john nash game theory dissertation

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) |

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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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• 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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John Nash: The Genius Who Shaped Game Theory and Economics

• Publication date January 18, 2024

John Nash’s profound impact on economics and mathematics is a story of intellectual brilliance, personal struggle, and enduring legacy. His journey from a precocious student to a Nobel laureate illuminates the intersection of pure mathematics and economic theory.

Early Life and Education

Born in 1928 in Bluefield, West Virginia, Nash showed early signs of extraordinary intellectual ability. His parents, recognizing his talent, nurtured his academic interests. Nash’s advanced understanding of mathematics led him to take college-level courses while still in high school.

Academic Prodigy at Carnegie and Princeton

Nash’s academic prowess continued to flourish at the Carnegie Institute of Technology, where he completed both a bachelor’s and a master’s degree in mathematics by the age of 19. His remarkable abilities were encapsulated in the succinct recommendation from his adviser, attesting to his “mathematical genius.”

Groundbreaking Work at Princeton

Nash’s time at Princeton University was pivotal. His doctoral dissertation, “Non-Cooperative Games,” was a mere 28 pages but laid the groundwork for modern game theory. The Nash equilibrium, a concept introduced in this work, transformed the understanding of decision-making processes in economics, where multiple actors with conflicting interests are involved.

Professional Life and Mental Health Struggles

Nash’s professional tenure at the Massachusetts Institute of Technology and his work as a codebreaker for the U.S. government were marked by his developing symptoms of mental illness. Diagnosed with paranoid schizophrenia, Nash’s life took a turn as he faced immense personal challenges. Despite these struggles, his intellectual contributions continued, and he resumed his academic career at Princeton.

Nobel Prize and Recognition

In 1994, Nash’s groundbreaking work was recognized with the Nobel Prize in Economics. This accolade brought his contributions to a wider audience, bridging the gap between abstract mathematical theories and practical economic applications.

Cultural Impact and “A Beautiful Mind”

Nash’s life story, marked by both triumph and adversity, was vividly captured in Sylvia Nasar’s biography “A Beautiful Mind” and the subsequent Academy Award-winning film. These works brought Nash’s story and the complexity of his theories to a global audience, making Nash a household name.

A Tragic End and Enduring Legacy

John Nash’s life tragically ended in a taxi crash in 2015, soon after receiving the Abel Prize, one of the highest honors in mathematics. His death marked the loss of one of the most brilliant minds of the 20th century.

Nash’s work continues to influence a wide range of fields, from economics and mathematics to biology and political science. His legacy lives on through the Nash equilibrium, a concept that has become a fundamental tool in understanding complex systems where strategic interactions occur. John Nash remains a symbol of how intellectual prowess can overcome personal challenges and contribute to the broader understanding of our world.

John Nash (1928–2015)

• First Online: 29 January 2023

Cite this chapter

• Panayotis G. Michaelides 3 &
• Theodoulos Eleftherios Papadakis 3  

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Nash ( 1995 ).

Nash ( 1996 ).

Leonard ( 1994 ).

Fragnelli and Gambarelli ( 2015 ).

Nasar ( 1998 ).

Rubinstein ( 1995 ).

Our discussion follows Myerson ( 1999 ).

Cournot ( 1838 ).

Myerson ( 1999 ).

Borel ( 1921 ).

von Neumann ( 1928 ).

Myerson ( 1999 )

von Neumann and Morgenstern ( 1944 ).

Screpanti and Zamagni ( 2005 ).

Nash ( 1950b ).

Nash ( 1950a ).

Nash ( 1951 ).

Mornati ( 2018 ).

Varoufakis ( 2007 ).

Milnor ( 1995 ).

Economist ( 2016 ).

Colman et al. ( 2018 ).

Myerson ( 1978 ).

Kreps and Wilson ( 1982 ).

Harsanyi ( 1967 –1968).

Aumann ( 1974 ).

Fellman ( 2007 )

Daskalakis et al. ( 2009 ).

Babichenko and Rubinstein ( 2020 ).

Daskalakis et al. ( 2009 , p. 196).

See also Karlin and Perez ( 2017 , p. 84).

Schwartz-Shea ( 2002 )

Margaret Thatcher in Brittan ( 2013 ).

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Colman, A. M., Pulford, B. D., & Krockow, E. M. (2018). Persistent cooperation and gender differences in repeated Prisoner’s Dilemma games: Some things never change. Acta Psychological, 187 , 1–8.

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Michaelides, P.G., Papadakis, T.E. (2023). John Nash (1928–2015). In: History of Economic Ideas. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-19697-3_10

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Year 91 – 1951: “Non-cooperative Games” by John Nash, in: Annals of Mathematics 54 (2)

Posted on April 7, 2011 in All years , Uncategorized

Over the past 60 years, game theory has been one of the most influential theories in the social sciences, pervasive in economics, political science, business administration, and military strategy – the disciplines most consulted by the powers-that-be for “real-world,” high-stakes decisions. But just as there would be no semiconductors or (God forbid) laser pointers if not for the abstruse mathematics of quantum theory, game theory can be traced back to theoretical work by academic mathematicians. In a set of papers in the 1950s, mathematician John Forbes Nash set forth breakthrough ideas that helped transform game theory from an ivory tower abstraction into an indispensable analytical tool used by strategists from Wall Street to the Pentagon.

The foundational game theory work of mathematician John von Neumann and economist Oskar Morgenstern, published in 1944, provided a framework for solutions to zero-sum games, where one player’s win was the other’s loss. Nash, in his dissertation research at Princeton (published in this and three other papers), extended game theory to n -person games in which more than one party can gain, a better reflection of practical situations. Nash demonstrated that “a finite non-cooperative game always has at least one equilibrium point” or stable solution. This result came to be called the “Nash equilibrium,” a situation where no one player can get a better payoff by changing strategies, so long as other players also keep their strategies. Using Nash’s framework, predictions can be made about the outcomes of strategic interactions.

Based on Nash’s advances, game theory developed into one of the pre-eminent tools of economics in the second half of the 20th century. In recognition of his breakthrough work, Nash was joint recipient of the Nobel Prize for Economics in 1994 for “pioneering analysis of equilibria in the theory of non-cooperative games.”

If visions of Russell Crowe have danced in your head while you’ve been reading this post, that’s probably because you remember that Crowe played John Forbes Nash in the 2001 film A Beautiful Mind (at least we hope that’s why). Part of the movie takes place at MIT, portraying Nash’s years as an instructor in mathematics at the Institute, where he worked from 1951 to 1959, until mental illness curtailed his mathematical career.

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John Nash and his contribution to Game Theory and Economics

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A two-page paper published by John Nash in 1950 is a seminal contribution to the field of Game Theory and of our general understanding of strategic decision-making. That paper, “ Equilibrium points in N-person games ”, introduced a cornerstone concept which came to be known as Nash equilibrium .

Game theory is concerned with situations where decisions interact – where the “payoff” or reward for a decision maker depends not only on his or her own decision but also on the decisions of others.

Such situations are pervasive in real life. The payoff for a buyer in an auction, for example, depends not only on the amount he bids but also on the bids of the other buyers. If the buyer’s bid is not the highest, then he loses the auction. Likewise, the profit realised by a firm depends not only on the price it sets for its product but also on the prices set by its competitors. In a tennis match, the likelihood the server will win a point depends on whether she delivers the serve to the receiver’s left or right and whether the receiver correctly anticipates it.

Auctions, price setting and tennis are all examples of “non-cooperative” strategic interactions that mathematicians and economists refer to as “games”. They are non-cooperative because decision makers take their actions independently and are unable to enter into binding agreements with others regarding their actions, either because such agreements are illegal (when setting prices) or because they have no incentive to do so (as in tennis).

The notion of Nash equilibrium, developed in Nash’s 1950 paper, is the basis of how economists predict the outcome of strategic interactions.

Informally, a Nash equilibrium is a list of actions, one for each decision maker, such that each decision maker’s action is best for him, given the actions of the others. Such a list of actions is an equilibrium (or stable point), since no decision maker has an incentive to change his action.

Consider a driver approaching an intersection. She stops when she approaches a red light and she continues without concern when she approaches a green light. It is a Nash equilibrium when all drivers behave this way. When approaching a red light it is best to stop since the crossing traffic has a green light and will continue. When approaching a green light it is best to continue since the crossing traffic has a red light and will stop. Thus it is in each driver’s own interest to play her part in the equilibrium, given that everyone else does. No traffic cop is required.

Nash equilibrium also allows for the possibility that decision makers follow randomised strategies. Allowing for randomisation is important for the mathematics of game theory because it guarantees that every (finite) game has a Nash equilibrium.

Randomisation is also important in practice in commonly played games such as Two-up, Rock-Paper-Scissors, poker and tennis. We all know from our own experience how to play Rock-Paper-Scissors against a sophisticated opponent: play each action with equal probability, independently of the actions and outcomes in past plays. Indeed, this is exactly what Nash equilibrium predicts. Nash’s theory applies to any game with any number of decision makers, whereas John von Neumann’s 1928 Minimax Theorem applies only to “zero-sum” games with two players.

Interestingly, data collected from championship tennis matches has shown that the serve-and-return behaviour of professional players is consistent with both von Neumann’s Minimax Theory and Nash’s generalisation.

Nash’s work dealt with games in which each decision maker takes his or her action without knowing the actions taken by others, and in which no decision-maker has private information. John Harsanyi extended the notion of Nash equilibrium to deal with strategic interactions, such as in auctions, in which decision-makers have private information. (In an auction, buyers know the value they place on the item being sold, but they don’t know how other buyers value the item.)

Reinhardt Selten extended the notion of Nash equilibrium to deal with dynamic interactions, in which one or more decision-makers observe the action of another before taking their own action. In 1994, Nash shared the Nobel Prize in Economics with Harsanyi and Selten for these contributions.

While Nash is best known for his contribution to non-cooperative game theory, he also made a seminal contribution to cooperative game theory with the development of the Nash bargaining solution.

Nash’s work has had a profound impact in economics. Knowledge of game theory is essential training for every professional economist and it is a common – and popular – subject for undergraduate students as well. Nash’s work not only revolutionised modern economics, it has also had an important impact in fields as diverse as computer science, political science, sociology and biology.

His work on game theory won him a Nobel Prize for economics in 1994 and he just recently received Norway’s Abel prize for mathematics.

John Nash remained active at scientific conferences around the world. He was happy to talk with students, many of whom wanted a picture with him too. He and his wife, Alicia were both killed in a car accident on the New Jersey Turnpike on Saturday, May 24 on their way home from receiving the prize.

Both were kind people and they will be missed.

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John F. Nash, Jr.

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.”

-By Morgan Kelley, Princeton University Office of Communications

John F Nash PhD

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In this page you can find Nash’s PhD thesis:

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*: Thanks to Rebeca Duarte Miguel for this, and to Jeek Midford for spotting some spelling mistakes.

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