WASHINGTON, May 24, 2015 — John and Alicia Nash died yesterday in a car accident on the New Jersey Turnpike. Nash was 86, and his wife was 82.
Nash was an extraordinary mathematician. He shared the 2015 Abel Prize for mathematics, which he received Tuesday from King Harald V in Norway with his colleague Louis Nirenberg for his work in nonlinear partial differential equations. The Abel Prize, which comes with an $800,000 cash award, is considered one of the most prestigious honors in mathematics.
While his later work in mathematics is profound, Nash is best remembered for his early work on game theory. It is impossible to earn an undergraduate degree in mathematics, economics, political science or ecology without hearing the term “Nash equilibrium,” a concept that springs from Nash’s work in non-cooperative game theory. It was not his most sophisticated work, but it was by far his most influential in disciplines outside of mathematics.
Nash’s work on game theory was required reading for students in my doctoral program in economics 25 years ago. Courses in game theory had become almost obligatory, and Nash’s name was invoked daily. Yet many of us were shocked in 1994 when he was announced as a recipient of the Nobel Memorial Prize in Economics for his work. The prize is not given posthumously, and we’d assumed he was dead.
The assumption arose from his absence from the professional economics journals in the decades after the late 1950s. We were completely unaware of Nash’s struggles with schizophrenia, his hospitalization and his slow return to sanity and productive mathematical scholarship. Every citation of his work in the economics literature was from work he did in the 1950s. For budding economists in 1990, Nash was a mythic figure from a distant past, as dead and gone as Caesar.
Nash was emphatically neither dead nor gone. His struggles were described in a 1998 best-seller, Sylvia Nasar’s A Beautiful Mind, which subsequently was made into a movie staring Russell Crowe. Nash was back and far more famous than a man of his genius would have been after a more conventional life.
In his 20s, Nash solved a series of problems that had until then been considered nearly intractable. Nasar recounts one particular episode that reveals much about the young John Nash. He was prone to harsh putdowns of his colleagues, and fellow mathematician Warren Ambrose was a favorite target. Nash loudly muttered “hack, hack” from the back of the room when Ambrose lectured and posted a sign announcing a “Seminar on REAL mathematics” to meet at the same time that Ambrose was teaching a graduate course in analysis in another room.
In response to the needling, Ambrose retorted, “If you’re so good, why don’t you solve the embedding problem for manifolds?” In response, writes Nasar, “Nash did.”
What Nash did was show that Riemannian manifolds can be embedded in three-dimensional spaces. That is, he showed how smooth objects in higher dimensions can be represented in three-dimensional space. This problem, while much less famous than the four-color map problem, was both tremendously difficult and profound. He solved it by introducing techniques that were both dazzlingly brilliant and utterly original. According to mathematician Jürgen Moser,
“The difficulty [that Levinson had pointed out], to anyone in his right mind, would have stopped them cold and caused them to abandon the problem. But Nash was different. If he had a hunch, conventional criticisms didn’t stop him. He had no background knowledge. It was totally uncanny. Nobody could understand how somebody like that could do it. He was the only person I ever saw with that kind of power, just brute mental power.”
According to Nasar,
“Geniuses, the mathematician Paul Halmos wrote, ‘are of two kinds: the ones who are just like all of us, but very much more so, and the ones who, apparently, have an extra human spark. We can all run, and some of us can run the mile in less than four minutes; there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue.’ Nash’s genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences. It wasn’t merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were non-rational. … even after he’d try to explain some astonishing result, the actual route he had taken remained a mystery to others who tried to follow his reasoning. …
“No one was more obsessed with originality, more disdainful of authority, or more jealous of his independence.”
Nash married Alicia Larde, a brilliant and beautiful physics student at MIT, in 1957, when he was 29. At 30 he was already one of the most important mathematicians of the 20th century, at the pinnacle of his powers and ready to storm the ramparts.
And then he went mad.
He spent the next 25 years in and out of hospitals, unable to hold a job, wandering around the Princeton campus leaving mathematical scribblings on blackboards, calling himself the “Prince of Peace.” Alicia divorced him, but she remained devoted to him, supporting him, caring for him and for their son, another talented mathematician diagnosed as schizophrenic. She remained at her ex-husband’s side until his astonishing spontaneous remission from the schizophrenia that nearly destroyed him, and they remarried.
Nash’s Nobel Prize came in 1994, soon after his disease lifted. He went on to pick up his life and his work, his mind once again brilliant.