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Nash, John (1928-2015)

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Noted mathematician John Nash, Jr. (1928-2015) received his Ph.D. from Princeton University in 1950. The impact of his 27 page dissertation on the fields of mathematics and economics was tremendous. In 1951 he joined the faculty of the Massachusetts Institute of Technology in Cambridge. His battle with schizophrenia began around 1958, and the struggle with this illness would continue for much of his life. Nash eventually returned to the community of Princeton. He was awarded the Nobel Prize in Economics in 1994. The 2001 film A Beautiful Mind , staring Russell Crowe, was loosely based on the life of Nash.

University Archives

John Nash's Dissertation

Non-cooperative Games, May 1950, is available in PDF format  Non-Cooperative_Games_Nash.pdf . The dissertation is provided for research use only. 

[Note: Chapter 6 of  The Essential John Nash,  edited by Harold W. Kuhn and Sylvia Nasar (Princeton, New Jersey: Princeton University Press, 2001) contains a facsimile of Nash's 1950 Ph.D. dissertation on non-cooperative games.]

In the movie  A Beautiful Mind  there is a scene in which faculty members present their pens to Nash. What is the origin of the pen ceremony? When did it start?

The scene in the movie,  A Beautiful Mind,  in which mathematics professors ritualistically present pens to Nash was completely fabricated in Hollywood. No such custom exists. What it symbolizes is that Nash was accepted and recognized in the mathematics community for his accomplishments. While some movies are based on books, the film A Beautiful Mind states that it was  inspired  by the life of John Nash. There are many discrepancies between the book and the film.

May I see Nash’s graduate school records?

John F. Nash, Jr's records have been digitzed and are available to view here:  Graduate Alumni Records

May I see Nash’s faculty file personnel records?

Personnel files transferred to the archives after 2003 : Files are closed until 100 years after the person's year of birth or 5 years after the person's year of death, whichever is longer. Therefore, John F. Nash's personell files are closed until, June 13, 2028.

May I have a copy of Nash’s 1994 Nobel Prize acceptance speech?

At the Nobel Prize Award ceremony, His Majesty the King of Sweden hands each Laureate a diploma, a medal, and a document confirming the Prize amount. The Laureates do not give acceptance speeches . The scene in the movie A Beautiful Mind in which Nash thanks his wife Alicia for her continued support during his illness is fictional.

Laureates are each invited to give an hour-long lecture; however, the Nobel committee did not ask Nash to do so, due to concerns over his mental health.

Additional Resources

Princetoniana Committee Oral History Project Records , Interview with Harold Kuhn, Part 1, pp. 31-40.  In this part of the interview, Prof. Kuhn discusses his behind the scenes work for John Nash’s Nobel Prize.

Historical Subject Files Collection, 1746-2005 : A Beautiful Mind.

Article:  John Nash automobile accident May 23, 2015, in Monroe Township, New Jersey.

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• Published: 24 June 2015

John Forbes Nash (1928–2015)

• Martin A. Nowak 1  

Nature volume  522 ,  page 420 ( 2015 ) Cite this article

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• Mathematics and computing

Master of games and equations.

John Forbes Nash, an exalted mathematician whose life took dramatic turns between genius, mental illness and celebrity status, made major contributions to game theory, geometry and the field of partial differential equations.

Nash, who died on 23 May, was born in Bluefield, West Virginia, in 1928. His father was an electrical engineer and his mother a schoolteacher. In 1945, after excelling in mathematics at high school, he attended the Carnegie Institute of Technology (now Carnegie Mellon University) in Pittsburgh, Pennsylvania. At first he studied chemical engineering, but soon after enrolling he switched to chemistry and then to maths.

In Nash's final year, one of his professors wrote a recommendation letter for the 19-year-old supporting his application to graduate school. It simply stated: “He is a mathematical genius.” In 1948, Nash was accepted by Harvard University in Cambridge, Massachusetts, and by Princeton University in New Jersey. He chose Princeton.

As a PhD student, Nash proved the existence of the equilibrium that now carries his name. His 1950 paper 'Equilibrium points in n -person games', contains about 330 words, two references and not one equation (J. F. Nash Jr Proc. Natl Acad. Sci. USA 36 , 48–49; 1950). One of the citations is the 1944 book Theory of Games and Economic Behavior — in which mathematician John von Neumann and economist Oskar Morgenstern introduce game theory, a mathematical approach for studying strategic and economic decisions.

The Nash equilibrium is a position in a game from which none of the players can change their strategy to improve their pay-off. Imagine a game with two players (yourself and another person) and two strategies, A and B. If you both choose A, your pay-off is 2. If you choose A and your opponent chooses B, you score 0. If you choose B and the other player chooses A, your pay-off is 3. If you both choose B, you score 1. The same applies to your opponent.

In this example, the Nash equilibrium occurs when both players choose B. If both players choose B, their pay-off is 1; if either player switches to A, their pay-off falls to 0. In other words, neither player can independently switch their strategy and improve their pay-off. Observe that if both players select A, there is no Nash equilibrium because you could improve your pay-off by switching to B.

Calculating the Nash equilibrium can be a formidable task in a complex game. There is also the uncertainty over whether the person you are playing against is sufficiently rational to play the equilibrium strategy. If both players are rational and their rationality is common knowledge, they would play it. But experiments often reveal that people are not rational. Regardless of whether people actually play the Nash equilibrium in social or economic interactions, working out what it is (or what the Nash equilibria are) is the first step to analysing any game.

Although dismissed at the time by von Neumann as a triviality, the Nash equilibrium has been used to analyse all sorts of competitive situations. As well as being key to decision-making in economics and politics, the idea is important in biology. Here, the nearly equivalent concept, formulated by evolutionary biologist John Maynard Smith in the 1970s is called an evolutionarily stable strategy (ESS). If all members of a population adopt an ESS, then natural selection prevents a rare mutant from spreading.

On completing his PhD, Nash joined the Massachusetts Institute of Technology (MIT) in Cambridge in 1951. He worked — first as an instructor and later as a professor — in the mathematics faculty until he resigned in 1959. It was while he was at MIT that Nash met and married Alicia Lopez-Harrison de Lardé, a physics student there.

Among mathematicians, Nash is best known for his work in real algebraic geometry and nonlinear partial differential equations. He was not afraid to tackle the hardest problems in the field, and he succeeded. In 1957, he — in parallel with Italian mathematician Ennio de Giorgi — solved Hilbert's nineteenth problem involving partial differential equations.

It was during a talk in 1959 on what is seen to be one of the hardest problems in maths — the Riemann hypothesis — that the audience realized that there was something wrong with Nash. His talk was incomprehensible.

He was diagnosed with paranoid schizophrenia that year. Over the next two decades, Nash was in and out of hospitals. He underwent therapy, and for a while left the United States and sought asylum in Switzerland in an attempt to escape his imagined tormentors. For many years he wandered around the Princeton campus. Throughout this period, Alicia, who divorced Nash in 1963, oversaw much of his care.

In the late 1980s, Nash reappeared in academic circles, and in 1994 he was awarded the Nobel Memorial Prize in Economic Sciences for his work on game theory. The Nobel and the 2001 film A Beautiful Mind , based on journalist Sylvia Nasar's book of the same name, which recounted Nash's struggles, propelled him into the limelight.

In May this year, Nash received the Abel prize from the Norwegian Academy of Science and Letters for his work on partial differential equations. On the way back from the celebration in Norway, John and Alicia (who had remarried in 2001) were killed in a car accident in a taxi on the New Jersey turnpike. John was 86.

I met John in 1998 at the Institute for Advanced Study in Princeton. Over the years, I gave several talks there that he attended. One summer's day, when the usual sitting arrangements for lunch were disrupted by the closure of the main kitchen, I noticed John, the physicist Edward Witten and Andrew Wiles, the British mathematician who proved Fermat's last theorem, sitting down together at a small table. I wondered which of them would start the conversation. None of them did. I seem to remember that they ate their meal in silence.

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Martin A. Nowak is professor of mathematics and biology, and director of the Program for Evolutionary Dynamics at Harvard University in Cambridge, Massachusetts, USA.,

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Correspondence to Martin A. Nowak .

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Nowak, M. John Forbes Nash (1928–2015) . Nature 522 , 420 (2015). https://doi.org/10.1038/522420a

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Published : 24 June 2015

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John Nash’s Super Short PhD Thesis: 26 Pages & 2 Citations

in Math | July 9th, 2018 2 Comments

When John Nash wrote  “Non Coop­er­a­tive Games,”   his Ph.D. dis­ser­ta­tion at Prince­ton in 1950, the text of his the­sis ( read it online ) was brief. It ran only 26 pages. And more par­tic­u­lar­ly, it was light on cita­tions. Nash’s diss cit­ed two texts:  John von Neu­mann & Oskar Mor­gen­stern’s  The­o­ry of Games and Eco­nom­ic Behav­ior   (1944), which  essen­tial­ly cre­at­ed game the­o­ry and rev­o­lu­tion­ized the field of eco­nom­ics; the oth­er cit­ed text, “Equi­lib­ri­um Points in n‑Person Games,”  was an arti­cle writ­ten by Nash him­self. And it laid the foun­da­tion for his dis­ser­ta­tion, anoth­er sem­i­nal work in the devel­op­ment of game the­o­ry, for which Nash won the Nobel Prize in Eco­nom­ic Sci­ences in 1994 .

The reward of invent­ing a new field is hav­ing a slim bib­li­og­ra­phy.

Note: An ear­li­er ver­sion of this post appeared on our site in June, 2015.

Relat­ed Con­tent:

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

The World Record for the Short­est Math Arti­cle: 2 Words

Free Online Math Cours­es

Free Math Text­books

by OC | Permalink | Comments (2) |

Related posts:

Comments (2), 2 comments so far.

Some­times doc­tor­al dis­ser­ta­tions are long on foot­notes and bib­li­og­ra­phy — and short on orig­i­nal think­ing. John Nash reversed the aca­d­e­m­ic trend. Reminds me of the Renais­sance painter who was asked for evi­dence of his abil­i­ty to draw. He drew a near-per­fect cir­cle on a can­vas, and was accept­ed by the mas­ter as an appren­tice.

Excel­lent con­cept and articles.…worth reading.…pl for­ward more read­ing

Thanks and regards

Dr B Vijay Sarthi

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PhD Thesis of John Nash

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John F Nash PhD

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John F. Nash, Jr.

In memoriam, life & work.

John Nash Jr., a legendary fixture of Princeton University’s Department of Mathematics renowned for his breakthrough work in mathematics and game theory as well as for his struggle with mental illness, died with his wife, Alicia, in an automobile accident May 23 in Monroe Township, New Jersey. He was 86, she was 82.

During the nearly 70 years that Nash was associated with the University, he was an ingenious doctoral student; a specter in Princeton’s Fine Hall whose brilliant academic career had been curtailed by his struggle with schizophrenia; then, finally, a quiet, courteous elder statesman of mathematics who still came to work every day and in the past 20 years had begun receiving the recognition many felt he long deserved. He had held the position of senior research mathematician at Princeton since 1995.

Nash was a private person who also had a strikingly public profile, especially for a mathematician. His life was dramatized in the 2001 film “A Beautiful Mind” in which he and Alicia Nash were portrayed by actors Russell Crowe and Jennifer Connelly. The film centered on his influential work in game theory, which was the subject of his 1950 Princeton doctoral thesis and the work for which he received the 1994 Nobel Prize in economics.

At heart, however, Nash was a devoted mathematician whose ability to see old problems from a new perspective resulted in some of his most astounding and influential work, friends and colleagues said.

At the time of their deaths, the Nashes were returning home from Oslo, Norway, where John had received the 2015 Abel Prize from the Norwegian Academy of Science and Letters, one of the most prestigious honors in mathematics. The prize recognized his seminal work in partial differential equations, which are used to describe the basic laws of scientific phenomena. For his fellow mathematicians, the Abel Prize was a long-overdue acknowledgment of his contributions to mathematics.

For Nash to receive his field’s highest honor only days before his death marked a final turn of the cycle of astounding achievement and jarring tragedy that seemed to characterize his life. “It was a tragic end to a very tragic life. Tragic, but at the same time a meaningful life,” said Sergiu Klainerman, Princeton’s Eugene Higgins Professor of Mathematics, who was close to John and Alicia Nash, and whose own work focuses on partial differential equation analysis.

“We all miss him,” Klainerman said. “It was not just the legend behind him. He was a very, very nice person to have around. He was very kind, very thoughtful, very considerate and humble. All that contributed to his legacy in the department. The fact that he was always present in the department, I think that by itself was very moving. It’s an example that stimulated people, especially students. He was an inspiring figure to have around, just being there and showing his dedication to mathematics.”

Princeton President Christopher L. Eisgruber said Sunday that the University community was “stunned and saddened by news of the untimely passing of John Nash and his wife and great champion, Alicia.”

“Both of them were very special members of the Princeton University community,” Eisgruber said. “John’s remarkable achievements inspired generations of mathematicians, economists and scientists who were influenced by his brilliant, groundbreaking work in game theory, 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.”

Although Nash did not teach or formally take on students, his continuous presence in the department over the past several decades, coupled with the almost epic triumphs and trials of his life, earned him respect and admiration, said David Gabai, the Hughes-Rogers Professor of Mathematics and department chair.

“John Nash, with his long history of achievements and his incredible battle with mental health problems, was hugely inspirational,” Gabai said. “It’s a huge loss not to have him around anymore.”

Gabai said the Nashes regularly attended department events such as receptions, special teas, and special dinners, and they also were very supportive of undergraduate education and regularly attended undergraduate events. Gabai, who was with the couple in Norway when John received the Abel Prize, likened their deaths to the department losing two family members.

Even in the 1970s when Nash, still struggling with mental illness, was an elusive presence known as the “Phantom of Fine Hall,” his reputation for bravely original thinking motivated aspiring mathematicians, said Gabai, who was a Princeton graduate student at the time. Nash’s creativity helped preserve the department’s emphasis on risk-taking and exploration, he said.

“In those days, he was very present, but rarely said anything and just wandered benignly through Fine Hall. Nevertheless, we all knew that the mathematics he did was really spectacular,” Gabai said. “It went beyond proving great results. He had a profound originality as if he somehow had insights into developing problems that no one had even thought about.

“I think he prided himself that he had his way of thinking about things,” Gabai continued. “He was such an extraordinary exemplar of the things that this department strives for. Beyond great originality, he demonstrated tremendous tenacity, courage and fearlessness.”

Since winning the Nobel Prize , Nash had entered a long period of renewed activity and confidence — which coincided with Nash’s greater control of his mental state — that allowed him to again put his creativity to work, Klainerman said. He met Nash upon joining the Princeton faculty in 1987, but his doctoral thesis had made use of a revolutionary method introduced by Nash in connection to the Nash embedding theorems, which the Norwegian Academy described as “among the most original results in geometric analysis of the twentieth century.”

“When he got the Nobel Prize, there was this incredible transformation,” Klainerman said. “Prior to that we didn’t realize he was becoming normal again. It was a very slow process. But after the prize he was like a different person. He was much more confident in himself.”

During their frequent talks in recent years, Nash would offer unique perspectives on numerous topics spanning mathematics and current events, Klainerman said. “Even though his mind wasn’t functioning as it did in his youth, you could tell that he had an interesting point of view on everything. He was always looking for a different angle than everybody else. He always had something interesting to say.”

Nash’s quick and distinctive mind still shone in his later years, said Michail Rassias, a visiting postdoctoral research associate in mathematics at Princeton who was working with Nash on the upcoming book, “Open Problems in Mathematics.” He and Nash had just finished the preface of their book before Nash left for Oslo. They agreed upon a quote from Albert Einstein that resonated with Nash (although Nash pointed out that Einstein was a physicist, not a mathematician, Rassias said): “Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning.”

“Even at 86, his mind was still open,” Rassias said. “He still wanted to have new ideas. Of course, he couldn’t work like when he was 20, but he still had this spark, the soul of a young mathematician. The fact that he moved slowly and talked with a quiet voice had nothing to do with the enthusiasm with which he did mathematics. It was very inspirational.”

Sixty years younger than Nash, Rassias said his work with Nash began with a conversation in the Fine Hall commons room in September.

“I could tell there was mathematical chemistry between us and that led to this intense collaboration. He was very simple, very open to discussing ideas with new people if you said something that attracted his interest,” Rassias said. “Nash gave this impression that he was distant, but when you actually had the opportunity to talk to him he was not like that. He tended to walk alone, but if you got the courage to talk to him it would be very natural for him to talk to you.”

Rassias has been inspired by the enthusiasm and willingness with which a person of Nash’s stature dedicated months of his time to working with a young mathematician. It was an example Rassias hopes to emulate during his own career.

“Remembering what John Nash did for me, I will definitely try to give all my heart and soul to younger people in all steps of their careers,” Rassias said. “I also will try to keep my mind and enthusiasm for math alive to the end. That is something I will try to achieve like him.”

Born in Bluefield, West Virginia, in 1928, Nash received his doctorate in mathematics from Princeton in 1950 and his graduate and bachelor’s degrees from Carnegie Institute of Technology (now Carnegie Mellon University) in 1948.

His honors included the American Mathematical Society’s 1999 Leroy P. Steele Prize for Seminal Contribution to Research and the 1978 John von Neumann Theory Prize. Nash held membership in the National Academy of Sciences and in 2012 was an inaugural fellow of the American Mathematical Society.

Nash is survived by his sister, Martha Nash Legg, and sons John David Stier and John Charles Martin Nash. He had his younger son, John Nash, with Alicia shortly after their marriage in 1957, which ended in divorce in 1963. They remarried in 2001.

Despite their divorce, Alicia, who was born in El Salvador in 1933, endured the peaks and troughs of Nash’s life alongside him, Klainerman said. Their deaths at the same time after such a long life together of highs and lows seemed literary in its tragedy and romance, he said.

“They were a wonderful couple,” Klainerman said. “You could see that she cared very much about him, and she was protective of him. You could see that she cared a lot about his image and the way he felt. I felt it was very moving.

“Coming home from Oslo, he must have been extremely happy, and she must have been extremely happy for him,” he continued. “They went for the apotheosis of his career, and died in this terrible way on the way back. But they were together.”

A memorial service for Nash will be planned at the University in the fall.