Schizophrenic genius, and a Nobel laureate

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(INYT): John F Nash Jr, who was killed in a car crash along with his wife, was a mathematician who shared a Nobel Prize in 1994 for work that greatly extended the reach and power of modern economic theory and whose decades-long descent into severe mental illness and eventual recovery were the subject of a book and a 2001 film, both titled “A Beautiful Mind”.

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Nash and his wife, Alicia, were in a taxi on the New Jersey Turnpike when the driver lost control while trying to pass another car and hit a guardrail and another vehicle. Nash was regarded as one of the great mathematicians of the 20th century, for the originality of his thinking and for his fearlessness in wrestling problems so difficult that few others dared tackle th-em. A one-sentence letter written in support of his application to Princeton’s doctoral programme in math said, “This man is a genius.”

Nash’s theory of noncooperative games, published in 1950 and known as Nash equilibrium, provided a conceptually simple but powerful mathematical tool for analysing a wide range of competitive situations, from corporate rivalries to legislative decision making. Nash’s approach is now pervasive in economics and throughout the social sciences and is applied routinely in other fields, like evolutionary biology.

Harold W Kuhn, an emeritus professor of mathematics at Princeton and a longtime friend and colleague of Nash’s who died in 2014, said, “I think honestly that there have been really not that many great ideas in the 20th century in economics and maybe, among the top 10, his equilibrium would be among them.” An economist, Roger Myerson of the University of Chicago, went further, comparing the impact of Nash finding “to that of the discovery of the DNA double helix in the biological sciences.”

Nash also made contributions to pure mathematics that many mathematicians view as more significant than his Nobel-winning work on game theory, including solving an intractable problem in differential geometry derived from the work of the 19th century mathematician GFB Riemann. His achievements were the more remarkable, colleagues said, for being contained in a small handful of papers published before he was 30.
“Jane Austen wrote six novels, Bach wrote six partitas,” said Barry Mazur, a professor of mathematics at Harvard who was a freshman at the Massachusetts Institute of Technology when Nash taught there. “I think Nash’s pure mathematical contributions are on that level. Very, very few papers he wrote on different subjects, but the ones that had impact had incredible impact.”

Yet, to a wider audience, Nash was probably best known for his life story, a tale of dazzling achievement, devastating loss and almost miraculous redemption. The narrative of Nash’s brilliant rise, the lost years when his world dissolved in schizophrenia, his return to rationality and the awarding of the Nobel, retold in a biography by Sylvia Nasar and in the Oscar-winning film, captured the public mind and became a symbol of the destructive force of mental illness and the stigma that hounds those who suffer from it.

John Forbes Nash was born on June 13, 1928, in Bluefield, West Virginia. His father, John Sr, was an electrical engineer. His mother, Margaret, was a schoolteacher. As a child, John Nash may have been a prodigy, but he was not a sterling student, Nasar noted in a 1994 article in The New York Times. “He read constantly. He played chess. He whistled entire Bach melodies,” she wrote.

Receiving his bachelor’s and master’s degrees at Carnegie, he arrived at Princeton in 1948, a time of great expectations, when American children still dreamed of growing up to be physicists like Einstein or mathematicians like the brilliant, Hungarian-born polymath John von Neumann, both of whom attended the afternoon teas at Fine Hall, the home of the math department.

Nash, tall and good-looking, quickly became known for his intellectual arrogance, his odd habits – he paced the halls, walked off in the middle of conversations, whistled incessantly – and his fierce ambition, his colleagues recalled. He invented a game, known as Nash, that became an obsession in the Fine Hall common room (The same game, invented independently in Denmark, was later sold by Parker Bros as Hex). He also took on a problem left unsolved by von Neumann and Oskar Morgenstern, the pioneers of game theory, in their now classic book, “Theory of Games and Economic Behaviour.”

Von Neumann and Morgenstern, also an economist at Princeton, addressed only so-called zero-sum games, in which one player’s gain is another’s loss. But most real world interactions are more complicated, where players’ interests are not directly opposed, and there are opportunities for mutual gain. Nash’s solution, contained in a 27-page doctoral thesis, he wrote when he was 21, provided a way of analysing how each player could maximise his benefits, assuming that the other players would also act to maximise their self-interest.

This deceptively simple extension of game theory paved the way for economic theory to be applied to a wide variety of other situations besides the marketplace. In 1957, after two years of on-and-off courtship, he married Alicia Larde, an MIT physics major from an aristocratic Central American family.

Landscape of paranoia
But early in 1959, with Alicia pregnant with their son, John, Nash began to unravel. His brilliance turned malignant, leading him into a landscape of paranoia and delusion, and in April, he was hospitalised at McLean Hospital, outside Boston, sharing the psychiatric ward with, among others, the poet Robert Lowell.

It was the first step of a steep decline. There were more hospitalisations. He underwent electroshock therapy and fled for a while to Europe, sending cryptic postcards to colleagues and family members. For many years, he roamed the Princeton campus, a lonely figure scribbling unintelligible formulas on the same blackboards in Fine Hall where he had once demonstrated startling mathematical feats.

By the early 1990s, when the Nobel committee began investigating the possibility of awarding Nash its memorial prize in economics, his illness had quieted. He later said that he simply decided that he was going to return to rationality. “I emerged from irrational thinking, ultimately, without medicine other than the natural hormonal changes of ageing,” he wrote in an email to Kuhn in 1996.

Colleagues, including Kuhn, helped persuade the Nobel committee that Nash was well enough to accept the prize – he shared it with two economists, John C Harsanyi of the University of California at Berkeley, and Reinhard Selten of the Rheinische Friedrich-Wilhelms University in Bonn, Germany – and defended him when some questioned giving the prize to a man who had suffered from a serious mental disorder.

The Nobel, the publicity that attended it, and the making of the film were “a watershed in his life,” Kuhn said of Nash. “It changed him from a homeless unknown person who was wandering around Princeton to a celebrity, and financially, it put him on a much better basis.”

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