John Nash revolutionised the mathematical field of game theory. He was endowed with a mind that was highly original and deeply troubled. But it became known to most people by its Hollywood description: he was a Nobel laureate whose descent into and recovery from mental illness inspired the Academy Award-winning film A Beautiful Mind.
By the time Nash emerged from his illness, his ideas had influenced economics, foreign affairs, politics, biology – virtually every sphere of life fuelled by competition. But he had been absent from professional life for so long that some scholars assumed that he was dead.
“We helped lift him into the daylight,” Assar Lindbeck, the former chairman of the committee for the Nobel Prize in Economics, told Sylvia Nasar, Nash’s biographer. “We resurrected him in a way.”
Nasar’s book, A Beautiful Mind, was published in 1998 and adapted for the screen three years later. The film, although criticised by some viewers for presenting a romanticised version of the mathematician’s life, won four Oscars, including one for best picture. Nash, portrayed by Russell Crowe in the film, became an international celebrity – perhaps the most famous mathematician in recent memory.
Modern game theory was first articulated by the mathematician John von Neumann and the economist Oskar Morgenstern in the 1944 volume Theory of Games and Economic Behavior. Its objective was to understand and ultimately predict the interactions between rivals in given circumstances. During the Cold War stand-off between the US and the Soviet Union, game theory became increasingly fashionable – and immensely useful.
Von Neumann and Morgenstern had assumed the existence of a “zero-sum” game such as draughts, in which one party’s loss was the adversary’s gain. Nash – who, ironically, was said to have struggled since childhood with social interactions – observed that few human rivalries function in so simple a fashion.
He expanded game theory to include cooperative games (in which binding agreements can be made) and non-cooperative games (in which they cannot), and to allow for the possibility of mutual gain. Such an outcome became known as the Nash equilibrium.
Nash equilibriums, which he described in the hieroglyphics of mathematical symbols, exist everywhere. Two magazines might charge the same price so that each may achieve maximum profit. Two rival nations might agree to arms treaties that limit each of their stockpiles, but guarantee both countries a measure of security.
The utility of Nash’s work had limitations. One is that rivals frequently do not fully know each other’s strategies, as his theories assumed. Another limitation is that in many cases, there is not a single possible outcome for a conflict, but rather many potential outcomes. Game theorists John Harsanyi and Reinhard Selten shared the 1994 Nobel Prize with Nash for contributions in those areas of the field. The prize citation recognised all three men for their “pioneering analysis”.
Nash was described as having insights before he could hammer out the proofs of their accuracy, the ideas coming to him more like revelations than scholarly findings. As early as 1958, Fortune magazine had ranked him among the greatest mathematicians of the era.
“Everyone else would climb a peak by looking for a path somewhere on the mountain,” Nasar quoted a former colleague as saying. “Nash would climb another mountain altogether and from a distant peak would shine a searchlight back on the first peak.”
His mental illness came on when he was about 30, during what might have been one of the richest periods of his career. Nash was working at the Massachusetts Institute of Technology and was studying quantum theory. As his condition worsened, Nash suffered delusions, hallucinations and had the impression that he was being hunted. Men wearing red ties, he came to believe, were part of a “crypto-Communist Party.”
He also thought that The New York Times was publishing messages from extraterrestrials and that he could understand them – and he once gave a student an intergalactic driver’s license, Nasar wrote.
At one point, he declined a prestigious appointment at the University of Chicago because he believed that he was in line to become emperor of Antarctica. At another point, he concluded that he was a “messianic figure of great but secret importance” and searched numerals – once the object of his brilliance – for hidden messages.
“I felt like I might get a divine revelation by seeing a certain number; a great coincidence could be interpreted as a message from heaven,” Nash said years later in the PBS documentary A Brilliant Madness.
He let his hair grow long. He travelled abroad and attempted to give up his US citizenship, and at various times considered himself a Japanese shogun, the Biblical figure Job and a Palestinian refugee, among other identities.
During one of his stays in mental institutions, a former colleague came for a visit. “How could you, a mathematician devoted to reason and logical proof... believe that extraterrestrials are sending you messages?” he asked. “Because,” Nash responded, “the ideas about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”
John Forbes Nash Jr. was born in 1928, in Bluefield, West Virginia. His father was an electrical engineer and his mother was an English and Latin teacher.
John Jr. was a precocious child and acquired a nickname: “Big Brains”. His family encouraged him during his education – although he recalled in his Nobel biographical sketch the need to “learn from the world’s knowledge rather than from the knowledge of the immediate community.”
In 1945, he enrolled at what is now Carnegie Mellon University in Pittsburgh and completed his undergraduate work after switching from chemical engineering to chemistry and finally to mathematics.
So great was his progress that he received a master’s degree in addition to his bachelor’s degree, both in mathematics, upon his graduation in 1948. He then moved to Princeton University, where, as a second-year student, he wrote the thesis that became the intellectual underpinning of his contributions to game theory.
Nash was “handsome as a god”, a former classmate told Nasar, but deeply unusual. He would ride a bicycle around in figure-of-eights – and he joined a group of students who carried on the long tradition at Princeton of playing complex games, and even invented a game of his own.
Nash received his doctorate in 1950, joined the MIT faculty and soon took a research position at the Rand Corp. in California. In that period of his career, he untangled what he described as a “classical unsolved problem” related to differential geometry and to general relativity.
Also during that period, Nash met Eleanor Stier, a nurse with whom he had a son, John David Stier, in 1953. A year later, Nash was arrested for indecent exposure in a men’s toilet in Santa Monica, California, and was immediately dismissed from Rand. According to Nasar’s biography, he denied that he was gay, showing a picture of Stier and their infant son – although Nash had left Stier when he found out about the pregnancy – to Rand officials as evidence.
He then returned to MIT, where he met Alicia Larde, a physics student from El Salvador, and they married in 1957. Shortly thereafter, Alicia became pregnant with their son, John Charles Martin Nash, and Nash began to show signs of mental instability.
During his illness, Nash and Alicia divorced, and he moved in and out of hospitals, enduring dangerous treatments that included insulin coma therapy. Alicia later took him into her home and cared for him even though they were no longer married.
He spent much of his time on the Princeton campus, where some recognised him as the genius that he was. Others knew him as “the Ghost of Fine Hall”, a reference to the building that houses the mathematics department. He seemed to have overcome his illness, and he remarried Alicia in 2001.
The couple were in a taxi on the New Jersey turnpike when their driver lost control while overtaking. The driver survived the crash.
John Forbes Nash, mathematician: born Bluefield, West Virginia 13 June 1928; Nobel Prize in Economics 1994; married 1957 Alicia Larde (marriage dissolved, one son; remarried 2001, died 2015); died New Jersey 23 May 2015.
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