Mathematical genius who battled demons

John Forbes Nash was far more than just a character played by Russell Crowe in a Hollywood film. He was a mathematical genius who emerged with his genius intact from a bout of mental illness

MANY people would know the name John Forbes Nash as the central character from the Russell Crowe film A Beautiful Mind. But Nash, who died this week in a car accident, was one of the greatest minds applied to mathematics and in particular the field of game theory, which is the study of how people make interdependent decisions and is particularly useful in economics.

While the film focuses more on Nash’s dark periods of mental illness, and fudges some of the biographical details and explanations of his work, as Hollywood is wont to do, it did at least make the world aware of his particular kind of genius. A genius that recovered from a bout with paranoid schizophrenia to continue to make contributions to mathematics.

Nash was born in Bluefield, West Virginia in 1928, the son of John Forbes Nash senior, who had a degree in electrical engineering and worked for the Appalachian Electric Power Company. His mother, daughter of a physician, also had a degree and was a schoolteacher before she married.

With such a strong family tradition of higher education, young Nash was stimulated intellectually by his parents and their impressive library. At school he was recognised as being of high intelligence, but encountered resistance because he could see ways of solving problems that were different to those being offered by his teachers.

John Nash with his wife Alicia in 2012. Picture: Getty Images

Although he had been determined to follow his father’s career path in electrical engineering he signed up for chemical engineering when he went to Carnegie Institute of Technology on a full scholarship in 1945. He later switched to mathematics, thanks to encouragement from professors who recognised his genius for the discipline.

While at Carnegie he took an elective class on economics that resulted in a paper on The Bargaining Problem, looking at the outcomes of a game of two players who must bargain for a share of a prize.

He was recommended for the doctoral program at Princeton which he began in 1948. At Princeton he invented a game using hexagonal pieces that he played with other students. They called it Nash, but Parker Brothers later brought out a version they called Hex.

Gaining his PhD in 1950, in 1951 he went to the Massachusetts Institute of Technology (MIT), where he solved a classical unsolved problem relating to Euclidean geometry. In 1952 he had a relationship with a nurse named Eleanor Stier but left her when he found out she was pregnant. She gave birth to a son she named John David Stier.

John Nash talks to reporters at Princeton university after being awarded the Nobel Prize for economics in 1994.

Triumph turned to disappointment in 1956 when he discovered that his solution to a mathematical problem involving differential equations had already been solved by Italian mathematician Ennio de Giorgi. In 1957, while on a sabbatical, he married Alicia Lopez-Harrison de Larde, a physics graduate he had met at MIT.

But some time in 1958-59 the brilliant mind that had made him such a respected academic began to go awry. He started telling colleagues that he was receiving messages from space, wrote letters to ambassadors and the UN saying he was forming a world government and became worried that men with red ties around campus were part of a communist conspiracy.

He was hospitalised for a time and when he was released travelled to Europe, attempting to renounce his US citizenship to have himself declared the first citizen of the world.

He was deported to the US, returning to Princeton, where his bizarre behaviour resulted in another period of hospitalisation.

His son was born in 1960, also named John, but he and Alicia divorced in 1963. Through the rest of the ’60s into the ’70s he would alternate between delusions and periods of lucidity. Living with his ex-wife again in the ’70s, he began to recognise and reject the delusional thinking. Eventually he was able to return to teaching and research. In 1978 he was awarded the John von Neumann Prize for his work on equilibrium.

In 1994 he shared a Nobel prize with John C. Harsanyi and Reinhard Selten “for their pioneering analysis of equlibria in the theory of noncooperative games.”

He and Alicia remarried in 2001. Both were killed on May 23 when the driver lost control of the taxi in which they were passengers. 

NASH ON CROWE’S MOVIE

Nash didn’t regard the film A Beautiful Mind, in which he was played by Russell Crowe (pictured), as giving “accurate information about me as a person” but said it was interesting and helpful as a depiction of how there might be a “favourable outcome” in a case of a person suffering mental illness. He said it was inaccurate in describing his case because it depicted him as still dependent on medicines after many years of mental illness when in reality he had weaned himself off the drugs.

Russell Crowe in A Beautiful Mind (2002).