The genius of mathematics John Nash was talked about all over the world after the release of the film "A Beautiful Mind". After 30 years of debilitating treatment and fighting insanity, he got over his schizophrenia and learned to live with it. Nash made an enormous contribution to economics and was awarded the Nobel Prize.

The birth of a great genius

On June 13, 1928, a boy was born to a mechanical engineer from Bluefield, West Virginia - John Forbes Nash. A religious family of American provincials raised him - and later his younger sister Martha - according to strict Protestant canons.

At school, young Nash was often bored. He did not demonstrate any special ability to study, and he was not interested in mathematics at all. The boy was remembered by the teachers for his irrepressible thirst for reading, an excellent game of chess and the ability to whistle all the works of Bach from memory.

As a child, John Nash was uncommunicative, touchy and sometimes very suspicious. He spent a lot of time reading books or, retiring in his room, trying to conduct chemical experiments. But everything changed when he got hold of the book by Eric Temple Bell “The Creators of Mathematics. The predecessors of modern mathematics ”. The American writer forever turned the world of a 14-year-old boy and awakened his interest in the exact sciences. Later in his autobiography, Nash writes: "After reading this book, I was able to prove Fermat's little theorem myself, without outside help.".

The young man's zeal for knowledge was appreciated - he, among other 10 lucky ones, received a prestigious scholarship to study and entered the Carnegie Polytechnic Institute as a chemical engineer. But for a long time he could not decide who he really wants to become. Studying chemistry did not bring him any pleasure, but the course in international economics he attended dispelled all doubts: the future scientist realized that he wanted to connect his life with mathematics.

Game theory in the fate of John Nash

Nash transferred to the math department and in record time - in just 3 years! - graduated from the master's course. Having received two degrees, bachelor's and master's in mathematics, the scientist entered the graduate school of Princeton University in 1947. He rarely attended classes, convinced that this dulls the novelty of research ideas. However, a letter of recommendation written by professor Richard Duffin said, "He is a genius in mathematics."

While at university, Nash first heard about game theory from John von Neumann and Oscar Morgenstern. New knowledge captured the imagination of the young mathematician. Two years later, the 21-year-old scientist wrote his doctoral dissertation on game theory. His work was only 27 pages, but they fit the foundations of a new scientific method created by Nash, which played a huge role in the development of the world economy. It was this work 45 years later that was awarded the Nobel Prize in Economics "for a fundamental analysis of equilibrium in the theory of non-cooperative games." In 1951, the dissertation was published as a separate article in the journal Annals of Mathematics.

In the early 1950s, Nash joined the Massachusetts Institute of Technology and also became a development consultant for the RAND Corporation. The firm was engaged in research in the fields of game theory, mathematical economics and the general theory of rational behavior in game situations.

Complex character and personal life

However, the work in Massachusetts did not work out. It was difficult for an arrogant, arrogant and eccentric scientist to get along in a team. Nash's desire to compete with colleagues, selfishness and painful ambition became the cause of frequent conflicts with management. For the same reason, the mathematician had to part with the RAND project. The development of new strategic concepts was commissioned by the US government, and during the Cold War took place under the code of special secrecy. A man from whom no one knew what to expect posed a great threat to the entire project.

During his time with RAND, Nash contributed extensively to the corporation's research. He succeeded in solving a classical problem related to differential geometry. And yet, despite the merits, in 1954 he was removed from all projects.

John Nash's personal life was no less difficult. His first love was nurse Leonora Steer. As a result of their short union, a boy was born, who, like his father, was named John. However, the mathematician broke up with Leonora even before the birth of the child, completely denying his son financial support and custody. True, some sources indicate that the scientist had no other choice: this was the only way he could protect Leonora and the child from possible persecution due to the conflict with RAND. But be that as it may, John Jr. spent almost all of his childhood in an orphanage.

Scientific works

Prior to 1959, Nash published four significant papers on economics that were highly regarded by other scholars. In the articles "Equilibrium points in games with N-number of participants" and "The problem of making deals" he mathematically accurately deduced the rules for the actions of participants who win in accordance with the chosen strategy. The scientist described cooperative (allowing free exchange of information and coercive conditions between players), noncooperative (not allowing free exchange of information and coercive conditions) and noncooperative (without controlling interaction between participants) games and pointed out the differences between them from the point of view of classical theory. Today, game theory is widely used in economics and other social sciences in the study of socio-economic and socio-political relations.

Nash's interest in mathematics has not cooled down either. He published a series of brilliant papers on the theory of Riemannian manifolds and algebraic geometry. Fortune magazine named him America's Rising Star in New Math.

Nash Equilibrium

By carefully studying classical game theory and developing a series of new mathematical games, Nash sought to understand how the market functions, how economic actors make risk-based decisions, and why they act the way they do. Indeed, in order to make a step in the economy, company leaders must take into account not only the recent, but also the previous actions of competitors, as well as many other factors. Participants in economic relations can only take justified risks. That is why each of them must have their own strategy.

In this way, Nash developed a method of "non-cooperative equilibrium", which was later called "Nash equilibrium." Nash's theory allows you to analyze a variety of situations, ranging from competition within the company to decision-making in the legislative field. Based on the "Nash equilibrium", there are games in which no player can unilaterally increase his winnings. All participants either cooperate with each other and benefit from this, or lose together. Players are forced to resort to strategies that create a stable balance, which has been called the "Nash equilibrium".

A classic example of this balance is when union talks with an employer. If the participants cooperate with each other, this can lead to an agreement that will be beneficial to both parties. Refusal to cooperate will result in a strike that is unprofitable for everyone. Nash Equilibrium - all strategies or actions, from which each participant chooses the optimal ones in order to get ahead of the opponent. At the same time, both sides use a strategy that leads to a stable balance.

In the future, many scientists continued to study and improve the Nash equilibrium in order to bring the theory as close as possible to real economic reality.

The Quirks of the Mind of John Nash

In 1957, John Nash married Colombian student Alicia Lard, who studied physics at Massachusetts Institute of Technology. The marriage was happy, but a difficult 1958 almost destroyed their union: soon after the marriage, Nash began to show the first symptoms of schizophrenia.

For mathematicians, the age of 30 is considered critical, because most of the great scientists made their most important discoveries before that time. John Nash crossed the 30-year mark, considering himself a failure. His attempts to prove the Riemann theorem ended in failure, and the responses to his work were not bright and authoritative enough to glorify the scientist.

The trigger for Nash's disease was his wife's pregnancy. The feelings of imminent paternity were reflected in the behavior of the mathematician, and the genius appeared at the New Year's party in a baby costume. After that, Nash began to have delusional ideas and developed delusions of grandeur. It also seemed to the mathematician that he was constantly being persecuted. The scientist claimed that he was being watched by international organizations that want to ruin his career. And in the portrait of Pope John XXIII, the scientist saw himself, explaining such a coincidence by the fact that his favorite prime number is 23.

John Nash rejected the offer to take the prestigious post of dean of the Faculty of Mathematics at the University of Chicago, as he did not intend to waste his time in vain, because he believed that he had already accepted the high office of Emperor of Antarctica. Also, the mathematician suspected all people wearing red ties that they were in the Communist Party and organized a conspiracy against him. The scientist began to see secret symbols in everything that surrounded him. Nash was convinced that he was a prophet, and aliens get in touch with him, who send people encrypted messages through the New York Times and other media.

The disease progressed. Nash experienced constant fear, wrote meaningless messages to former colleagues, and delivered long, confusing monologues over the phone. The state of the scientist could not be hidden further, and his wife placed him in a private psychiatric clinic near Boston. Doctors diagnosed - paranoid schizophrenia. Mathematics was treated with a combination of pharmacotherapy and psychoanalysis. But Nash soon learned to hide the symptoms, and after 50 days he was discharged from the hospital.

Escape to Europe

Still ill, John decided to flee America, where, according to the scientist, a secret conspiracy was being built against him. He retired from the institute and went to France in search of political asylum. Alicia left her newborn son with her mother and followed her husband. However, under pressure from the US State Department, France refused to shelter the scientist. The same as later the GDR and Switzerland.

All this time, the actions of Nash were followed by the American naval attaché, who blocked the mathematician's appeals to the embassies of different countries. After 9 months of wandering around Europe, Nash was arrested by the French police and deported back to America with a special escort.

Returning to their homeland, the couple settled in Princeton, where Alicia found work. But Nash's disease progressed: he was constantly afraid of something, talked about himself in the third person, called his former colleagues with meaningless discussions about numerology and world politics.

John Nash: "I dare not say that mathematics and madness are directly related, but many great mathematicians suffered from schizophrenia, mental disorders and delusions."

Retreatment

2 years after the first hospitalization, Nash was admitted to the hospital again. He spent six months there, and this time the scientist was treated using the only method known at that time - insulin therapy. It was aimed at killing nerve cells in the brain and making the patient calm and obedient. Insulin therapy is now banned in all civilized countries.

After being discharged, John's condition improved briefly. He began to spend more time with Alicia and his son, and even wrote the first scientific work in 4 years on the dynamics of fluids. Nash's colleagues at Princeton University offered him a job as a researcher, but the mathematician refused and soon fled to Europe again. There he again began to think that he was receiving signals from space aliens. Nash transcribed them, wrote them down in digital codes, and sent them to family and colleagues in numerous postcards.

The second hospitalization did not give a positive result. The mathematician's wife, Alicia, tired of the constant struggle with her husband's invisible persecutors, divorced him in 1962. She practically raised her son herself, who, like the first, illegitimate, was named after her father - John.

In 1964, John Nash developed auditory hallucinations. The scientist himself described this period of his life as follows: “I also heard voices when I was sick. As in a dream. At first I had hallucinatory ideas, and then these voices began to respond to my own thoughts, and this went on for several years. In the end, I realized that this is only a part of my thinking, a product of the subconscious or an alternative stream of consciousness. "

Fighting the disease

From time to time, John Nash experienced short-term remissions. He finally gave up taking medications in the 1970s, believing that they interfere with the genius of his thought. At the same time, Alicia was finally convinced that she had made a mistake in betraying her husband, and again got along with him. And it is likely that it was only thanks to moving to his ex-wife that Nash did not end his days on the street.

Colleagues-mathematicians continued to help the scientist: when the illness receded for a while, they provided him with a place at the university. Between 1970 and 1980, the mathematician spent all his time wandering the hallways and auditoriums of Princeton University, leaving numerous calculations and formulas on the blackboards. The students nicknamed the eccentric man "Phantom."

For many years, Nash's life was a series of exacerbations between taking medications and remissions with attempts to return to scientific activities. His only friend during this period was mathematician David Bayer of Columbia University. Only by the mid-1980s, the scientist recovered from his illness and was able to resume his studies in mathematics. To the surprise and delight of colleagues, attacks of schizophrenia practically did not recur, and Nash began to gradually return to "big" science. John himself admitted that he decided to think more rationally, as befits a scientist, and not listen to voices. Of course, Nash could not just be cured of schizophrenia at will. However, he did something that required tremendous effort - he learned to peacefully coexist with his hallucinations.

John Nash:“Now I think quite rationally, like any scientist. I will not say that this gives me the joy that everyone who recovers from a physical illness experiences. Rational thinking limits the idea of ​​a person about his connection with the cosmos. "

Confession

Despite the fact that between 1966 and 1996, John Nash did not publish any scientific work, on October 11, 1994, at the age of 66, he received the Nobel Prize in economics "For fundamental analysis of equilibrium in the theory of non-cooperative games." Together with him, the awards were given to Reinhard Selten and John C. Harsagni.

The newly-minted Nobel laureate did not give a solemn speech. The scientist feared for his own health, and the Nobel Committee decided to play it safe in order to avoid possible troubles during the presentation of the prize. Instead, a seminar was organized with the participation of John Nash, where they discussed his invaluable contribution to science. After the award, the scientist was invited to give a lecture on cosmology at the University of Uppsala. After completing all the celebrations, Nash returned to Princeton and continued his math studies.

In 1998, the American journalist Sylvia Nazar, who is also a professor of economics at Columbia University, wrote a biography of the scientist entitled "A Beautiful Mind: The Life of the Genius of Mathematics and Nobel Laureate John Nash." The book instantly became a bestseller. Thanks to this, the whole world learned the amazing story of the scientist. And in 1998, the American Guild of Literary Critics recognized the work of a journalist as the best biographical work. Sylvia Nazar has been nominated for the prestigious Pulitzer Prize.

In 2001, Ron Howard's Beautiful Mind, starring Russell Crowe, was released in the United States. The title of the film, created from the book of Nazar, literally translates into Russian as "impeccable consciousness", but the Russian-speaking viewer of the film became known as "Games of the Mind". The film won four Oscars, a Golden Globe and several BAFTA awards.

Of course, there are inaccuracies and fiction in the motion picture. For example, the scene in the library when all the university professors give Nash their writing materials. There is no tradition at Princeton of donating pens to recognized scientists. The film also shows people who surrounded the protagonist and subsequently turned out to be visual hallucinations. Fortunately, Nash never suffered from this kind of disorder.

John Nash: “I love this film and am glad that it was filmed, but still this picture can hardly be considered the ultimate truth, since I turned out to be very good in it!”

Triumph mathematician

38 years after their divorce, in 2001, John and Alicia tied the knot again. Their son inherited his father's talent and became a mathematician. Alas, from the brilliant parent he inherited not only abilities, but also illness.

In 2008, John Nash made a presentation on the topic "Ideal and Asymptomatically Ideal Money" at the international conference Game Theory and Management at the Graduate School of Management, St. Petersburg State University.

Nash's lectures have always been popular with the public. English physicist Marjorie Griffith, who was lucky enough to visit one of them, recalled: “ We are all looking forward to the future, and Professor Nash is one of the few who anticipates this future. Of course, when the announcement was posted that he would give a lecture, the news spread like wildfire in a dry forest. He scattered his ideas in front of us, like sparkling diamonds, which he does not value in the least. They listened to him with bated breath. The silence in the audience was such that it seemed that if someone coughed, the ceilings would collapse. But no one coughed, of course ... The silence was burst from time to time only with laughter - a reaction to the magnificent humor of Nash, with which he generously poured his lecture, like sparkling handfuls of precious jewelry. When he finished ... I wanted to say that he was given a standing ovation, but this is not enough - I have not seen such delight even at the Rolling Stones concert.

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American mathematician, Nobel laureate John Forbes Nash, Jr. was born on June 13, 1928 in Bluefield (West Virginia, USA).

His father was an electrical engineer, his mother was a school teacher. At school, Nash did not show outstanding success, was withdrawn, read a lot.

In 1945 he entered the Carnegie Institute of Technology (now Carnegie Mellon) in the Department of Chemical Engineering. Then he became interested in economics and mathematics.

In 1948 he received his bachelor's and master's degrees in mathematics, after which he went to work at Princeton University.

In 1949 he wrote his doctoral dissertation on the mathematical principles of game theory.

In 1951 he left Princeton and took up teaching work at the Massachusetts Institute of Technology. While at university, Nash developed an iterative method, later refined by Jurgen Moser, now known as the Nash-Moser theorem.

In the early 1950s, he worked as a consultant for the RAND Corporation in Santa Monica, California, funded by the US Department of Defense.

In 1956 he won one of the first Sloan Fellowships and took a one-year sabbatical from the Institute for Advanced Study in Princeton. During this period he lived in New York, collaborated with the Richard Courant Institute of Applied Mathematics at the University of New York.

In 1959, Nash began to suffer from schizophrenia and severe paranoia, which eventually forced him to quit his job.

In 1961, at the insistence of relatives, he was sent for treatment at Trenton State Hospital in New Jersey. After completing a course of therapy, he traveled a lot across Europe, doing individual research.

By the 1990s, Nash's mental state had returned to normal, and he received a number of awards for his professional work.

In 1994, the scientist was awarded the Nobel Prize in Economics "For the analysis of equilibrium in the theory of non-cooperative games." Nash shared the prize with Hungarian economist John C. Harsanyi and German mathematician Reinhard Zelten.

In 1996 he was elected a member of the National Academy of Sciences.

In 1999, for his 1956 investment theorem, together with Michael D. Crandall, he received the Steel Prize "For fruitful contributions to research", awarded by the American Mathematical Society.

The scientist continued to collaborate with Princeton University.

In 2015 he was awarded the prestigious Abel Prize in Mathematics for his contribution to the study of differential equations.

John Forbes Nash Jr. and his wife were killed in a traffic accident in New Jersey. According to preliminary data, the victims were not wearing their seatbelt.

Since 1957, Nash has been married to Alicia Larde. In 1962, the couple divorced due to the scientist's mental disorder, but in 1970 the family was reunited. The scientist has a son.

John Forbes Nash, Jr., a brilliant mathematician at Princeton University whose life formed the basis of the Oscar-winning film A Beautiful Mind, died last weekend with his wife, Alicia.

The police found that the taxi driver who lost control of the taxi was to blame for the deaths of the 86-year-old scientist and his 82-year-old wife. The driver of the Ford Crown Victoria was trying to overtake another car on the left side and crashed into a barrier lane. The accident happened on the New Jersey Turnpike. New Jersey State Police spokesman Gregory Williams clarified in a comment to NJ.com that, apparently, the couple were not wearing seat belts. John and Alicia from the impact flew out of the taxi and died on the spot. The driver survived and was taken to hospital with minor injuries.

Just a few days earlier, John Nash received from the hands of King Harald V of Norway the Abel Prize - it is called the mathematical "Nobel Prize". The prize of $ 800,000 was presented to Nash and his colleague Louis Nirenber, recognized giants of mathematics of the 20th century, for "pioneering contributions to the theory of nonlinear partial differential equations in geometric analysis." As noted, each of the scientists worked on his own, however, mathematicians had a great influence on each other, and the results of the work were long ahead of their time. The Nirenberg and the Nash couple flew in from Oslo together, said goodbye at the airport, and took 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 still won it in the Economics category for his analysis of equilibrium in the theory of non-cooperative games.

In the mathematical environment, there is an opinion that John Nash became famous for the simplest of his works, while many of his developments are still inaccessible for the understanding of his colleagues.

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

Math creator

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 communities and high technologies. However, the vocation found him on its own.

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

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

By the time he entered Princeton, John Nash had a bachelor's and master's degree, and college professor Richard Duffin had provided him with a one-line letter of introduction: "This guy is a genius." At Princeton, in 1949, at the age of 21, Nash defended his dissertation on game theory, which 40 years later would be awarded the Nobel Prize in economics. He developed the foundations of the scientific method, which had a particular impact on the development of the world economy. Prior to 1953, he published four papers on deep analysis of non-zero-sum games. The situation he modeled would later be called the "Nash equilibrium".

Still from the film "A Beautiful Mind"

An example of such a balance can be, for example, negotiations between trade unions and company management for wage increases. Such negotiations can end either with a prolonged strike and losses for both parties, or with 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

Since the 1950s, Nash has worked at the Massachusetts Institute of Technology in Cambridge and has written a number of articles 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.

Still from the film "A Beautiful Mind"

Nash was a recognized genius, but relationships with colleagues did not work out for him. His work mathematically substantiated Karl Marx's theory of surplus value. At the time of the "witch hunt" such views in the United States seemed heretical. So when Nash's friend, Nurse Eleanor Steer, gave birth to a baby, Nash refused to give him his name or provide any financial support to keep the mother and baby from being harassed by the McCartney Commission.

Under 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 the dissidents' orphanage, and Nash quickly became one of the leading experts in the Cold War, using developments in game theory. However, he did not manage to get along in RAND. The scientist was fired after the police arrested him for indecent behavior.

Shortly thereafter, Nash met with a student from El Salvador Alicia Lard, in 1957 they got married. Everything went well, the couple was expecting a child, Fortune magazine named Nash a rising American star of new mathematics. He received an invitation to become one of Princeton's youngest professors. However, the mathematician reacted very strangely to the invitation. “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.

Escaping from 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 messages from aliens that only he can decipher. The scientist tried to obtain political refugee status in France, Switzerland and the GDR and renounce his American citizenship. However, under pressure from the US State Department, these countries refused to give the couple an asylum. It is now known that Nash was indeed being spied on, 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, talked about himself in the third person, wrote meaningless letters and told his 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 place John at 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.

Still from the film "A Beautiful Mind"

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

In thirty "dark" years, Nash has not written a single article. In the scientific world, there were rumors about his untimely death, about the transferred lobotomy. And he himself considered himself the savior of the Universe and wandered in a world of illusions, blaming the 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 ended up at Princeton again. Sometimes he walked around the university and left mysterious formulas and messages to nowhere on the blackboards in the audience. The students nicknamed him the Ghost.

In the movie A Beautiful Mind, Nash was never cured of schizophrenia — it’s simply impossible — but he learned to live with the disease. In reality, his return to the real world in the early 1990s remained inexplicable. 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 illusion from reality. And again he took up science.

Nash Opposed Dirty Money and Denied 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 condition. However, the following years showed that the genius did not lose the sharpness of his mind.

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

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

Still from the film "A Beautiful Mind"

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

Nash was critical of capitalist policies that equalize good money and dirty money. “You cannot think that dirty money is better than honestly earned money. The new Japanese government adhered to this policy and is now clearing out the negative consequences. Japan wanted to reduce the prices of exported goods, it wanted to artificially keep 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 taking and giving loans not in money, but in goods.

The theories developed by Nash refuted Adam Smith's idea of ​​"every man for himself" and had a major impact on the formation of the global 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 is successful in jurisprudence, social psychology, sports and politics.

Biography

John Forbes Nash, Jr. is an American mathematician who worked in the fields of game theory and differential geometry. 1994 Nobel Prize in Economics for Equilibrium Analysis in Noncooperative Game Theory (with Reinhard Selten and John Harsanyi). Known to the general public for the most part from the biographical drama of Ron Howard "A Beautiful Mind" about his mathematical genius and the fight against schizophrenia.

John Nash was born on June 13, 1928, in Bluefield, West Virginia, to a strict Protestant family. My father worked as an electrical engineer at Appalachian Electric Power, and my mother worked as a school teacher for 10 years before her marriage. At school he studied secondary, and did not like mathematics at all - at school it was taught boringly. When Nash was 14 years old, he got his hands on the book by Eric T. Bell, The Creators of Mathematics. “After reading this book, I was able to prove Fermat’s Little Theorem myself, without outside help,” writes Nash in his autobiography.

Studies

After school, he studied at the Carnegie Polytechnic Institute (now the private Carnegie Mellon University), where Nash tried to study chemistry, took a course in international economics, and then finally established himself in the decision to study mathematics. In 1947, after graduating from the institute with two degrees - bachelor's and master's, - he entered Princeton University. Nash's institute professor Richard Duffin provided him with one of the most succinct letters of recommendation ever. It had a line: "He is a genius of mathematics" (English He is a mathematical genius).

Work

At Princeton, John Nash heard about game theory, at that time only presented by John von Neumann and Oscar Morgenstern. Game theory struck his imagination, so much so that at the age of 20, John Nash was able to create the foundations of the scientific method, which played a huge role in the development of the world economy. In 1949, the 21-year-old scientist wrote a dissertation on game theory. Forty-five years later, he received the Nobel Prize in Economics for this work "for his fundamental analysis of equilibrium in the theory of non-cooperative games."

Between 1950 and 1953, Nash published four groundbreaking works on non-zero-sum games. He discovered the possibility of “non-cooperative equilibrium,” in which both sides use a strategy that leads to a stable equilibrium. This result was later called the "Nash equilibrium".

In 1951 he joined the Massachusetts Institute of Technology (MIT). He wrote a number of articles on real algebraic geometry and the theory of Riemannian manifolds, which were highly appreciated by his contemporaries.

In 1954, he was arrested by the Santa Monica police for indecent behavior in a men's locker room on the beach. The charge was soon dropped, but Nash was denied access to classified projects at the RAND Corporation, where he worked as a part-time consultant.

Disease

John Nash soon met a student, Colombian beauty Alicia Lard, and they married in 1957. In July 1958, Fortune magazine named Nash America's Rising Star in New Math. Nash's wife soon became pregnant, but this coincided with Nash's disease - he developed symptoms of schizophrenia. At this time, John was 30 years old, and Alicia - 26. Alicia tried to hide everything that happened from friends and colleagues, wanting to save Nash's career. The deterioration of her husband's condition depressed Alicia more and more. In 1959 he lost his job. After some time, Nash was forcibly admitted to a private psychiatric clinic in the Boston suburb, McLean Hospital, where he was diagnosed with paranoid schizophrenia and underwent psychopharmacological treatment. Nash's lawyer managed to get him out of the hospital after 50 days. After being discharged, Nash decided to leave for Europe. Alicia left her newborn son with her mother and followed her husband. Nash tried to obtain political refugee status in France, Switzerland and the GDR and renounce his American citizenship. Biographer Sylvia Nazar reports that in March 1960, Nash visited Leipzig and lived for several days with the Turmer family while the authorities decided on his status. Finally, the US authorities managed to secure the return of Nash - he was arrested by the French police and deported to the United States. Upon their return, they settled in Princeton, where Alicia found work. But Nash's illness progressed: he was constantly afraid of something, talked about himself in the third person, wrote meaningless postcards, called former colleagues. They patiently listened to his endless discussions about numerology and the state of political affairs in the world.

In January 1961, completely depressed Alicia, John's mother, and his sister Martha placed John at Trenton State Hospital in New Jersey, where John received insulin therapy. After his discharge from Princeton, Nash's colleagues decided to help him by offering him a job as a researcher, but John again went to Europe, but this time alone. He sent home only cryptic letters. In 1962, after three years of turmoil, Alicia divorced John. With the support of her mother, she raised her son herself. Subsequently, he also developed schizophrenia.

Colleagues in mathematics continued to help Nash - they gave him a job at the university and arranged a meeting with a psychiatrist, who prescribed antipsychotic medications. Nash's condition improved and he began spending time with Alicia and his first son John David. “It was a very encouraging time,” recalls John's sister Martha. - It was quite a long period. But then everything began to change. " John stopped taking his medication for fear that it might interfere with his mental activity, and the symptoms of schizophrenia reappeared.

In 1970, Alicia Nash, being sure that, having betrayed her husband, made a mistake, accepted him again, and this, possibly, saved the scientist from a state of homelessness. In the years that followed, Nash continued to go to Princeton, writing strange formulas on whiteboards. Princeton students nicknamed him "The Phantom." Then, in the 1980s, Nash felt noticeably better - the symptoms subsided and he became more involved in the life around him. The disease, to the surprise of the doctors, began to recede. In fact, Nash began to learn to ignore her and went back to math.

Now I think quite rationally, like any scientist, - writes Nash in his autobiography. - I will not say that it gives me the joy that everyone who recovers from a physical illness experiences. Rational thinking limits the idea of ​​a person about his connection with the cosmos.

Confession

On October 11, 1994, at the age of 66, John Nash received the Nobel Prize in Economics for his analysis of equilibrium in the theory of non-cooperative games.

However, he was deprived of the opportunity to read the traditional Nobel lecture at Stockholm University, as the organizers feared for his condition. Instead, a seminar was organized (with the laureate) to discuss his contributions to game theory. After that, John Nash was still invited to give a lecture at another university - Uppsala. According to the inviting professor of the Mathematical Institute of the University of Uppsala Christer Kiselman, the lecture was devoted to cosmology.

In 2001, 38 years after their divorce, John and Alicia got married again. Nash returned to his office in Princeton, where he continued to study mathematics.

In 2008, John Nash made a presentation on "Ideal Money and Asymptotically Ideal Money" at the international conference Game Theory and Management at the Graduate School of Management, St. Petersburg State University.

In 2015, John Nash received the highest honor in mathematics - the Abel Prize for his contribution to the theory of nonlinear differential equations.

A noteworthy fact: having received both the Nobel and Abel prizes, John Forbes Nash became the first person in the world to be awarded both prestigious awards.

Doom

John Nash died on May 23, 2015 (aged 86) with his wife, Alicia Nash (she was 83), in a car accident in New Jersey. The taxi driver in which the spouses were traveling lost control during overtaking and crashed into a separation barrier. Both unfastened passengers were thrown out on impact, and the arriving doctors stated their death at the scene. The taxi driver was taken to hospital with a non-life-threatening injury.

Film "A Beautiful Mind"

Main article: A Beautiful Mind (2001 film)

In 1998, American journalist (and professor of business journalism at Columbia University) Sylvia Nazar wrote a biography of Nash titled A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash. ). The book became an instant bestseller.

In 2001, under the direction of Ron Howard, based on the book, the film A Beautiful Mind was shot (in the Russian box office - A Beautiful Mind). The film won four Oscars (for Best Picture, Best Adapted Screenplay, Directing and Supporting Actress), a Golden Globe and several BAFTA awards.

Bibliography

Books

Bargaining Problem = The Bargaining Problem. - 1950.
Non-cooperative Games. - 1951.

Articles

Real algebraic manifolds // Ann. Math. - 1952. - Vol. 56. - P. 405-421.
C1-isometric imbeddings // Ann. Math. - 1954. - Vol. 60. - P. 383-396.
Continuity of solutions of parabolic and elliptic equations // Amer. J. Math. - 1958. - Vol. 80. - P. 931-954.

Translated into Russian

J. Nash, C1-isometric embeddings // Mathematics 1957, volume 1, number 2, pp. 3-16.
J. Nash, The embedding problem for Riemannian manifolds // Uspekhi Mat.Nauk, 26: 4 (160) (1971), 173-216.

J. Nash, Analyticity of solutions to implicit function problems with analytical input data // Uspekhi Mat.Nauk, 26: 4 (160) (1971), 217-226.

The country:

USA

Scientific area: Place of work: Alma mater: Scientific adviser:

Albert Tucker

Known as: Awards and prizes

John Forbes Nash Jr.(eng. John Forbes Nash, Jr.; genus. June 13, Bluefield, West Virginia) is an American mathematician working in the field of game theory and differential geometry. 1994 Nobel Prize in Economics for the Analysis of Equilibrium in the Theory of Noncooperative Games (with Reinhard Selten and John Harsani). Known to the general public for the most part on the biographical drama of Ron Howard "A Beautiful Mind" (eng. A beautiful mind) about his mathematical genius and his fight against schizophrenia.

Biography

Neumann and Morgenstern were engaged in so-called zero-sum games, in which the gain of one side is equal to the loss of the other. In 1953, Nash published four, literally, revolutionary papers in which he presented an in-depth analysis of non-zero-sum games - a class of games in which the winners of the winning participants do not equal the losses of the losing participants. An example of such a game would be the negotiation of wage increases between the union and the management of the company. This situation can end either with a prolonged strike, in which both sides will suffer, or with the achievement of a mutually beneficial agreement. Nash was able to discern the new face of competition by simulating a situation later called "Nash equilibrium" or "non-cooperative equilibrium" in which both sides use an ideal strategy, which leads to the creation of a stable equilibrium. It is beneficial for the players to maintain this balance, since any change will only worsen their situation.

Nash has to leave MIT, although he was a professor there until 1959, and he leaves for California to work at the RAND Corporation, which is engaged in analytical and strategic development for the US government, in which leading American scientists worked. There, again through his research in game theory, Nash became one of the leading experts in the Cold War. Although the RAND Corporation is known as a haven for dissidents who oppose Washington, even there John did not get along. In 1954 he was fired after police arrested him for indecent behavior - dressing up in a men's room on the beach in Santa Monica.

Disease

John Nash soon met a student, Colombian beauty Alicia Lard, and they married in 1957. In July 1958, Fortune magazine named Nash America's Rising Star in New Math. Nash's wife soon became pregnant, but this coincided with Nash's disease - he developed symptoms of schizophrenia. At this time, John was 30 years old, and Alicia - 26. Alicia tried to hide everything that happened from friends and colleagues, wanting to save Nash's career. The deterioration of her husband's condition depressed Alicia more and more. In 1959 he lost his job. After some time, Nash was forcibly admitted to a private psychiatric clinic in the Boston suburb, McLean Hospital, where he was diagnosed with paranoid schizophrenia and was subjected to psychopharmacological treatment. Nash's lawyer managed to get him out of the hospital after 50 days. After being discharged, Nash decided to leave for Europe. Alicia left her newborn son with her mother and followed her husband. Nash tried to obtain political refugee status in France, Switzerland and the GDR and renounce his American citizenship. However, under pressure from the US State Department, these countries denied Nash asylum. In addition, the actions of Nash were followed by the American naval attaché, who blocked his appeals to the embassies of different countries. Finally, the US authorities managed to secure the return of Nash - he was arrested by the French police and deported to the United States. Upon their return, they settled in Princeton, where Alicia found work. But Nash's illness progressed: he was constantly afraid of something, talked about himself in the third person, wrote meaningless postcards, called former colleagues. They patiently listened to his endless discussions about numerology and the state of political affairs in the world.

Confession

"Mind games"

In 1998, Sylvia Nazar, an American journalist (and professor of economics at Columbia University), wrote a biography of Nash titled A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash. Beautiful Mind: The Life of Mathematics Genius and Nobel Laureate John Nash ). The book became an instant bestseller.

In 2001, under the direction of Ron Howard, based on the book, the film A Beautiful Mind was shot (in the Russian box office - A Beautiful Mind). The film won four Oscars (Best Picture, Best Adapted Screenplay, Directing and Supporting Actress), a Golden Globe and several BAFTA (British Film Achievement Awards) awards.

Bibliography

• The Bargaining Problem (1950);
• Non-cooperative Games (1951).
• Real algebraic manifolds, Ann. Math. 56 (1952), 405-421.
• C 1 -isometric imbeddings, Ann. Math. 60 (1954), 383-396.
• Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954.