Katie Howell
Ellsworth High
School
11/22/02
Calculus
John Forbes Nash
John Forbes Nash was born in Bluefield, West Virginia June 13, 1928. He is the son of John Forbes, Sr. and Margaret
Virginia Martin. Although John’s schoolteachers never saw his extraordinary
talent, his parents encouraged him, and he learned much at home. He attended
college first at Carnegie Tech. in Pittsburgh, and then went on to Princeton. John contributed to and solved many mathematical theories and won a
Nobel Prize in 1994, and though he has faced mental illness, still hopes to
contribute to the world of mathematics.
John’s parents helped him
become the mathematician he is. His father was an electrical engineer and a
veteran of WW1. He moved to Bluefield
from Texas to work for the Appalachian Electric Company. His
mother was born in Bluefield and was a teacher for 10 years before marrying John,
Sr. She lost her hearing later in life because of a scarlet fever infection she
had while she was studying at West Virginia University. John and Margaret, called Virginia, also bore a girl, Martha, two years after John.
While Martha was a “normal”
child, playing with her cousins and friends, John was introverted and preferred
playing with his toy airplanes and matchbox cars. His parents bought him a Compton’s Picture Encyclopedia, which he read and learned a
lot from as a child. His mother encouraged his studies both by watching that he
did his schoolwork and by teaching him herself. In high school, John was
reading “Men of Mathematics” by E. T. Bell, solving theorems, and performing
chemistry experiments, as well as taking supplementary math courses at Bluefield College. At this time, John planned to become an electrical
engineer like his father.
However, when John started
college at Carnegie Tech on a full scholarship, the George Westinghouse
Scholarship, he soon realized that he did not like the requirements for
chemical engineering major. After switching to chemistry, he found that it did
not fit his interests either, and at the encouragement of the mathematical
faculty, he switched to a math major. It was there, after a course in
“International Economics,” that he wrote a paper, “The Bargaining Problem,”
which led to his interest in game theory. He was so advanced that as well as his
B.S., he received his M.S. when he graduated.
Both Princeton and Harvard offered John fellowships to enter as a graduate student,
but John chose Princeton. The offer from Princeton was more generous, and they seemed to want him more. The location was
also closer. John’s studies there gained on previous studies, and he began to
study the game theories by von Nuemann and Morgenstein. He then developed the
idea of “Non -Cooperative Games” and worked on discoveries of manifolds and
real algebraic values. John earned his doctorate at age 22 and stayed and
taught at Princeton until he accepted a job of instructorship at M.I.T.
The theory of games is
concerned with the study of the best strategies to maximize pay-offs, given the
risks involved in judging the responses of adversaries, and the conditions
under which there is a unique solution (i.e. that the optimum strategy for X
and that of Y are both possible and not inconsistent). The Nash equilibrium is
a concept central to game theory, which characterizes any situation where all
the participants in a game are pursuing their best possible strategy given the
strategies of all the other participants. This theory is based on the idea that
one can maximize their pay-offs by not only looking at what is best for them,
but by looking at what is good for them and their opponent. The players will
not change their policy and still get what they want. John drew the important
distinction between cooperative games and non-cooperative games, where players
have contrary interests and are unable to make agreements to maximize joint
welfare. He outlined the equilibrium notion, in which all players' expectations
are satisfied, and all players' strategies are the best for them. It was for
this work that John jointly won the Novel Prize for Economics in 1994 with John
Harsanyi and Reinhard Selten.
John remained at his M.I.T.
job from 1951-1959. In this time he solved a problem relating to differential
geometry, proving the isometric embed ability of abstract Riemannian manifolds
in flat spaces. As well as writing Algebraic Manifolds, he also studied a
problem involving partial differential equations, and although he did solve it,
so did another. Ennio de Giorgi of Pisa,
Italy, was working on the problem as well, and de Giorgi
solved it first. In addition to his studies, John also married physics major at
M.I.T., Alicia.
It was in this time that John
began having problems with his thinking. Psychologists later diagnosed him with
schizophrenia. Beginning in 1959, the problems came at a time when Alicia was
pregnant. Alicia put him in the McLean hospital for observation, and afterward John traveled
to Europe. Doctors hospitalized him many times, until he began
to get better, and then he began mathematical work once again. Although he and
Alicia divorced, she took care of him after his hospitalizations, and they
remarried 50 years after their first wedding day. John continues trying to aide
the studies of mathematics despite his age, and when he was 66 years old, he
said, “I am still making the effort and it is conceivable that with the gap
period of about 25 years of partial deluded thinking providing a sort of
vacation my situation my be atypical. Thus I have hopes of being able to
achieve something of value through my studies or with any new ideas that come
in the future.”
BIBLIOGRAPHY
John F. Nash -
Autobiography. Nobel e-Museum. 10 Nov. 2002
<http://www.nobel.se/economics/laureates/1994/nash-autobio.html>.
Nash equilibrium. xrefer. 10 Nov. 2002 http://xrefer.com/entry.jsp?xrefid=445856.
Nash, John F. xrefer. 10 Nov. 2002 http://xrefer.com/entry/445855.
“The Mysterious West Virginia Genius”
John Forbes Nash
“I don’t like people much and they don’t like me.”