Biography. The real story of John Nash, which was much scarier than the one that we were shown in Mind Games John Nash game theory

John Forbes Nash Jr., the brilliant Princeton mathematician whose life inspired the Oscar-winning film A Beautiful Mind, died over the weekend along with his wife, Alicia.

The police found that a taxi driver who lost control was responsible for the death of the 86-year-old scientist and his 82-year-old wife. The driver of a Ford Crown Victoria tried to overtake another car on the left side and crashed into the guardrail. The accident happened on the New Jersey Turnpike. New Jersey State Police spokesman Gregory Williams told NJ.com that the couple were apparently not wearing seat belts. John and Alicia were thrown out of the cab by the impact and died on the spot. The driver survived and was taken to hospital with minor injuries.

Just a few days earlier, John Nash received the Abel Prize from the hands of King Harald V of Norway - it is called the mathematical “Nobel Prize”. The $800,000 prize was awarded to Nash and his colleague Louis Nierenbehr, recognized giants of 20th-century mathematics, for "groundbreaking contributions to the theory of non-linear partial differential equations in the field of geometric analysis." As noted, each of the scientists worked on his own, but the mathematicians had a great influence on each other, and the results of the work were far ahead of their time. Nirenberg and the Nash family flew in together from Oslo, said goodbye at the airport, and departed in a taxi. John and Alicia died on the way to their home in a suburb of Princeton.

As you know, the Nobel Prize is not awarded to mathematicians. However, John Nash nevertheless became her winner in the category "Economics" for his analysis of equilibrium in the theory of non-cooperative games.

There is an opinion in the mathematical community that John Nash became famous thanks to the simplest of his works, while many of his developments are still incomprehensible to his colleagues.

He is known to a wide circle thanks to the biopic A Beautiful Mind, in which the role of Nash was played by Russell Crowe. The film, which became the discovery of 2001, told the whole world that for most of his life the mathematical genius struggled with schizophrenia and remained a patient in psychiatric clinics for a long time. As is often the case, everything in life was more complicated, more tragic, and more surprising than in the movies.

Mathematician

John Forbes Nash Jr. was born on June 13, 1928 in Bluefield, West Virginia to a strict Protestant family. His father was an electrical engineer and his mother was an English and Latin teacher. Little John did not study well at school, and did not like mathematics - it was taught too boringly. In a small provincial town, he grew up far from the scientific community and high technology. However, the vocation found him by itself.

When Nash was 14 years old, he read Eric T. Bell's Math Makers. Having learned what he had read, he managed to prove Fermat's little theorem himself, without outside help. And soon he turned his room into a real laboratory, where he surrounded himself with books and conducted various experiments.

In 1945, John entered the Carnegie Polytechnic Institute in Pittsburgh and was going to become an engineer, like his father. He tried to study chemistry, but abandoned the idea. The course of economics also did not seem exciting to him. As a result, the gifted student fell deeply in love with mathematics and seriously took up number theory and Diophantine equations. And then he tackled the "negotiation problem" that John von Neumann had left unresolved in his Game Theory and Economic Behavior.

By the time he entered Princeton, John Nash had earned his bachelor's and master's degrees, and his institute lecturer, Richard Duffin, provided him with a letter of recommendation that consisted of just one line: "This guy is a genius." At Princeton, in 1949, at the age of 21, Nash completed his thesis on game theory, which would be awarded the Nobel Prize in Economics 40 years later. He developed the foundations of the scientific method, which had a particular impact on the development of the world economy. Until 1953, he published four papers with deep analysis of non-zero-sum games. The situation he modeled would later be called the "Nash equilibrium".

Shot from the movie "A Beautiful Mind"

An example of such a balance can be, for example, the negotiations between trade unions and company management to increase wages. Such negotiations can end either in a long strike and losses for both parties, or in a mutually beneficial agreement. Moreover, such an agreement cannot be violated by any of the parties, since violation will lead to losses.

The scientist was unable to obtain political asylum in Europe and was persecuted by the State Department

From the 1950s, Nash worked at the Massachusetts Institute of Technology in Cambridge and wrote a number of papers on real algebraic geometry and the theory of Riemannian manifolds. At the same time, he proved the Nash theorem on regular embeddings, which became one of the most important in differential geometry on manifolds.

Shot from the movie "A Beautiful Mind"

Nash was a recognized genius, but he did not develop relationships with his colleagues. His works mathematically substantiated Karl Marx's theory of surplus value. At the time of the witch hunt, such views in the United States seemed heretical. Therefore, when Nash's girlfriend, nurse Eleanor Stier, gave birth to a child, Nash refused to give him his name and provide any financial support - in order to protect mother and child from the persecution of the McCartney Commission.

BecomeUnder the pressure of circumstances, the mathematician leaves for California, to the RAND Corporation, which was engaged in analytical and strategic developments for the US government. The corporation was known as a haven for dissidents, and Nash quickly became one of the leading experts in the field of Cold War warfare, using the best practices in game theory. However, he failed to get along in RAND. The scientist was fired after the police arrested him for indecent behavior.

Shortly thereafter, Nash met Alicia Lard, a student from El Salvador, and they married in 1957. Everything went well, the couple was expecting a child, Fortune magazine named Nash a rising American star in new mathematics. He received an invitation to become one of the youngest professors at Princeton. However, the mathematician reacted to the invitation in a very strange way. “I cannot take this post. The throne of the Emperor of Antarctica awaits me.”

For several months, Alicia, frightened by the symptoms of schizophrenia, tried to hide her husband's condition from his colleagues and friends. However, in the end, John had to be forcibly hospitalized in a private psychiatric clinic in the suburbs of Boston. He was diagnosed with paranoid schizophrenia.

After breaking out of the clinic with the help of a lawyer, Nash leaves for Europe. Alicia left her newborn son with her mother and followed her husband. Nash constantly talked about the persecution, about alien messages that only he could decipher. The scientist tried to obtain political refugee status in France, Switzerland and the GDR and renounce American citizenship. However, under pressure from the US State Department, these countries refused to shelter the couple. Now it is known that Nash was really being monitored, his appeals to the embassies of different countries were blocked. After some time, the mathematician was arrested by the French police and deported to the United States. Together with Alicia, he settled in Princeton, she found a job. But John's condition worsened, he was afraid of everything, spoke of himself in the third person, wrote meaningless letters and told former colleagues about numerology and politics.

30 "dark" years ended with an inexplicable return to reality

In 1961, Alicia, John's mother, and his sister, after much hesitation, decided to admit John to Trenton State Hospital in New Jersey for risky and brutal insulin therapy. After being discharged, colleagues tried to get him a job, but John again left for Europe, this time alone. Alicia soon divorced him.

Shot from the movie "A Beautiful Mind"

Until 1970, Nash wandered through psychiatric hospitals and occasionally lived with his mother. One of the psychiatrists prescribed him the latest drugs, which gave him a visible improvement. But John refused to drink them, fearing side effects.

For thirty "dark" years, Nash did not write a single article. There were rumors in the scientific world about his untimely death, about the transferred lobotomy. And he himself considered himself the savior of the Universe and wandered in the world of illusions, blaming communists and mysterious enemies for his troubles.

After the death of his mother, he again turned to Alicia and asked for shelter. To everyone's surprise, she agreed. So John was back at Princeton. Sometimes he walked around the university and left mysterious formulas and messages to nowhere on the boards in the audience. The students nicknamed him the Ghost.

The movie A Beautiful Mind tells how Nash never recovered from schizophrenia - it's simply impossible - but learned to live with the disease. In reality, his return to the real world in the early 1990s remained unexplained. He again began to reason logically, operate with mathematical expressions, mastered the computer. Doctors said that age-related changes contributed to this. John himself is sure that he himself has learned to separate illusions from reality. And again engaged in science.

Nash spoke out against "dirty" money and refuted Adam Smith

In 1994, when Nash was awarded the Nobel Prize, the committee denied him the right to give the traditional laureate lecture, fearing for his fortune. However, subsequent years showed that the genius did not lose the sharpness of the mind.

“I remained in captivity of the disease long enough to finally give up my delusional hypotheses and return to thinking of myself as an ordinary person in order to again engage in mathematical research,” Nash wrote in his autobiography. In 2011, she and Alicia got married again.

Nash was again given an office at Princeton, and he did mathematics for the rest of his life. From time to time he was invited to give lectures in different countries. In 2013, the professor visited Kyrgyzstan and gave a lecture in Bishkek on ideal money.

Shot from the movie "A Beautiful Mind"

“When we talk about money, we immediately think about how to spend it faster and have fun. We do not perceive money as a radio that can convey valuable and important information. If we take advantage of the possibilities of money, invest it in education or in something else, then the money will double and enrich us, ”said the scientist.

Nash has been critical of capitalist policies that equate good and dirty money. “You can’t assume that dirty money is better than honestly earned money. The new government of Japan followed this policy and is now clearing up the negative consequences. Japan wanted to reduce the prices of exported goods, wanted to artificially maintain the exchange rate of the national currency. The cost of goods fell, exports really revived. But in Japan itself, prices have risen, the exchange rate has fallen, inflation is pestering the economy, ”he recalled.

John Nash advocated the creation of a global financial organization like the International Monetary Fund, which would allow borrowing and repaying loans not in money, but in goods.

The theories developed by Nash refuted the idea of ​​Adam Smith "every man for himself" and had a serious impact on the formation of the world economy. His developments are actively used in the analysis of oligopoly - the behavior of a small number of competitors in certain sectors of the economy. In addition, his game theory works successfully in jurisprudence, social psychology, sports and politics.

Biography and episodes of life John Nash. When born and died John Nash, memorable places and dates of important events in his life. quotes mathematician, Photo and video.

John Nash life years:

born June 13, 1928, died May 23, 2015

Epitaph

“And delusions, and insights;
Fantasy prisoner, genius of delirium ...
All life is a mirage, all life is a vision,
All life is a struggle.
All life is a victory."

Biography

The amazing story of a mathematician with schizophrenia, told in the film A Beautiful Mind, touched the hearts of millions of viewers around the world and deservedly received many prestigious film awards, including 4 Oscars. Moreover, before the film was released, few people could imagine that this is possible in reality. And in the meantime, that's exactly what happened. The great mathematician who fought and defeated the disease was called John Nash. He was a Nobel laureate and a courageous man.

Already during John's studies at the university, it became clear that Nash was extremely gifted. It seemed that bright prospects were opening up before him. Upon graduation, he entered a prestigious university, at the same time he met his future beautiful wife, who was soon expecting their son. But Nash's fate seems to have had a morbid sense of humor: a man whose main treasure and tool was his own brain could not control it. Nash began to show symptoms of paranoid schizophrenia.

At that time (as, in principle, today) there were no universally effective treatments for schizophrenia. Nash's only chance was to work on himself - and just work. Friends helped him get a job at the university, where he could continue his scientific work. And, to the surprise of others, the disease began to recede. Although Nash himself admitted that phantoms and obsessions have not gone away from his mind: he just learned to fence himself off from them.

It is not known how the life of a mathematician would have turned out if it were not for his wife. Once, with a young son in her arms and an uncontrollable husband, she made, as she later considered, a mistake by filing for divorce. Later, Alicia Nash repented of her act and took her husband back just when Nash returned from Europe in the whole world had nowhere to go. After that, the couple lived together for 45 years. They died on the same day in a car accident. When this happened, Nash was 86 years old.

life line

June 13, 1928 Birth date of John Forbes Nash Jr.
1949 Dissertation on game theory.
1950-1953 Four original studies of non-zero-sum games and the discovery of the Nash equilibrium principle.
1951 Applying for a job at the Massachusetts Institute of Technology.
1957 Marriage to Alicia Lard.
1959 Dismissal and forced placement in a psychiatric clinic. Attempt to emigrate to Europe.
1961 A room in a clinic in New Jersey.
1962 Divorce.
1970 Restoration of relations with his wife.
1994 Receiving the Nobel Prize in Economics.
2001 Remarriage to Alicia Nash.
2015 Receiving the Abel Prize.
May 23, 2015 Date of death of John Nash.

Memorable places

1. Bluefield (West Virginia), where John Nash was born.
2. Carnegie Polytechnic Institute (now Carnegie Mellon University), where Nash studied.
3. Princeton University, where Nash entered after graduation.
4. Massachusetts Institute of Technology, where Nash worked.
5. Clinic McLean in the suburbs of Boston, where Nash was admitted with a diagnosis of paranoid schizophrenia.
6. The Trenton Clinic in New Jersey, where Nash was placed in 1961
7. Graduate School of Management, St. Petersburg State University, where Nash made a presentation at the international conference "Game Theory and Control" in 2008.

Episodes of life

At school, Nash did not study very well and did not like math at all.

For admission to the university, the institute teacher of the future great mathematician made him a recommendation. It consisted of one sentence: "This man is a genius."

Nash received the Nobel Prize for his dissertation, written 45 years earlier.

Nash became the only Nobel Prize winner in the world and at the same time - the highest prize in the field of mathematics, the Abel Prize.

Testaments

"Rational thinking limits man's ideas about his connection with the cosmos."

“People are always selling the idea that those with a mental illness are suffering. I think insanity can be a release. If things aren't going well, you might want to imagine something better."

“Some things tend to get more moderate with age. Schizophrenia is something in that series."

The story of meeting John Nash for the filming of A Beautiful Mind

condolences

“Stunned… My heart goes out to John and Alicia. Amazing union. Great minds, great hearts."
Russell Crowe, actor who plays Nash in A Beautiful Mind

"I sincerely believe that the twentieth century did not have many great ideas in economics and perhaps its balance among the top 10."
Harold W. Kuhn, Princeton professor of mathematics, friend and colleague of Nash

“John's remarkable achievements have inspired generations of mathematicians, economists and scientists. And the story of his life with Alicia touched millions of readers and moviegoers who marveled at their courage in the face of ordeals."
Christopher L. Eisgruber, President of Princeton

The name of John Nash may not be known to everyone, but almost everyone is familiar with his story - it was this story that formed the basis of the biographical drama A Beautiful Mind starring Russell Crowe. Nash authored an influential work on game theory at the age of 21 and defended it as a dissertation while studying at Princeton University. In the scientific world, he quickly became known as the author of the formulation of the "Nash equilibrium". Decades later, his work was awarded the Nobel Prize in Economics.

At the age of 30, the "rising star of American science" began to show noticeable signs of mental illness. When they could no longer be attributed to typical extravagance for a scientist, Nash lost his job and was placed in a psychiatric clinic, where he was given a disappointing diagnosis: "paranoid schizophrenia."

A long struggle with the disease began, from which Nash eventually emerged victorious.

During this time, he visited several clinics and tried several antipsychotic medications. His wife left him. Temporary improvements were interspersed with long periods of frustration. Nash was obsessed with ideas of persecution and could not distinguish his own fantasies from reality. He still continued to live in Princeton and from time to time went into the classrooms, covering the boards for him alone with understandable formulas. At some point, he again began to live with his wife Alicia, who provided him with support and a relatively quiet existence. And in the end, the disease began to recede.

The mathematician, who had already been forgotten in the scientific world, was able to return to work again. In his autobiography, he wrote: "I think if you want to get rid of a mental illness, you should, without relying on anyone, set yourself a serious goal yourself." A triumphant Nobel Prize ceremony followed in 1994, and in 2015 Nash received the equally prestigious Abel Prize for contributions to the theory of non-linear differential equations. Shortly thereafter, he and his wife were in a car accident and died. He was 86 years old.

For a wide audience, Nash became a famous and important hero after the publication of the book A Beautiful Mind by Sylvia Nazar (a film about mathematics was later based on it). In 2016, the book was translated into Russian and published by Corpus under the title "Mind Games".

We publish an excerpt from the book, which describes the symptoms of schizophrenic disorder and talks about how Nash took his own return to "normal" life.

Persistent, complex, and compelling delusions are one of the diagnostic features of schizophrenia. Crazy ideas are false ideas, ideas that deviate sharply from generally accepted reality. Often they are associated with a misinterpretation of what is perceived or experienced. It is now generally accepted that they arise mainly due to a serious distortion of sensory data and due to the way thoughts and emotions are processed in the depths of the brain.

That is, the confused and mysterious logic of delusional ideas is sometimes seen as the result of attempts by a completely separate consciousness to penetrate the meaning of the strange and inexplicable.

Edwin Fuller Torrey, a researcher at St. Elizabeth's Hospital in Washington and author of Schizophrenia, calls them "the logical offshoots of what the brain experiences" as well as "a heroic effort to maintain mental balance."

The syndrome we now call schizophrenia was once called dementia praecox(formerly dementia) - although in fact the delusional states typical of schizophrenia often have little to do with dementia associated, for example, with Alzheimer's disease. Instead of confusion, confusion and illogicality in schizophrenia, there is increased sensitivity, sharpening of perception and severe insomnia. A person is obsessed with obsessive ideas, comes up with sophisticated justifications and original theories.

No matter how literal, irrelevant or self-contradictory his thoughts may seem, they are never random and always obey specific rules, no matter how obscure and confusing. At the same time, surprisingly, the ability to clearly understand certain aspects of everyday reality remains.

If Nash were asked what year it is, where he lives, or who is the current president of the United States, he would no doubt be able to answer all these questions perfectly if he wanted to. And indeed, even when Nash hatched the most surreal concepts, he showed an ironic understanding that his ideas are exclusively private, intended only for himself, and should seem strange and implausible to others.

“The concept that I am about to present ... you may find it absurd” - this is a typical introduction for him.

His speech was full of phrases like “suppose”, “as if”, “we can count” - as if he was conducting a thought experiment or understood that whoever reads what he wrote would have to translate it into another language. Like all other manifestations of this syndrome, delusions do not unambiguously indicate schizophrenia - they occur in a variety of mental disorders, including mania and depression, as well as in a number of somatic diseases. But the delusions with which Nash was seized are especially characteristic of schizophrenia, in particular paranoid schizophrenia - the kind of syndrome from which, apparently, Nash suffered. Their content reflected, as often happens, both megalomania and delusions of persecution, sometimes switching from one to the other, sometimes combining them.

Sometimes, as we know, Nash considered himself extremely powerful, such as a prince or emperor; at times very weak and vulnerable, like a refugee or a defendant. His ideas, which is quite typical, were in the nature of the so-called delusions of attitude, that is, he believed that myriad signs in the surrounding reality - from newspaper texts to certain numbers - were addressed personally to him and only he could understand their true meaning. Moreover, he had a lot of various delusional ideas - this is a common symptom of paranoid schizophrenia - although they were all implicitly grouped around related topics.

For schizophrenic delusions, bizarreness is considered especially characteristic. Nash's ideas were absolutely incredible, they were difficult to understand, they were not deduced in an obvious way from his life experience. Yet overall, they were less bizarre than many of the delusions reported by other schizophrenic patients, and they were often connected, however indirectly, to Nash's biography and life circumstances (or could be traced if someone of his relatives wanted to study this issue as carefully as the faithful wife of the Balzac hero Louis Lambert did).

Many people with schizophrenia believe that their thoughts are being taken over by external forces or that external forces have planted these thoughts in their heads, but in Nash's case, such representations do not appear to have been predominant. Sometimes, as in Rome, it might seem to him that thoughts were being loaded into his brain by a machine, or, as in Cambridge in early 1959, that God was directing his actions. But for the most part, Nash considered his "I" (or his "I") to be the main character.

Moreover, many of his ideas - for example, that for ideological reasons he evades military service and that he is in danger of being drafted; that he is a stateless person; that members of the American Mathematical Society are hurting his career; that people pretending to sympathize with him were in fact conspiring to commit him to a mental hospital was no more improbable than, say, a person's belief that he was being followed by the police or the CIA. Thus, in a sense, his detachment from reality and the boundaries between himself and the outside world had their limits. In particular, although Nash later called his delusional disorders "periods of irrationality", even during these periods he remained in the role of a thinker, theorist, scientist, trying to understand complex phenomena.

He "improved the ideology of liberation from slavery", searched for a "simple method", created a "model" or "theory".

All the actions he mentions are connected with the work of the mind or with speech. At the very least, he "negotiated" or "interceded" or tried to persuade. His letters were Joyceian monologues, written in a secret language of his own invention, full of illusory logic and incoherent conclusions. He built theories in the field of astronomy, game theory, geopolitics and religion. And while years later, Nash often mentioned the pleasant side of delusional states, it seems clear that these waking dreams were very unpleasant, full of anxiety and fear.

Nash considered himself an outcast ("I fell out of favor"), ostracized. He was constantly afraid of bankruptcy and dispossession: “If the accounts are opened in the interests of a person who, due to the lack of “rational coherence”, is like dead ... It is as if the accounts were opened in the name of the martyrs in Hell. They will never be able to use these accounts, because for this they would have to come from Hell to the bank office and receive money, but for this the revolution must end Hell before they have the opportunity to use their accounts.

Nash proceeds from the presumption of guilt. Punishment, regret, repentance, redemption, confession and repentance are his constant themes, along with the fear of exposure and the need for secrecy and secrecy; they seem to be directly related to his attitude towards homosexuality, but are not completely reduced to this. He speaks of "clearly dubious acts he has committed throughout his life" including "draft evasion and absenteeism". Arrests, trials and imprisonment were also a recurring theme.<...>

Peter Newman, an economist at Johns Hopkins University, edited a collection of selected papers in mathematical economics. He wanted to include Nash's note on the Nash equilibrium, published in the Journal of the National Academy of Sciences. First it had to be found.

“I discovered him at a small women's college near Roanoke where he seems to have taught. I sent a letter there to get permission from him to publish it. In response, I received an envelope on which my address was written in colored pencils. It also had a list of all kinds of “you” and “you” in different languages: Du, Vous, You, etc., as well as a call for universal brotherhood. There was nothing inside the envelope.”

Most of the letters written during this period end something like this: “Let me (humbly) ask you to support the view that I should be protected from the danger of hospitalization in a psychiatric hospital (forced or “fraudulent”) ... simply for the sake of personal intellectual survival as a “conscious and a “relatively conscientious” human being… and “keeping memory intact”.”

Nash gave an extremely harsh assessment of his position in front of an audience of psychiatrists to whom he was presented as a "symbol of hope" [after his recovery - ed.]. At the end of his speech in Madrid in 1996, in response to some question, he said: “To return to rational thinking after the irrational, to return to normal life is wonderful!”

But then he paused, stepped back slightly, and said in a much more confident tone, “Maybe not so great.

The Nobel Prize cannot make up for lost time. For Nash, the main pleasure in life has always been creative activity, not emotional closeness with others. Therefore, although the recognition of past achievements is pleasant, it throws a merciless light on his present possibilities. As Nash said in 1995, winning the Nobel Prize after a long period of mental illness is not very impressive; truly amazing would be "a person who, having experienced a mental illness, then would have reached a high level of intellectual activity.

(Translated from English: Anna Arakelova, Maryana Skuratovskaya and Natalia Shakhova).

Sometimes the line between genius and mental disorders seems completely invisible. The examples of many great people confirm this sad truth. The eminent mathematician John Nash, winner of the 1994 Nobel Prize in Economics, has long struggled with paranoid schizophrenia...

In 2001, A Beautiful Mind was released in the United States, based on the book of the same name by Sylvia Nazar. This film, which tells about the tragic fate of John Nash, shocked the public and the American Academy of Motion Picture Arts, which awarded the film several Oscars. And the fees of this picture amounted to 312 million dollars.

The famous actor Russell Crowe, who played the role of a mathematician, played his image so convincingly that it seemed that all the passions and complex life collisions of John Nash came to life on the screen. But the real story of the mathematician was even more tragic than it is shown in the movie...

John Forbes Nash Jr. was born on June 13, 1928 in West Virginia to an electrical engineer and former school teacher. It is interesting that, like many future geniuses, he studied at school rather averagely, and did not like mathematics at all. In his autobiography, he said that his unusual abilities were revealed after he read Eric T. Bell's book "Great Mathematicians" at the age of 14. And the teenager's abilities turned out to be truly phenomenal: "After reading this book, I was able to prove Fermat's little theorem myself, without outside help."

After graduating from high school, Nash initially intended to follow in his father's footsteps and become an electrical engineer. But instead, he enrolled at Carnegie Polytechnic Institute and took up chemistry. However, this science did not interest the young genius at all, and he became interested in economics.

In 1948, Nash graduated and went to Princeton University with a short letter of recommendation from his professor, Richard Duffin. There was only one line in this letter: "This man is a genius!"...

Game time

Princeton in the late forties and early fifties was a special place. For example, Albert Einstein worked there. John von Neumann and Oskar Morgenstern, scientists who published the landmark book Game Theory and Economic Behavior in the mid-forties, also had a Princeton residence.
Game theory has become for American science a kind of key to solving a wide variety of problems: from microeconomics to the strategy of US foreign policy.

However, while declaring the enormous potential of the theoretical concept, within which almost any social phenomenon can be represented as the interaction of two players acting according to certain rules, Neumann and Morgenstern could not explain how it can be applied to everyday life.

Nash figured out how to fill that gap. His dissertation, which consisted of only 27 pages, was devoted to cooperative and non-cooperative games, as well as the equilibrium of their strategies. He defended it at the age of 22 and in fact received the Nobel Prize for it 45 years later.

One of the main achievements of Nash is the formulation of the "Nash equilibrium": in each game there is a certain set of strategies of its participants, in which none of them can change their behavior in order to be more successful if the other participants do not change their strategies. In other words, it is disadvantageous for players to give up this balance, because otherwise they will only make the situation worse.

At the same time, Nash assumed that any game, in essence, can be reduced to a non-cooperative one - the players act on their own, without agreeing. However, such a game does not assume that opponents are initially aimed at the logic of "make or break". They can pursue a dual goal - to benefit both for themselves and for all participants in the game. It is in the state of "Nash equilibrium" that the most successful combination of personal and collective benefits is possible.

Thanks to this point, game theory gained new life - Morgenstern and Neumann tried to deal with games that result in an absolute loss of one of the parties: ousting a competitor from the market or winning a war. Nash showed that it is wiser to look for a common benefit.

In addition, the scientist developed the "bargaining theory" - a mathematical model of the interaction of participants with initially unequal knowledge, and therefore - able to build behavior patterns in different ways. Over time, the "bidding theory" formed the basis of modern strategies for conducting auctions, making deals, where the interested party itself determines the amount of information that the "partner" in the game should know.

In the film, Nash's discovery was illustrated with an episode of five pretty girls. If all Nash's friends rushed to the most beautiful of them (that is, they began to play each for themselves), then, firstly, pushing each other aside, they would not achieve her, and secondly, turning their backs on her friends, they would rejected by them too, because no one wants to be a "consolation prize." "Nash Equilibrium" offered them another option - to start courting each girl individually, as a result of which, almost everyone got what they wanted.

In the scientific world, John Nash's theory is usually presented through another striking example - the Prisoner's Dilemma problem, which was invented by Nash's teacher Albert W. Tucker. The task is as follows: John and Jack are thieves who got caught by the police after committing a robbery. They are put in separate cells and offered to confess. They have two options for behavior - confess or deny everything. If one confesses, and the other is silent, then the first is released, and the second receives 10 years in prison. If they both confess, then each of them will have to serve five years. If both are silent, then each faces 1 year in prison for illegal possession of weapons. It is important that neither of them knows which path the other has chosen.

How should they do it? From the point of view of the "Nash equilibrium", John and Jack must both remain silent, in which case, each of them is guaranteed to receive a minimum term.

Such a state of balance can be found, according to experts in game theory, in any area of ​​human life. But the gaming approach did not take root right away - and for several reasons.

It turned out that the "Nash equilibrium" is an excellent analytical tool for working with simple situations of interaction between two objects. However, the more complex the situation becomes, the more sets of strategies that satisfy the criterion of "Nash equilibrium" in it. Which one will the players choose? Nash did not answer this.

The theory of games was also not attractive because it "undermined" the foundations of classical capitalism, where the main commandment was "my interests are above all." Concern for the achievement of a collective goal hinted at a planned economy, which in the 1950s during the witch hunts could not be approved. It is curious that the theory of games would not have hurt the Soviet economy either - experts say that it could have prevented such a global, but completely unjustified project as the construction of the BAM.

In addition, the mathematician's belief that players make decisions in isolation also turned out to be an abstraction - at least in the field of microeconomics. The seller and the buyer, competitors - always have the opportunity to enter into negotiations in order to agree on a joint optimal model of behavior.

Schizophrenia

But back to Nash's life path. Thanks to his developments, John Nash ended up in the laboratories of the RAND Corporation, the largest US think tank during the Cold War. Americans now openly admit that game theory and the notion of balance, which implies that destroying the enemy is not the best goal, helped keep the "degree of war" from rising.

After RAND, Nash taught briefly at the Massachusetts Institute of Technology, climbing the academic ladder fairly quickly. There he met Alicia Larde, a promising young physicist who eventually became his wife.

John and Alicia are newlyweds

Nash had little interest in economics and other real-world problems, moving more and more into the realm of abstract mathematics. Riemann spaces interested him much more than the use of "Nash equilibrium". He has written some brilliant papers on some of the toughest problems in math - differential equations, differential geometry, and more. He was destined for a great future. In 1957, Fortune magazine named Nash the Outstanding New Generation Mathematician. Nash's colleagues joked that if the Nobel Prizes were awarded to mathematicians, he could become their laureate more than once.

It would seem that everything was going great, Alicia was expecting a baby, and Nash, at the age of 30, was supposed to become one of the youngest professors - already Princeton. However, the mathematician reacted to the message about this in a completely different way than those around him expected. "I cannot take this post," he said, "the throne of the Emperor of Antarctica awaits me." Nash was hospitalized with a diagnosis of paranoid schizophrenia.

For the next 30 years, he did not write a single article. Many believed that Nash had died. Those more in the know whispered that he had been lobotomized. Nash lost everything - his job, his friends, his family. In real life, Alicia could not stand this burden and in 1963 divorced John

However, he was not up to it, he fled to Europe, considered himself the savior of the world, blamed the communists and Jews for his troubles, raved, was treated and could not leave the world of illusions. Medicines didn't help.

After divorcing his wife, Nash moved into his mother's house. However, she died in 1970. Then Nash called Alicia and asked to be taken in. To everyone's surprise, she agreed (they had recently remarried). They settled near Princeton. Nash went for walks around the campus of the university, entering classrooms and leaving mysterious mathematical formulas and messages to nowhere on the boards. For this, the students nicknamed him "Phantom".

Return

However, in the early 1990s, Nash gradually began to return to the real world. His statements have found logic. He began to operate with meaningful mathematical expressions. He began to learn how to work with a computer and made friends with some students. Doctors attributed this amazing remission to age-related changes in his body. Nash himself says that he got better because he learned to separate the illusion from the real world. This does not mean that he recovered - he learned to live with the disease. "Intellectually I refused it," he wrote in his autobiography.

When the Swedish Academy of Sciences recognized his achievements in the field of game theory, Nash took the news quite calmly, however, a limited range of emotions is a characteristic feature of schizophrenics. He was more interested in the fact that he would finally be able to support his family on his own. After all, besides him, Alicia also has their son, a talented young man who also fell ill with schizophrenia.

Nash received the Nobel Prize in 1994 for "a pioneer in equilibrium analysis in non-cooperative game theory". After that, Princeton decided to give him an office and gave him the opportunity to teach students. Nash claims that, regardless of age and health, he is ready to take new mathematical heights.

John Nash and Paul Krugman (Nobel Laureate)

Nash's case lives on and...

Where are Nash's discoveries applied today?

Having experienced a boom in the seventies and eighties, game theory has taken a strong position in some branches of social knowledge. Experiments in which the Nash team at one time recorded the behavior of the players in the early fifties were regarded as a failure. Today they formed the basis of "experimental economics". "Nash equilibrium" is actively used in the analysis of oligopolies: the behavior of a small number of competitors in a particular market sector.
In addition, in the West, game theory is actively used when issuing licenses for broadcasting or communications: the issuing authority mathematically calculates the most optimal variant of frequency distribution.

In the same way, a successful auctioneer determines what information about the lots can be provided to specific buyers in order to obtain optimal income. With the theory of games successfully work in jurisprudence, social psychology, sports and politics. For the latter, a characteristic example of the existence of a "Nash equilibrium" is the institutionalization of the concept of "opposition".

However, game theory has found its application not only in the social sciences. Modern evolutionary theory would not be possible without the concept of "Nash equilibrium", which mathematically explains why wolves never eat all hares (because otherwise they will starve to death in a generation) and why animals with defects contribute to the gene pool of their species (because that in this case the species can acquire new useful characteristics).
Now Nash is not expected to make grandiose discoveries. It doesn't seem to matter anymore, because he managed to do two of the most important things in his life: he became a recognized genius in his youth and defeated an incurable disease in his old age.

Letter from John Nash to the NSA, 1955

The US National Security Agency has declassified the amazing letters that the famous mathematician John Nash sent them in 1955.

John Nash proposed a completely revolutionary idea for those times: to use the theory of computational complexity in cryptography. If you read the letter dated January 18, 1955, you will admire how prophetic Nash's analysis of computational complexity and cryptographic strength turned out to be. It is on these principles that modern cryptography is based. The first work in this area was published only in 1975.

At one time, the authorities showed no interest in the work of an eccentric professor of mathematics. Or, which is also possible, they used Nash's ideas without him knowing.

In his letter, John Nash develops Claude Shannon's 1949 idea of ​​communication theory in secret systems without mentioning it, but goes much further. He proposes to base the security of cryptosystems on computational complexity, exactly on the principle that, in 1975, two decades later, formed the basis of modern cryptography. Nash goes on to clearly describe the difference between polynomial time and exponential time, which is the basis of computational complexity theory. This principle was first described in 1965, although Gödel's famous letter to von Neumann of 1956 refers to it, but not in relation to cryptography.
John Nash:

“So the logical way to classify encryption processes would be by the way in which the difficulty of calculating the key increases with the length of the key. It is exponential at best, and at worst probably at least a relatively small power of ar2 and ar3, in substitution ciphers.

Elsewhere, he seems to be talking about a one-way function, although such terms, of course, did not exist then:

“My general hypothesis is as follows: for almost all fairly complex types of encryption, especially where instructions given by different parts of the key act on the complex interaction of instructions with each other in determining their effect on the final result of encryption, the average complexity of calculating the key grows exponentially with key length.

The mathematician is well aware of the importance of his hypothesis for practical cryptography, because the use of new methods will put an end to the eternal "game" of ciphers and code breakers.
“The importance of this general hypothesis, if we assume its truth, is easily seen. It means that it becomes quite likely to create ciphers that will be virtually unbreakable. As the complexity of the cipher increases, the cipher-breaking game between skillful teams, etc., will become history.”

Actually, that's how it happened.
It is also interesting that John Nash is open about using methods whose theoretical basis he cannot prove (P = NP). Moreover, he explicitly says in the letter that he "does not expect his proof", which is unusual for a mathematician.

Scanned copies of John Nash's handwritten letters

Interesting facts about the film

1. The director's spot was originally assigned to Robert Redford.


2. John Nash could have been played by Tom Cruise.


3. The bed scene between the characters Crowe and Connelly was cut from the final version of the picture.


4. John Nash (played by Russell Crowe in the film) was brought on set to help the actors play their roles more authentically. Russell Crowe later admitted that he was fascinated by John's hand movements and tried to do the same during filming.


5. Salma Hayek was invited to play the role of Alicia Lard.


6. The Harvard scenes were actually filmed at Manhattan College.


7. For the right to film the life of John Nash, two applicants-producers fought. Brian Grazer won the argument, and Scott Rudin was the loser.


8. Professor Dave Byer became the main consultant of the picture and even got into the frame. It is his hands that draw complex formulas on the windows.


9. Despite the fact that the picture is a kind of biography of the life of John Nash, some details of the life of the great mathematician were deliberately omitted:


10. 1) John has been married several times;


11. 2) in his youth, John was bisexual - had close relationships with both women and men;


12. 3) John had an illegitimate child.


13. John Nash really received the Nobel Prize, but not alone, but together with colleagues - Reinhard Selten and the Hungarian Janos Harsanyi. Moreover, another Hungarian, Janos Newman, became the founder of Game Theory. Nash distinguished himself by being able to apply the provisions of "game theory" in the business world.


14. Robert Redford was offered to direct the film, but he was not satisfied with the filming schedule.


15. When Nash first sees Parker, he refers to him as "big brother" (an allusion to Orwell's 1984). Another reference to Orwell comes later, when we see the number on the door of Nash's office - 101.


16. The manuscript that young John Nash shows to his curator, Professor Helinger, is a genuine copy of an article published in the journal Econometrica under the heading "The Transaction Problem".


17. The screenwriter of the film, Akiva Goldsman, had considerable experience in dealing with mentally ill people: when he was a doctor, he personally developed methods for restoring the mental health of children and adults.


18. The Mathematics Curator of the film was Dave Bayer, a professor at Barnard College — it was with his hand that Russell Crowe “brings out” tricky formulas on the blackboard. "Wise formulas" on closer examination are just a meaningless set of Greek letters, arrows and mathematical signs. Apparently, the professor was paid a salary in vain.


19. Unlike his on-screen counterpart, who was distinguished by rare devotion to his "half", the real John Nash was married several times in his life, and at the age of twenty he adopted an illegitimate child.


20. In the film, Jennifer Connelly plays the wife of Russell Crowe. In real life, her husband is Paul Bettany, who plays Crowe's friend.

“I can’t say that I understand this disease,” the scientist said in an interview with the film, “but I don’t think anyone understands this.”

“In my madness, I thought that I was given a very important role, and that I was chosen to convey alien messages to people. In the same way, the prophet Mohammed called himself the messenger of Allah. I think this is the standard wording,” the scientist said.

“The Nobel Prize opened for me the recognition of the world ... I became an honorary member of various scientific societies and organizations ... It is clear to me that all this would not have happened if it were not for her,” he added self-critically.

Quotes by John Nash

But Newton was right!
Yes, the old man had sound ideas.

“If we all go up to the blonde, we will block each other’s paths, and none of us will get it.” We'll go to her friends and they'll turn their backs on us because nobody wants to feel second-rate. What if neither of us approaches the blonde? ... We will not interfere with each other and will not offend other girls. This is the only way to win.

Tell me, is he real?
- Yes.
— Do you see him?
- Yes Yes.
“I am wary of new people.

“I don't know what I should say to have sex with you. But let's assume that I've already said all this and go directly to it.

I believed in numbers and terms, equations and logic, in common sense… But having spent my life in such research, I don’t know what logic is, what defines common sense… I have come a long way through physics, metaphysics, illusion… and back again. And I made the most important of my discoveries - the main discovery of my life: logical foundations can only be revealed in the mysterious equations of love.

Based on the biography of John Nash, the film "A Beautiful Mind" was made, which received four Oscars. The film makes you look differently at people suffering from mysterious schizophrenia. This picture is one of the most beautiful and touching stories of madness, recovery, discovery, fame, uselessness, loneliness - everything that makes up the life of a genius. John Nash is one of the most revered and famous mathematicians in the world and worked in the field of game theory and differential geometry. In 1994 he received the Nobel Prize in Economics. Nash's dissertation, where he proved the existence of what was later called the Nash Equilibrium, was only 27 pages long. The mathematician struggled tragically for many years with his own madness, bordering on genius. In our selection of 12 of his quotes - they will conquer you with their depth and originality.

1. Good scientific ideas wouldn't come to my mind if I thought like normal people.

1. At times I thought differently than everyone else, did not follow the norm, but I am sure that there is a connection between creative thinking and abnormality.

1. It seems to me that when people are unhappy, they become mentally ill. Nobody goes crazy when they win the lottery. This happens when you don't win it.

1. Now I think quite sensibly, like any scientist. I will not say that this gives me the joy that every person who recovers from a physical illness experiences. Sound thinking limits man's ideas about his connection with the cosmos.

1. Something can be considered incredible and unrealizable, but everything is possible.

1. I never saw imaginary people, sometimes I heard them. The majority sees imaginary people all their lives, having no idea about real ones.

1. My main scientific achievement is that all my life I have been doing things that really interest me, and I have not spent a single day doing all sorts of nonsense.

1. In mathematics, it is not so much the ability to strain the brain that is important, but the ability to relax it. I think ten out of a hundred can do it, no more. In youth, for some reason, it succeeds better.

1. You can't make money with math, but you can organize your brain in such a way that you start earning it. In general, it is those who do not know how to count that are able to earn money. Money does not lend itself to a rational account, their quantity almost never corresponds to your quality, all conflicts are based on this.

1. At least three people can understand me, yes. We have a systematized language for this communication. And another person - for example, you - no one can understand at all, precisely because you cannot formalize yourself. It is impossible to understand people in general.

1. I need contact with those people who can check my results. Otherwise, I think not.

1. Illumination does not happen. In my case, the task was solved at the moment when it was set.

In the library "Main Thought" you can read reviews of books that develop, activate creative, non-trivial thinking. For example, books