I started to see
crypto-communists everywhere ... I started to think I was a man of great
religious importance, and to hear voices all the time. I began to hear
something like telephone calls in my head, from people opposed to my ideas. ...The
delirium was like a dream from which I seemed never to awake.
Despite
spending periods in hospital because of his mental condition, his mathematical
work continued to have success after success. He said:
I would not
dare to say that there is a direct relation between mathematics and madness,
but there is no doubt that great mathematicians suffer from maniacal
characteristics, delirium and symptoms of schizophrenia.
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. He said:
I would not
treat myself as recovered if I could not produce good things in my work.
Nash was
awarded (jointly with Harsanyi and Selten) the 1994 Nobel Prize
in Economic Science for his work on game theory. In 1999 he was awarded the
Leroy P Steele Prize by the American Mathematical Society:
... for a
seminal contribution to research.