John Nash Obit

John F. Nash Jr., a mathematician who shared a Nobel Prize in 1994 for work that

greatly extended the reach and power of modern economic theory and whose long

descent into severe mental illness and eventual recovery were the subject of a book

and a film, both titled A Beautiful Mind, was killed, along with his wife, in a car

crash on Saturday in New Jersey. He was 86.

Dr. Nash and his wife, Alicia, 82, were in a taxi on the New Jersey Turnpike in

Monroe Township around 4:30 p.m. when the driver lost control while veering from

the left lane to the right and hit a guardrail and another car, Sgt. Gregory Williams of

the New Jersey State Police said.

The couple were ejected from the cab and pronounced dead at the scene. The

State Police said it appeared that they had not been wearing seatbelts. The taxi driver

and the driver of the other car were treated for injuries. No criminal charges had

been filed on Sunday.

The Nashes were returning home from the airport after a trip to Norway, where

Dr. Nash and Louis Nirenberg, a mathematician from New York University, had

received the Abel Prize from the Norwegian Academy of Science and Letters.

Dr. Nash was widely regarded as one of the great mathematicians of the 20th

century, known for the originality of his thinking and for his fearlessness in wrestling

down problems so difficult that few others dared tackle them. A one-sentence letter

written in support of his application to Princetons doctoral program in math said

simply, This man is a genius.

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Johns remarkable achievements inspired generations of mathematicians,

economists and scientists, the president of Princeton, Christopher L. Eisgruber,

said on Sunday, and the story of his life with Alicia moved millions of readers and

moviegoers, who marveled at their courage in the face of daunting challenges.

Russell Crowe, who portrayed Dr. Nash in the 2001 film adaptation of A

Beautiful Mind, posted on Twitter that he was stunned by the deaths. An

amazing partnership, he wrote. Beautiful minds, beautiful hearts.

Dr. Nashs theory of noncooperative games, published in 1950 and known as

Nash equilibrium, provided a conceptually simple but powerful mathematical tool

for analyzing a wide range of competitive situations, from corporate rivalries to

legislative decision-making. Dr. Nashs approach is now pervasive in economics and

throughout the social sciences and applied in other fields as well, including

evolutionary biology.

Harold W. Kuhn, an emeritus professor of mathematics at Princeton and a

longtime friend and colleague of Dr. Nashs who died in 2014, once 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. A

University of Chicago economist, Roger Myerson, went further, comparing the

impact of the Nash equilibrium on economics to that of the discovery of the DNA

double helix in the biological sciences.

Dr. Nash also made contributions to pure mathematics that many

mathematicians view as more significant than his Nobel-winning work on game

theory. In one he solved an intractable problem in differential geometry derived

from the work of the 19th century mathematician G. F. B. Riemann.

His achievements were the more remarkable, colleagues said, for being

presented in papers published before he was 30.

Jane Austen wrote six novels, said Barry Mazur, a professor of mathematics at

Harvard who was a freshman at M.I.T. when Dr. Nash taught there. I think Nashs

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.

To a wider audience Dr. Nash was probably best known for his life story, one of

dazzling achievement, devastating loss and almost miraculous redemption. The tale

of Dr. Nashs brilliant rise, the years lost to schizophrenia, his return to rationality

and his receiving the Nobel retold in a biography by Sylvia Nasar and in the Oscar-



winning film, which also starred Jennifer Connelly as Alicia Nash captured the

public mind as a portrait of the destructive force of mental illness and the stigma

that can hound those who suffer from it.

Arrogant, Ambitious and Odd

John Forbes Nash was born on June 13, 1928, in Bluefield, W.Va. His father,

John Sr., was an electrical engineer. His mother, Margaret, was a Latin teacher.

As a child, John Nash may have been a prodigy, but he was not a sterling

student, Ms. Nasar noted in a 1994 article in The New York Times. He read

constantly. He played chess. He whistled entire Bach melodies, she wrote.

In high school he stumbled across E. T. Bells book Men of Mathematics, and

soon demonstrated his own mathematical skill by independently proving a classic

Fermat theorem, an accomplishment he recalled in an autobiographical essay

written for the Nobel committee.

Intending to become an engineer like his father, he entered Carnegie Mellon

University (then called Carnegie Institute of Technology) in Pittsburgh. But he

chafed at the regimentation of the coursework and switched to mathematics,

encouraged by professors who recognized his mathematical genius.

Receiving his bachelors and masters degrees from Carnegie, he arrived at

Princeton in 1948. It was 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.

John Nash, tall and good-looking, became known for his intellectual arrogance,

his odd habits he paced the halls, walked off in the middle of conversations and

whistled incessantly and his fierce ambition, his colleagues have 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 Brothers as Hex.) He also took on a problem left unsolved by Dr. von

Neumann and Oskar Morgenstern, the pioneers of game theory, in their now-classic

book, Theory of Games and Economic Behavior.

Dr. von Neumann and Dr. Morgenstern, an economist at Princeton, addressed

only so-called zero-sum games, in which one players gain is anothers loss. But most

real-world interactions are more complicated; players interests are not directly

opposed, and there are opportunities for mutual gain. Dr. Nashs solution, contained



in a 27-page doctoral thesis he wrote when he was 21, provided a way of analyzing

how each player could maximize his benefits, assuming that the other players would

also act to maximize their self-interest.

This deceptively simple extension of game theory paved the way for economic

theory to be applied to an array of situations besides the marketplace.

It was a very natural discovery, Dr. Kuhn said. A variety of people would have

come to the same results at the same time, but John did it and he did it on his own.

Brilliance Turns Malignant

After receiving his doctorate at Princeton, Dr. Nash worked as a consultant to

the RAND Corporation and as an instructor at M.I.T. while continuing to attack

problems that no one else could solve. On a dare, he developed an entirely original

approach to a longstanding problem in differential geometry, showing that abstract

geometric spaces called Riemannian manifolds could be squished into arbitrarily

small pieces of Euclidean space.

As his career flourished and his reputation grew, however, Dr. Nashs personal

life became increasingly complex. A turbulent romance in Boston with a nurse,

Eleanor Stier, resulted in the birth of a son, John David Stier, in 1953. Dr. Nash also

had a series of relationships with men, and while at RAND in the summer of 1954 he

was arrested in a mens bathroom for indecent exposure, according to Ms. Nasars

biography. And doubts about his accomplishments gnawed at him: Two of

mathematics highest honors, the Putnam Competition and the Fields Medal, had

eluded him.

In 1957, after two years of on-and-off courtship, he married Alicia Larde, an

M.I.T. physics major from an aristocratic Central American family and one of only 16

women in the class of 1955.

He was very, very good looking, very intelligent, Ms. Nash told Ms. Nasar. It

was a little bit of a hero-worship thing.

But early in 1959, with his wife pregnant with their son, John, Dr. Nash began to

unravel. His brilliance turned malignant, leading him into a landscape of paranoia

and delusion, and in April he was hospitalized 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 hospitalizations. Dr.

Nash 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 on which he had once demonstrated startling mathematical

feats.

Though game theory was gaining in prominence, and his work cited ever more

frequently and taught widely in economics courses around the world, Dr. Nash had

vanished from the professional world.

He hadnt published a scientific paper since 1958, Ms. Nasar wrote in the 1994

Times article. He hadnt held an academic post since 1959. Many people had heard,

incorrectly, that he had had a lobotomy. Others, mainly those outside of Princeton,

simply assumed that he was dead.

Indeed, Dr. Myerson recalled in a telephone interview that one scholar who

wrote to Dr. Nash in the 1980s to ask permission to reprint an article received the

letter back with one sentence scrawled across it: You may use my article as if I were

dead.

Reaching a Watershed

Still, Dr. Nash was fortunate in having family members, colleagues and friends

who protected him, got him work and in general helped him survive. Ms. Nash

divorced him in 1963, but continued to stand by him, taking him into her house to

live in 1970. (The couple married a second time in 2001.)

Ms. Nash supported her ex-husband and her son by working as a computer

programmer, with some financial help from family, friends and colleagues.

By the early 1990s, when the Nobel committee began investigating the

possibility of awarding Dr. Nash its memorial prize in economics, his illness had

quieted. He later said that he had 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 aging, he wrote in an email to Dr. Kuhn in

1996.

Colleagues, including Dr. Kuhn, helped persuade the Nobel committee that Dr.

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 they 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, Dr. Kuhn said of Dr. 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.

Dr. Nash is survived by his sons, John David Stier and John Charles Martin

Nash, and a sister, Martha Nash Legg.

He continued to work, traveling and speaking at conferences and trying to

formulate a new theory of cooperative games. Friends described him as charming

and diffident, socially awkward, a little quiet, with scant trace of the arrogance of his

youth.

You dont find many mathematicians approaching things this way now,

barehandedly attacking a problem, the way Dr. Nash did, Dr. Mazur said.

Correction: May 24, 2015

An earlier version of this obituary misstated the title of a book by E.T. Bell. It is

Men of Mathematics, not Men and Mathematics. It also misstated the poet with

whom Dr. Nash spent time in the psychiatric ward at McLean Hospital. It was

Robert Lowell, not Ezra Pound.

Michael Schwirtz and Ashley Southall contributed reporting.



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