JOHN NASH
John Nash is an American mathematician whose work in many different fields, notably,
game theory, have proved hugely influential in areas such as market economics, biology,
artificial intelligence, computing, accounting, politics and military theory. He has received
many awards in recognition of his invaluable work, such as the Nobel Memorial Prize in
Economics, which he shared with two other mathematicians working in game theory as
well. Also, the Oscar winning 2001 film, A Beautiful Mind, was a biopic based on his life and
the schizophrenia that he suffered for a long time.
EARLY LIFE
John Forbes Nash Junior was born in Bluefield, Virginia in 1928. His father, whose name he
shares, was an electrical engineer for the Appalachian Power Company and his mother was
a schoolteacher.
In contrast to his father, who had a very unhappy childhood and had decided to pursue
electrical engineering as an escape from his fractured home life, John Nash, or Johnny as his
family called him, was surrounded by caring family members from an early age. For
example, his grandmother played the piano in her home and Nash always enjoyed listening
to her whenever they visited.
Nash showed little interest in fellow children and would often read by himself or play his
own games by himself as opposed to socialising with others. Both of his parents encouraged
his love of reading. His father would give him science books and encyclopaedias in place of
colouring books and his mother made sure that he received high-quality schooling, even
teaching him herself.
However, despite all this support, Nash did not excel in school. Due to his lack of social skills
he was labelled as backward by the teachers. It did not help that he was often very bored in
class and even did not have much of an interest in mathematics! Instead he enjoyed to do
scientific experiments at home, where he probably learned more than at school. It was not
until he read Men of Mathematics by E. T. Bell that he began to have a passion for maths.
This book sparked his interest in the subject and it was here that he realised that maths
could be more exciting than what he was taught at school.
When he entered Bluefield College in 1941 he took courses on mathematics and also
chemistry, a subject which he was very fond of. Many things quickly marked him out as
being different from his classmates. He enjoyed pulling pranks which often had a nasty edge
to them. He also dabbled in explosives, and this actually led to the death of a fellow pupil.
He also drew caricatures of pupils he disliked and even tortured animals for fun.
Despite all of this, he was accepted into the Carnegie Institute of Technology, where the
professors recognised his abilities in mathematics very early on. However, he still did not get
on very well with other students. One of them wrote “He was a country boy unsophisticated
even by our standards. He behaved oddly, playing the same 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.” Regardless of his social problems, his
professor’s heaped mountains of praise onto him and he eventually went to study in
Princeton University. He was also accepted into Harvard (which he was initially keen to
attend), Michigan and Chicago but he went to Princeton because he felt that they valued
him the most.
In Princeton he would write the paper on game theory that, 45 years later, would win him a
Nobel Prize, and is now hugely important in many areas of modern society, which I listed in
the opening paragraph.
CONTRIBUTIONS TO MATHEMATICS
In 1950 he published his thesis entitled Non-Cooperative Games. This was to prove hugely
influential. As the political scientist Peter Ordeshook said, “The concept of a Nash
equilibrium n-tuple is perhaps the most important idea in non-cooperative 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.”
In the summer of 1950, he year he received his doctorate, Nash began working for the
RAND Corporation (a company that seeks to help policymakers in the world to make
important decisions) where his knowledge of game theory proved invaluable in RAND’s
research into the Cold War. For the next couple of years, he worked for this company nowand-again, as they tried to apply his work in game theory to military and diplomatic strategy.
After his initial spell at RAND, he began to focus more on problems that were of a purely
mathematical nature. For example, he solved the problem regarding imbedding a
Riemannian manifold in Euclidean space (to be honest I don’t have a clue what that means,
but it was a major achievement in the mathematics community at the time). While this did
not have a practical application, as his work in game theory did, it was highly commendable
nevertheless.
Despite his mental illness which he suffered for many decades he still produced high quality
work. Currently he is working on advanced game theory and writing about the role of
money in society, in particular how people can be influenced by it.
JOHN NASH’S INFLUENCE AND AWARDS
John Nash was, in many ways, one of the most influential mathematicians of the 20th century.
His work in game theory remains hugely important in many areas which I have listed several
times above. His input in this field has proven invaluable for many individuals and companies
throughout the world.
Thankfully, Nash has received many awards in honour of his achievements. Most notably, as
I said in the opening paragraph, he won a Noble Memorial Prize in Economics. He narrowly
missed out on winning the Field’s Medal, a major maths award, but he was discounted for the
prize due to his paranoid schizophrenia. For his discovery of what is now known as the Nash
Equilibria he received the John von Neumann Theory Prize in 1994. More recently, he won
the Double Helix Medal in 2010.
MENTAL ILLNESS
Excluding his extraordinary work in maths, what is perhaps the defining factor of Nash’s later
life is the mental disorders that he suffered for many years.
Although he had always been a bit odd, it was not until his later life that people began to
notice increasingly stranger behaviour. For example, one time he disappeared for several
weeks leaving a graduate in charge of his class at MIT. When he returned he wandered around
with a copy of the New York Times saying that it contained a secret message from outer space
meant only for him. It was only after several days that the students realised that this was not
an elaborate practical joke.
Nash was eventually diagnosed with paranoid schizophrenia and spent most of the next
several decades on drugs to treat it, in a mental institution or often both. Thankfully, in the
late 90s he began to show signs of recovery and nowadays his mental issues are more or less
gone.
A BEAUTIFUL MIND
This was the title of the 2001 film based on Nash’s life. It was directed by Ron Howard and
had Russell Crowe playing Nash. It in particular focused on his schizophrenia. It also won a
slew of Oscars, including Best Picture and Best Director. I think that proves that not all
mathematicians are dry and boring!