John F. Nash Jr., a mathematician who shared a Nobel 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.

r. 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 Princeton’s doctoral program in math said simply, “This man is a genius.”

“John’s 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. Nash’s 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. Nash’s 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. Nash’s 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 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.”

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. Nash’s brilliant rise, the years lost to schizophrenia, his return to rationality and his receiving the Nobel Memorial Prize in Economic Sciences — 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. Bell’s 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 bachelor’s and master’s 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, primarily addressed so-called zero-sum games, in which one player’s gain is another’s loss. But most real-world interactions are more complicated; players’ interests are not directly opposed, and there are opportunities for mutual gain. Dr. Nash’s solution, contained in a 27-page doctoral thesis he wrote when he was 21, provided a way of predicting the possible outcome of a game with multiple players, in which each was acting to maximize 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. Nash’s 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 men’s bathroom for indecent exposure, according to Ms. Nasar’s 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 was injected with insulin 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 hadn’t published a scientific paper since 1958,” Ms. Nasar wrote in the 1994 Times article. “He hadn’t 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 don’t find many mathematicians approaching things this way now, barehandedly attacking a problem,” the way Dr. Nash did, Dr. Mazur said.

**___________________________________________________________________________________**

**John Forbes Nash, Jr.**(June 13, 1928 – May 23, 2015) was an American mathematician with fundamental contributions in game theory, differential geometry, and partial differential equations.

^{[2]}

^{[3]}Nash's work has provided insight into the factors that govern chance and decision making inside complex systems in daily life.

His theories are used in economics, computing, evolutionary biology, artificial intelligence, accounting, computer science,games of skill, politics and military theory. Serving as a Senior Research Mathematician at Princeton University during the latter part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Seltenand John Harsanyi. In 2015, he was awarded the Abel Prize for his work on nonlinear partial differential equations.

In 1959, Nash began showing clear signs of mental illness, and spent several years at psychiatric hospitals being treated for paranoid schizophrenia. After 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s.

^{[4]}His struggles with his illness and his recovery became the basis for Sylvia Nasar's biography,*A Beautiful Mind*, as well as a film of the same name starring Russell Crowe.^{[5]}^{[6]}^{[7]}
On May 23, 2015, Nash and his wife Alicia Nash were killed in a car crash while riding in a taxi on the New Jersey Turnpike.

## Contents

[hide]## Early life and education[edit]

Nash was born on June 13, 1928, in Bluefield, West Virginia, United States. His father, John Forbes Nash, was an electrical engineer for the Appalachian Electric Power Company. His mother, Margaret Virginia (née Martin) Nash, had been a schoolteacher before she married. He was baptized in the Episcopal Church.

^{[8]}He had a younger sister, Martha (born November 16, 1930).
Nash attended kindergarten and public school, and he learned from books provided by his parents and grandparents.

^{[9]}Nash's parents pursued opportunities to supplement their son's education, and arranged for him to take advancedmathematics courses at a local community college during his final year of high school. He attended Carnegie Institute of Technology through a full benefit of the*George Westinghouse Scholarship*, initially majoring in chemical engineering. He switched to a chemistry major and eventually, at the advice of his teacher John Lighton Synge, to mathematics. After graduating in 1948 with both a B.S. and M.S. in mathematics, Nash accepted a scholarship to Princeton University, where he pursued further graduate studies in mathematics.^{[9]}
Nash's adviser and former Carnegie professor Richard Duffin wrote a letter of recommendation for Nash's entrance to Princeton stating, "He is a mathematical genius."

^{[10]}^{[11]}Nash was accepted at Harvard University, however, the chairman of the mathematics department at Princeton,Solomon Lefschetz, offered him the John S. Kennedy fellowship, convincing Nash that Princeton valued him more.^{[12]}Further, he considered Princeton more favorably because of its proximity to his family in Bluefield.^{[9]}At Princeton, he began work on his equilibrium theory, later known as the Nash equilibrium.^{[citation needed]}## Major contributions[edit]

### Game theory[edit]

Nash earned a Ph.D. degree in 1950 with a 28-page dissertation on non-cooperative games.

^{[13]}^{[14]}The thesis, which was written under the supervision of doctoral advisor Albert W. Tucker, contained the definition and properties of the Nash equilibrium. A crucial concept in non-cooperative games, it won Nash the Nobel Memorial Prize in Economic Sciences in 1994.
Publications authored by Nash relating to the concept are in the following papers:

- Nash, John Forbes (1950). "Equilibrium Points in N-person Games".
*Proceedings of the National Academy of Sciences***36**(1): 48–49.doi:10.1073/pnas.36.1.48. MR 0031701. PMC 1063129. PMID 16588946. - Nash, John Forbes (1950). "The Bargaining Problem" (PDF).
*Econometrica***18**(2): 155–62. doi:10.2307/1907266. JSTOR 1907266. MR 0035977. - Nash, John Forbes (1951). "Non-cooperative Games" (PDF).
*Annals of Mathematics***54**(2): 286–95. doi:10.2307/1969529. JSTOR 1969529. MR 0043432. - Nash, John Forbes (1953). "Two-person Cooperative Games" (PDF).
*Econometrica***21**(1): 128–40. doi:10.2307/1906951. MR 0053471.

### Other mathematics[edit]

Nash did groundbreaking work

^{[citation needed]}in the area of real algebraic geometry:- Nash, John Forbes (1952). "Real algebraic manifolds".
*Annals of Mathematics***56**(3): 405–21. doi:10.2307/1969649. JSTOR 1969649. MR 0050928. See"Proc. Internat. Congr. Math". AMS. 1952. pp. 516–17.

His work in mathematics includes the Nash embedding theorem, which shows that every abstract Riemannian manifold can be isometrically realized as a submanifoldof Euclidean space. He also made significant contributions to the theory of nonlinear parabolic partial differential equations and to singularity theory.

John Milnor gives a list of 21 publications.

^{[15]}
In the Nash biography,

*A Beautiful Mind*, author Sylvia Nasar explains that Nash was working on proving Hilbert's nineteenth problem, a theorem involving elliptic partial differential equations when, in 1956, he suffered a severe disappointment. He learned that an Italian mathematician, Ennio de Giorgi, had published a proof just months before Nash achieved his proof. Each took different routes to get to their solutions. The two mathematicians met each other at the Courant Institute of Mathematical Sciences of New York University during the summer of 1956. It has been speculated that if only one had solved the problem, he would have been given the Fields Medal for the proof.^{[9]}
In 2011, the National Security Agency declassified letters written by Nash in the 1950s, in which he had proposed a new encryption–decryption machine.

^{[16]}The letters show that Nash had anticipated many concepts of modern cryptography, which are based on computational hardness.^{[17]}## Mental illness[edit]

Nash's mental illness first began to manifest in the form of paranoia; his wife later describing his behavior as erratic. Nash seemed to believe that all men who wore red ties were part of a communist conspiracy against him; Nash mailed letters to embassies inWashington, D.C., declaring that they were establishing a government.

^{[4]}^{[18]}Nash's psychological issues crossed into his professional life when he gave an American Mathematical Society lecture at Columbia University in 1959. Originally intended to present proof of theRiemann hypothesis, the lecture was incomprehensible. Colleagues in the audience immediately realized that something was wrong.^{[19]}
He was admitted to McLean Hospital in April 1959, staying through May of the same year. There, he was diagnosed with paranoid schizophrenia. According to the

*Diagnostic and Statistical Manual of Mental Disorders*, or DSM, a person suffering from the disorder is typically dominated by relatively stable, often paranoid, fixed beliefs that are either false, over-imaginative or unrealistic, and usually accompanied by experiences of seemingly real perception of something not actually present. Further signs are marked particularly by auditory and perceptional disturbances, a lack of motivation for life, and mild clinical depression.^{[20]}^{[21]}
In 1961, Nash was admitted to the New Jersey State Hospital at Trenton.

^{[22]}Over the next nine years, he spent periods in psychiatric hospitals, where he received both antipsychotic medications and insulin shock therapy.^{[21]}^{[23]}^{[24]}
Although he sometimes took prescribed medication, Nash later wrote that he did so only under pressure. After 1970, he was never committed to a hospital again, and he refused any further medication. According to Nash, the film

*A Beautiful Mind*inaccurately implied he was taking what were the new atypical antipsychotics of the time period. He attributed the depiction to the screenwriter who was worried about the film encouraging people with the disorder to stop taking their medication.^{[25]}Journalist Robert Whitaker wrote an article suggesting recovery from illnesses like Nash's can be hindered by such drugs.^{[26]}
Nash felt psychotropic drugs were overrated and that the adverse effects were not given enough consideration once someone was deemed mentally ill.

^{[27]}^{[28]}^{[29]}According to Sylvia Nasar, author of the book*A Beautiful Mind*, on which the movie was based, Nash recovered gradually with the passage of time. Encouraged by his then former wife, de Lardé, Nash worked in a communitarian setting where his eccentricities were accepted. De Lardé said of Nash, "it's just a question of living a quiet life".^{[4]}
Nash dated the start of what he termed "mental disturbances" to the early months of 1959, when his wife was pregnant. He described a process of change "from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'".

^{[9]}For Nash, this included seeing himself as a messenger or having a special function of some kind, of having supporters and opponents and hidden schemers, along with a feeling of being persecuted and searching for signs representing divine revelation.^{[30]}Nash suggested his delusional thinking was related to his unhappiness, his desire to feel important and be recognized, and his characteristic way of thinking, saying, "I wouldn't have had good scientific ideas if I had thought more normally." He also said, "If I felt completely pressureless I don't think I would have gone in this pattern".^{[31]}He did not draw a categorical distinction between schizophrenia andbipolar disorder.^{[32]}Nash reported he did not hear voices until around 1964, and later engaged in a process of consciously rejecting them.^{[33]}He further stated he was always taken to hospitals against his will. He only temporarily renounced his "dream-like delusional hypotheses" after being in a hospital long enough to decide he would superficially conform – to behave normally or to experience "enforced rationality". Only gradually on his own did he "intellectually reject" some of the "delusionally influenced" and "politically oriented" thinking as a waste of effort. By 1995, however, even though he was "thinking rationally again in the style that is characteristic of scientists," he said he felt more limited.^{[9]}^{[34]}
Nash wrote in 1994:

## Recognition and later career[edit]

In 1978, Nash was awarded the John von Neumann Theory Prize for his discovery of non-cooperative equilibria, now called Nash Equilibria. He won the Leroy P. Steele Prize in 1999.

In 1994, he received the Nobel Memorial Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten) as a result of his game theory work as a Princeton graduate student. In the late 1980s, Nash had begun to use email to gradually link with working mathematicians who realized that he was

*the*John Nash and that his new work had value. They formed part of the nucleus of a group that contacted the Bank of Sweden's Nobel award committee and were able to vouch for Nash's mental health ability to receive the award in recognition of his early work.^{[35]}
Nash's later work involved ventures in advanced game theory, including partial agency, which show that, as in his early career, he preferred to select his own path and problems. Between 1945 and 1996, he published 23 scientific studies.

Nash has suggested hypotheses on mental illness. He has compared not thinking in an acceptable manner, or being "insane" and not fitting into a usual social function, to being "on strike" from an economic point of view. He has advanced views in evolutionary psychology about the value of human diversity and the potential benefits of apparently nonstandard behaviors or roles.

^{[36]}
Nash developed work on the role of money in society. Within the framing theorem that people can be so controlled and motivated by money that they may not be able to reason rationally about it, he criticized interest groups that promote quasi-doctrines based on Keynesian economics that permit manipulative short-term inflation anddebt tactics that ultimately undermine currencies. He suggested a global "industrial consumption price index" system that would support the development of more "ideal money" that people could trust rather than more unstable "bad money". He noted that some of his thinking parallels economist and political philosopher Friedrich Hayek's thinking regarding money and a nontypical viewpoint of the function of the authorities.

^{[37]}^{[38]}
Nash received an honorary degree, Doctor of Science and Technology, from Carnegie Mellon University in 1999, an honorary degree in economics from the University of Naples Federico II on March 19, 2003,

^{[39]}an honorary doctorate in economics from the University of Antwerp in April 2007, an honorary doctorate of science from the City University of Hong Kong on November 8, 2011,^{[1]}and was keynote speaker at a conference on game theory.^{[citation needed]}He has also been a prolific guest speaker at a number of world-class events, such as the Warwick Economics Summit in 2005 held at the University of Warwick. In 2012 he was elected as a fellow of the American Mathematical Society.^{[40]}On May 19, 2015, a few days before his death, Nash, along with Louis Nirenberg, was awarded the 2015 Abel Prize by King Harald V of Norway at a ceremony in Oslo.^{[41]}## Personal life[edit]

In 1951, Nash was hired by the Massachusetts Institute of Technology (MIT) as a C. L. E. Moore instructor in the mathematics faculty. About a year later, Nash began a relationship in Massachusetts with Eleanor Stier, a nurse he met while admitted as a patient. They had a son, John David Stier,

^{[1]}but Nash left Stier when she told him of her pregnancy.^{[42]}The film based on Nash's life,*A Beautiful Mind*, was criticized during the run-up to the 2002 Oscars for omitting this aspect of his life. He was said to have abandoned her based on her social status, which he thought to have been beneath his.^{[43]}
In 1954, while in his 20s, Nash was arrested for indecent exposure in a law enforcement sting operation focusing on homosexual behavior in Santa Monica, California. Although the charges were dropped, he was stripped of his top-secret security clearance and fired from RAND Corporation, where he had worked as a consultant.

^{[44]}
Not long after breaking up with Stier, Nash met Alicia Lopez-Harrison de Lardé (January 1, 1933 – May 23, 2015), a naturalized U.S. citizen from El Salvador. De Lardé graduated from MIT, having majored in physics.

^{[9]}They married in February 1957; although Nash was an atheist, the ceremony was performed in a Roman Catholicchurch.^{[45]}^{[46]}
In 1958, Nash earned a tenured position at MIT, and his first signs of mental illness were evident in early 1959. At this time, his wife was pregnant with their first child. He resigned his position as a member of the MIT mathematics faculty in the spring of 1959

^{[9]}and his wife had him admitted to McLean Hospital for treatment ofschizophrenia that same year. Their son, John Charles Martin Nash, was born soon afterward. The child was not named for a year^{[1]}because his wife felt Nash should have a say in the name given to the boy. Due to the stress of dealing with his illness, Nash and de Lardé divorced in 1963. After his final hospital discharge in 1970, Nash lived in de Lardé's house as a boarder. This stability seemed to help him, and he learned how to consciously discard his paranoid delusions.^{[47]}He stopped taking psychiatric medication and was allowed by Princeton to audit classes. He continued to work on mathematics and eventually he was allowed to teach again. In the 1990s, de Lardé and Nash resumed their relationship, remarrying in 2001.## Death[edit]

On May 23, 2015, John and Alicia Nash were killed in a collision on the New Jersey Turnpike near Monroe Township, New Jersey. They were on their way home after a visit to Norway, where Nash had received the Abel Prize. The driver of the taxicab in which they were riding from Newark Airport lost control of the vehicle and struck a guard rail. Both passengers were ejected from the car upon impact.

^{[48]}^{[49]}^{[50]}^{[51]}^{[52]}At the time of his death, Nash was 86 years old and a longtime resident of West Windsor Township, New Jersey.^{[53]}^{[54]}
Following his death, obituaries appeared in scientific and popular media throughout the world. In addition to their obituary for Nash,

^{[55]}*The New York Times*also published an article containing many notable quotes of Nash, assembled from diverse media and publications, providing his reflections on his life and achievements.^{[56]}## Representation in culture[edit]

At Princeton, Nash became known as "The Phantom of Fine Hall"

^{[57]}(Princeton's mathematics center), a shadowy figure who would scribble arcane equations on blackboards in the middle of the night. He is referred to in a novel set at Princeton,*The Mind-Body Problem*, 1983, by Rebecca Goldstein.^{[4]}
Sylvia Nasar's biography of Nash,

*A Beautiful Mind*, was published in 1998. A film by the same name was released in 2001, directed by Ron Howard with Russell Crowe playing Nash.## Awards[edit]

- 1978 – INFORMS John von Neumann Theory Prize
- 1994 – Nobel Memorial Prize in Economic Sciences
- 2010 – Double Helix Medal
^{[58]} - 2015 – Abel Prize
^{[59]}

_________________________________________________________________________________

# John Forbes Nash

### Born: 13 June 1928 in Bluefield, West Virginia, USADied: 23 May 2015 in New Jersey, USA

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**John F Nash**'s father, also called John Forbes Nash so we shall refer to him as John Nash Senior, was a native of Texas. John Nash Senior was born in 1892 and had an unhappy childhood from which he escaped when he studied electrical engineering at Texas Agricultural and Mechanical. After military service in France during World War I, John Nash Senior lectured on electrical engineering for a year at the University of Texas before joining the Appalachian Power Company in Bluefield, West Virginia. John F Nash's mother, Margaret Virginia Martin, was known as Virginia. She had a university education, studying languages at the Martha Washington College and then at West Virginia University. She was a school teacher for ten years before meeting John Nash Senior, and the two were married on 6 September 1924.

Johnny Nash, as he was called by his family, was born in Bluefield Sanitarium and baptised into the Episcopal Church. He was [2]:-

... a singular little boy, solitary and introverted ...

but he was brought up in a loving family surrounded by close relations who showed him much affection. After a couple of years Johnny had a sister when Martha was born. He seems to have shown a lot of interest in books when he was young but little interest in playing with other children. It was not because of lack of children that Johnny behaved in this way, for Martha and her cousins played the usual childhood games: cutting patterns out of books, playing hide-and-seek in the attic, playing football. However while the others played together Johnny played by himself with toy airplanes and matchbox cars.

His mother responded by enthusiastically encouraging Johnny's education, both by seeing that he got good schooling and also by teaching him herself. Johnny's father responded by treating him like an adult, giving him science books when other parents might give their children colouring books.

Johnny's teachers at school certainly did not recognise his genius, and it would appear that he gave them little reason to realise that he had extraordinary talents. They were more conscious of his lack of social skills and, because of this, labelled him as backward. Although it is easy to be wise after the event, it now would appear that he was extremely bored at school. By the time he was about twelve years old he was showing great interest in carrying out scientific experiments in his room at home. It is fairly clear that he learnt more at home than he did at school.

Martha seems to have been a remarkably normal child while Johnny seemed different from other children. She wrote later in life (see [2]):-

Johnny was always different.[My parents]knew he was different. And they knew he was bright. He always wanted to do things his way. Mother insisted I do things for him, that I include him in my friendships. ... but I wasn't too keen on showing off my somewhat odd brother.

His parents encouraged him to take part in social activities and he did not refuse, but sports, dances, visits to relatives and similar events he treated as tedious distractions from his books and experiments.

Nash first showed an interest in mathematics when he was about 14 years old. Quite how he came to read E T Bell's

*Men of Mathematics*is unclear but certainly this book inspired him. He tried, and succeeded, in proving for himself results due to Fermat which Bell stated in his book. The excitement that Nash found here was in contrast to the mathematics that he studied at school which failed to interest him.
He entered Bluefield College in 1941 and there he took mathematics courses as well as science courses, in particular studying chemistry, which was a favourite topic. He began to show abilities in mathematics, particularly in problem solving, but still with hardly any friends and behaving in a somewhat eccentric manner, this only added to his fellow pupils view of him as peculiar. He did not consider a career in mathematics at this time, however, which is not surprising since it was an unusual profession. Rather he assumed that he would study electrical engineering and follow his father but he continued to conduct his own chemistry experiments and was involved in making explosives which led to the death of one of his fellow pupils. [2]:-

Boredom and simmering adolescent aggression led him to play pranks, occasionally ones with a nasty edge.

He caricatured classmates he disliked with weird cartoons, enjoyed torturing animals, and once tried to get his sister to sit in a chair he had wired up with batteries.

Nash won a scholarship in the George Westinghouse Competition and was accepted by the Carnegie Institute of Technology (now Carnegie-Mellon University) which he entered in June 1945 with the intention of taking a degree in chemical engineering. Soon, however, his growing interest in mathematics had him take courses on tensor calculus and relativity. There he came in contact with John Synge who had recently been appointed as Head of the Mathematics Department and taught the relativity course. Synge and the other mathematics professors quickly recognised Nash's remarkable mathematical talents and persuaded him to become a mathematics specialist. They realised that he had the talent to become a professional mathematician and strongly encouraged him.

Nash quickly aspired to great things in mathematics. He took the William Lowell Putnam Mathematics Competition twice but, although he did well, he did not make the top five. It was a failure in Nash's eyes and one which he took badly. The Putnam Mathematics Competition was not the only thing going badly for Nash. Although his mathematics professors heaped praise on him, his fellow students found him a very strange person. Physically he was strong and this saved him from being bullied, but his fellow students took delight in making fun of Nash who they saw as an awkward immature person displaying childish tantrums. One of his fellow students wrote:-

He was a country boy unsophisticated even by our standards. He behaved oddly, playing a single chord on a piano over and over, leaving a melting ice cream cone melting on top of his cast-off clothing, walking on his roommate's sleeping body to turn off the light.

Another wrote:-

He was extremely lonely.

And a third fellow student wrote:-

We tormented poor John. We were very unkind. We were obnoxious. We sensed he had a mental problem.

He showed homosexual tendencies, climbing into bed with the other boys who reacted by making fun of the fact that he was attracted to boys and humiliated him. They played cruel pranks on him and he reacted by asking his fellow students to challenge him with mathematics problems. He ended up doing the homework of many of the students.

Nash received a BA and an MA in mathematics in 1948. By this time he had been accepted into the mathematics programme at Harvard, Princeton, Chicago and Michigan. He felt that Harvard was the leading university and so he wanted to go there, but on the other hand their offer to him was less generous than that of Princeton. Nash felt that Princeton were keen that he went there while he felt that his lack of success in the Putnam Mathematics Competition meant that Harvard were less enthusiastic. He took a while to make his decision, while he was encouraged by Syngeand his other professors to accept Princeton. When Lefschetz offered him the most prestigious Fellowship that Princeton had, Nash made his decision to study there.

In September 1948 Nash entered Princeton where he showed an interest in a broad range of pure mathematics: topology, algebraic geometry, game theory and logic were among his interests but he seems to have avoided attending lectures. Usually those who decide not to learn through lectures turn to books but this appears not to be so for Nash, who decided not to learn mathematics "second-hand" but rather to develop topics himself. In many ways this approach was successful for it did contribute to him developing into one of the most original of mathematicians who would attack a problem in a totally novel way.

In 1949, while studying for his doctorate, he wrote a paper which 45 years later was to win a Nobel prize for economics. During this period Nash established the mathematical principles of game theory. P Ordeshook wrote:-

The concept of a Nash equilibrium n-tuple is perhaps the most important idea in noncooperative game theory. ... Whether we are analysing candidates' election strategies, the causes of war, agenda manipulation in legislatures, or the actions of interest groups, predictions about events reduce to a search for and description of equilibria. Put simply, equilibrium strategies are the things that we predict about people.

He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well. However, my most vivid memory of this time is of the many games which were played in the common room. I was introduced to Go and Kriegspiel, and also to an ingenious topological game which we called Nash in honor of the inventor.

In fact the game "Nash" was almost identical to Hex which had been invented independently by Piet Hein in Denmark.

Here are three comments from fellow students:-

Nash was out of the ordinary. If he was in a room with twenty people, and they were talking, if you asked an observer who struck you as odd it would have been Nash. It was not anything he consciously did. It was his bearing. His aloofness.Nash was totally spooky. He wouldn't look at you. he'd take a lot of time answering a question. If he thought the question was foolish he wouldn't answer at all. He had no affect. It was a mixture of pride and something else. He was so isolated but there really was underneath it all a warmth and appreciation of people.A lot of us would discount what Nash said. ... I wouldn't want to listen. You didn't feel comfortable with the person.

He had ideas and was very sure they were important. He went to see Einstein not long after he arrived in Princeton and told him about an idea he had regarding gravity. After explaining complicated mathematics to Einstein for about an hour, Einstein advised him to go and learn more physics. Apparently a physicist did publish a similar idea some years later.

In 1950 Nash received his doctorate from Princeton with a thesis entitled

*Non-cooperative Games*. In the summer of that year he worked for the RAND Corporation where his work on game theory made him a leading expert on the Cold War conflict which dominated RAND's work. He worked there from time to time over the next few years as the Corporation tried to apply game theory to military and diplomatic strategy. Back at Princeton in the autumn of 1950 he began to work seriously on pure mathematical problems. It might seem that someone who had just introduced ideas which would, one day, be considered worthy of a Nobel Prize would have no problems finding an academic post. However, Nash's work was not seen at the time to be of outstanding importance and he saw that he needed to make his mark in other ways. We should also note that it was not really a move towards pure mathematics for he had always considered himself a pure mathematician. He had already obtained results on manifolds and algebraic varieties before writing his thesis on game theory. His famous theorem, that any compact real manifold is diffeomorphic to a component of a real-algebraic variety, was thought of by Nash as a possible result to fall back on if his work on game theory was not considered suitable for a doctoral thesis. He said in a recent interview:-I developed a very good idea in pure mathematics. I got what became Real Algebraic Manifolds. I could have published that earlier, but it wasn't rushed to publication. I took some time in writing it up. Somebody suggested that I was a prodigy. Another time it was suggested that I should be called "bug brains", because I had ideas, but they were sort of buggy or not perfectly sound. So that might have been an anticipation of mental problems. I mean, taking it at face value.

In 1952 Nash published

*Real Algebraic Manifolds*in the*Annals of Mathematics*. The most important result in this paper is that two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic. Although publication of this paper on manifolds established him as a leading mathematician, not everyone at Princeton was prepared to see him join the Faculty there. This was nothing to do with his mathematical ability which everyone accepted as outstanding, but rather some mathematicians such as Artin felt that they could not have Nash as a colleague due to his aggressive personality.
Halmos received the following letter in early 1953 from Warren Ambrose relating to Nash (see for example [2]):-

There's no significant news from here, as always. Martin is appointing John Nash to an Assistant Professorship(not the Nash at Illinois, the one out of Princeton by Steenrod)and I'm pretty annoyed at that. Nash is a childish bright guy who wants to be "basically original," which I suppose is fine for those who have some basic originality in them. He also makes a damned fool of himself in various ways contrary to this philosophy. He recently heard of the unsolved problem about imbedding a Riemannian manifold isometrically in Euclidean space, felt that this was his sort of thing, provided the problem were sufficiently worthwhile to justify his efforts; so he proceeded to write to everyone in the math society to check on that, was told that it probably was, and proceeded to announce that he had solved it, modulo details, and told Mackey he would like to talk about it at the Harvard colloquium. Meanwhile he went to Levinson to inquire about a differential equation that intervened and Levinson says it is a system of partial differential equations and if he could only[get]to the essentially simpler analog of a single ordinary differential equation it would be a damned good paper - and Nash had only the vaguest notions about the whole thing. So it is generally conceded he is getting nowhere and making an even bigger ass of himself than he has been previously supposed by those with less insight than myself. But we've got him and saved ourselves the possibility of having gotten a real mathematician. He's a bright guy but conceited as Hell, childish as Wiener, hasty as X, obstreperous as Y, for arbitrary X and Y.

Ambrose, the author of this letter, and Nash had rubbed each other the wrong way for a while. They had played silly pranks on each other and Ambrose seems not to have been able to ignore Nash's digs in the way others had learned to do. It had been Ambrose who had said to Nash:-

If you're so good, why don't you solve the embedding theorem for manifolds.

From 1952 Nash had taught at the Massachusetts Institute of Technology but his teaching was unusual (and unpopular with students) and his examining methods were highly unorthodox. His research on the theory of real algebraic varieties, Riemannian geometry, parabolic and elliptic equations was, however, extremely deep and significant in the development of all these topics. His paper

*C*^{1}*isometric imbeddings*was published in 1954 and Chern, in a review, noted that it:-... contains some surprising results on the C^{1}-isometric imbedding into an Euclidean space of a Riemannian manifold with a positive definite C^{0}-metric.

Nash continued to develop this work in the paper

*The imbedding problem for Riemannian manifolds*published in 1956. This paper contains his famous deep implicit function theorem. After this Nash worked on ideas that would appear in his paper*Continuity of solutions of parabolic and elliptic equations*which was published in the*American Journal of Mathematics*in 1958. Nash, however, was very disappointed when he discovered that E De Giorgi had proved similar results by completely different methods.
The outstanding results which Nash had obtained in the course of a few years put him into contention for a 1958 Fields' Medal but since his work on parabolic and elliptic equations was still unpublished when the Committee made their decisions he did not make it. One imagines that the Committee would have expected him to be a leading contender, perhaps even a virtual certainty, for a 1962 Fields' Medal but mental illness destroyed his career long before those decisions were made.

During his time at MIT Nash began to have personal problems with his life which were in addition to the social difficulties he had always suffered. Colleagues said:-

Nash was always forming intense friendships with men that had a romantic quality. He was very adolescent, always with the boys. He was very experimental - mostly he just kissed.

He met Eleanor Stier and they had a son, John David Stier, who was born on 19 June 1953. Eleanor was a shy girl, lacking confidence, a little afraid of men, did not want to be involved. She found in Nash someone who was even less experienced than she was and found that attractive. [2]:-

Nash was looking for emotional partners who were more interested in giving than receiving, and Eleanor, was very much that sort.

Nash did not want to marry Eleanor although she tried hard to persuade him. In the summer of 1954, while working for RAND, Nash was arrested in a police operation to trap homosexuals. He was dismissed from RAND.

One of Nash's students at MIT, Alicia Larde, became friendly with him and by the summer of 1955 they were seeing each other regularly. He also had a special friendship with a male graduate student at this time: Jack Bricker. Eleanor found out about Alicia in the spring of 1956 when she came to Nash's house and found him in bed with Alicia. Nash said to a friend:-

My perfect little world is ruined, my perfect little world is ruined.

Alicia did not seem too upset at discovering that Nash had a child with Eleanor and deduced that since the affair had been going on for three years, Nash was probably not serious about her. In 1956 Nash's parents found out about his continuing affair with Eleanor and about his son John David Stier. The shock may have contributed to the death of Nash's father soon after, but even if it did not Nash may have blamed himself. In February of 1957 Nash married Alicia; by the autumn of 1958 she was pregnant but, a couple of months later near the end of 1958, Nash's mental state became very disturbed.

At a New Year's Party Nash appeared at midnight dressed only with a nappy and a sash with "1959" written on it. He spent most of the evening curled up, like the baby he was dressed as, on his wife's lap. Some described his behaviour as stranger than usual. On 4 January he was back at the university and started to teach his game theory course. His opening comments to the class were:-

The question occurs to me. Why are you here?

One student immediately dropped the course! Nash asked a graduate student to take over his course and vanished for a couple of weeks. When he returned he walked into the common room with a copy of the New York Times saying that it contained encrypted messages from outer space that were meant only for him. For a few days people thought he was playing an elaborate private joke.

Norbert Wiener was one of the first to recognize that Nash's extreme eccentricities and personality problems were actually symptoms of a medical disorder. After months of bizarre behaviour, Alicia had her husband involuntarily hospitalised at McLean Hospital, a private psychiatric hospital outside of Boston. Upon his release, Nash abruptly resigned from MIT, withdrew his pension, and went to Europe, where he intended to renounce his US citizenship. Alicia left her newborn son with her mother, and followed the ill Nash. She then had Nash deported - back to the United States.

After their return, the two settled in Princeton where Alicia took a job. Nash's illness continued, transforming him into a frightening figure. He spent most of his time hanging around on the Princeton campus, talking about himself in the third person as Johann von Nassau, writing nonsensical postcards and making phone calls to former colleagues. They stoically listened to his endless discussions of numerology and world political affairs. Her husband's worsening condition depressed Alicia more and more.

In January 1961 the despondent Alicia, John's mother, and his sister Martha made the difficult decision to commit him to Trenton State Hospital in New Jersey where he endured insulin-coma therapy, an aggressive and risky treatment, five days a week for a month and a half. A long sad episode followed which included periods of hospital treatment, temporary recovery, then further treatment. Alicia divorced Nash in 1962. Nash spent a while with Eleanor and John David. In 1970 Alicia tried to help him taking him in as a boarder, but he appeared to be lost to the world, removed from ordinary society, although he spent much of his time in the Mathematics Department at Princeton. The book [2] is highly recommended for its moving account of Nash's mental sufferings.

Slowly over many years Nash recovered. He delivered a paper at the tenth World Congress of Psychiatry in 1996 describing his illness; it is reported in [3]. He was described in 1958 as the:-

... most promising young mathematician in the world ...

but he soon began to feel that:-

... the staff at my university, the Massachusetts Institute of Technology, and later all of Boston were behaving strangely towards me. ... I started to see crypto-communists everywhere ... I started to think I was a man of great religious importance, and to hear voices all the time. I began to hear something like telephone calls in my head, from people opposed to my ideas. ...The delirium was like a dream from which I seemed never to awake.

Despite spending periods in hospital because of his mental condition, his mathematical work continued to have success after success. He said:-

I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.

In the 1990s Nash made a recovery from the schizophrenia from which he had suffered since 1959. His ability to produce mathematics of the highest quality did not totally leave him. He said:-

I would not treat myself as recovered if I could not produce good things in my work.

Nash was awarded (jointly with Harsanyi and Selten) the 1994 Nobel Prize in Economic Science for his work on game theory. In 1999 he was awarded the Leroy P Steele Prize by the American Mathematical Society:-

... for a seminal contribution to research.

Nash and Louis Nirenberg were awarded the Abel prize in 2015 for:

... striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.

A few days after picking up the prize in Norway, Nash and his wife Alicia were killed in an accident to their taxi on the New Jersey turnpike.

**Article by:**

*J J O'Connor*and

*E F Robertson*

**Click on this link to see a list of the Glossary entries for this page**

**List of References**(10 books/articles)

**Some Quotations**(2)

**Mathematicians born in the same country**

**Additional Material in MacTutor**

Honours awarded to John F Nash(Click below for those honoured in this way) | |

Nobel Prize | 1994 |

AMS Steele Prize | 1999 |

Abel Prize | 2015 |

Popular biographies list | Number 25 |

**Other Web sites**

- Encyclopaedia Britannica
- Nobel prize winners
- Nobel prizes site (An autobiography of Nash and his Nobel prize presentation speech)
- Nash's home page
- AMS [registration required]
- PBS
- Mathematical Genealogy Project

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