In memory of John Nash - a collection of facts about an outstanding mathematician. Mind games: the great mathematician died, the man who defeated schizophrenia Control dynamics john nash

Last weekend, the media spread the news about the death of a landmark scientist of the twentieth century, who made a significant contribution to two sciences at once - economics and. John Nash was known to a wide range of Internet users as the prototype of the brilliant but mad scientist from the movie A Beautiful Mind. However, his biography is much more interesting and complex.

Our editors have collected 10 of the most entertaining and strange facts about John Forbes Nash Jr.

Childhood without math

The future mathematical genius was born on June 13, 1928 in a conservative Protestant family, but with technical roots. His father was an engineer at Appalachian Electric Power, and his mother worked as a school teacher for 10 years before her marriage. John was brought up in strictness, but he didn’t work out at all with the exact sciences - a mathematician in adulthood, as a child, Nash did not like math(taught her very boring and uninteresting). However, at the age of 14, Nash suddenly became interested in reading Eric T. Bell and his Great Mathematicians. In his autobiography, Nash would later write: "After reading this book, I was able to prove Fermat's little theorem on my own, without outside help."

Student years

However, he began his student studies - again - not with mathematics, but with chemistry, having attended the corresponding course at the Carnegie Polytechnic Institute (now it is a private Carnegie-Mallon University). Then he became a student of the course of international economics. And only then did he decide to do mathematics. In 1948 he graduated with two diplomas (bachelor's and master's) and entered Princeton. His letter of recommendation from professor Richard Duffin consisted of a single line: "This man is a genius!"

How Game Theory Developed

Exactly at Princeton, John Nash gets to know game theory presented by J. von Neumann and Oskar Morgenstern. He was so impressed by what he read that at the age of 20, Nash formulated the foundations of the scientific method, which representatives of economic science around the world would later use. In 1949, at the age of 21, he writes an entire dissertation on game theory. 45 years later, she will bring him the Nobel Prize.

Game theory is a mathematical method for studying strategies for any game process. At first, mathematicians studied relatively simple games, like tic-tac-toe or chess, and then moved on to games with the so-called "incomplete information" (where nothing is known about the opponent's capabilities or only a few facts are known) - poker and similar card games, for example. Then came the turn of the "games of a global scale" - divorces, economic processes, technological progress. Each of the parties in each case has its own strategy, peculiarities of thinking and opportunities that it uses in a given situation.

If the mathematicians Neumann and Morgenstern were only interested in games with the so-called. "zero sum" (the victory of one side in them means the inevitable defeat of the other), then for 3 years in the 50s of the twentieth century, Nash publishes four works with an in-depth analysis of "non-zero sum games"- in them all participants either win or lose. As an example of such games, we can talk about strikes at enterprises, manifestations of intra-industry competition and other economic phenomena. Modeling such situations gave the scientist the opportunity to derive the so-called "Nash equilibrium"(or "non-cooperative equilibrium"), in which both parties use an ideal strategy, which leads to a stable long-term balance of interests and opportunities. Maintaining such a balance is beneficial to all parties, because any change in the current situation will only worsen the economic situation for them.

Teaching and career peak

Since 1951, John Nash began teaching at MIT. His selfishness and arrogance were not very liked by his colleagues at the university, but his mathematical abilities were so overwhelming that his colleagues put up with his difficult character. During the same period, Nash had a child, but the mathematician refused to give the newborn his last name or provide financial assistance to his mother, Eleanor Stier.

Despite some scandalousness, as a person, Nash was very successful during these years: the RAND corporation begins to work with him- a real "Mecca for scientists": a place where the best of the best worked on analytical and strategic developments, creating technologies and solutions for the Cold War.

Living with schizophrenia

In 1957, the mathematical genius marries Alicia Lard.. In the summer of 1958, he was named "America's Rising Star in New Mathematics" by Fortune magazine. The wife was pregnant when Nash suddenly developed symptoms of schizophrenia. She is 26, he is 30, his career is at its peak and his wife, fearing that her husband will lose his prestigious job and authority, carefully concealed the symptoms of her husband's illness. However, in just a couple of months, Nash has become so out of control that Alicia Lard has him committed to a private psychiatric clinic. The diagnosis does not console - "paranoid schizophrenia", doctors will write in the Nash chart.

A small course of therapy, the scientist is discharged - and he declares his intention to move to Europe. Alicia leaves her first child with her grandmother (her mother) and travels with her husband to bring him back to the States. Upon returning to the US, Alicia goes to work at Princeton, but Nash's symptoms prevent them from living a normal life. Panic attacks, constant talking about yourself in the third person, meaningless postcards and calls to former colleagues, many hours of monologues about politics and numerology - this is what Lard and Nash's life together turns into.

In 1959, a mathematician loses his job, and in 1961, a joint council of Alicia, Nash's mother and sister decides to place John in the Trenton Hospital, where he is treated with huge doses of insulin. Treatment does not help much, and when colleagues offer him a research job at Princeton, he refuses and leaves for Europe. There is practically no connection with him, with the exception of confusing and strange letters. In 1962, his wife files for divorce and raises her son on her own. Only later it turns out that the son inherited his father's disease and also suffers from schizophrenia.

Fellow mathematicians decide not to leave Nash in a difficult period, they still arrange a job for him and even find a psychiatrist who conducts drug therapy. The scientist's condition improves, he even begins to meet with the mother of his first child and with the first-born, John David, whom he did not want to recognize and support financially before.

However, the drugs make Nash less efficient, and he stops taking them, fearing for the sharpness of perception and thinking. The symptoms return.

Return of a mathematician to a more or less normal life

In 1970, Alicia Nash (Lard) decides to take her husband back, repenting that she pushed him away during a difficult period of his life. Nash by that time turns into an eccentric pensioner who goes to Princeton every now and then and writes strange mathematical formulas on the boards in the classrooms. The students call him "Phantom" behind his back. In the 80s of the last century, the symptoms suddenly recede. Nash himself claimed that he simply learned to ignore her and began to do mathematics again. In his autobiography, he wrote about this period that his condition does not cause much joy (unlike ordinary convalescents), because "sane thinking limits a person's idea of ​​\u200b\u200bhis connection with the cosmos."

Death

John Nash's life ended as abruptly and strangely as it had lasted. On May 23, 2015, the 86-year-old scientist died in a car accident with his wife, Alicia, in New Jersey. According to the police, death occurred instantly: neither the mathematician nor his wife were wearing seat belts in the taxi in which they were traveling. The car collided with another car on the highway, and from the impact flew to the side of the road and crashed into a wall.

Nobel Prize and cinema

The prestigious scientific award found Nash at an advanced age. In 1994, at the age of 66, Nash received the Nobel Prize for his contributions to game theory. In 2001, he remarried his wife Alicia, remarried her, and returned to the Princeton office. In the same period, his life and work become the property of the silver screen: Russell Crowe played a mathematician with schizophrenia in the film A Beautiful Mind.

(1928)

Mathematician and Nobel laureate John Forbes Nash Jr. was born on June 14, 1928. John Nash is a mathematician who has worked in the fields of game theory and differential geometry. He shared the 1994 Nobel Prize in Economics with two other game theorists, Reinhard Selten and John Harsanyi.

There are rumors in the scientific world that John was awarded the Nobel Prize for just one of his simplest papers, and many of Nash's theories are simply incomprehensible. The most interesting thing is that John Nash did not use the works of his predecessors, he simply created most of his theories about “out of nowhere”, without using ready-made materials and theory. During his studies, John Nash even refused to attend lectures, arguing that he would not learn anything new there, but would just lose precious time.

After a promising start to his mathematical career, John Nash began to develop schizophrenia in his 30s, a disease that the mathematician learned about 25 years later.

John Forbes Nash Jr. was born in Bluefield, West Virginia to John Nash Sr. and Virginia Martin. His father was an electrical engineer, his mother was an English teacher. As a teenager, John spent a lot of time reading books and doing various experiments in his room, which soon became a laboratory. At the age of 14, John Nash proved Fermat's Little Theorem on his own.

From June 1945 to June 1948, John Nash attended Carnegie Polytechnic Institute in Pittsburgh, intending to become an engineer like his father. Instead, John fell deeply in love with mathematics and had a particular interest in topics such as number theory, the Diophantine equations of quantum mechanics, and the theory of relativity. Nash was especially fond of solving problems.

At Carnegie, Nash became interested in the "negotiation problem" that John von Neumann had left unresolved in his book Game Theory and Economic Behavior (1928).

After Pittsburgh, John Nash Jr. went to Princeton University, where he worked on the theory of equilibrium. He received his Ph.D. in 1950 with a thesis on non-cooperative games. The dissertation contained the definition and properties of what would later be called the "Nash Equilibrium", 44 years later, it would win him the Nobel Prize. His research on the subject led to three papers, the first titled "Points of Equilibrium in N-Number Games" published in Proceedings of the National Academy of Sciences (USA) (1950) and the rest in "Econometrics" on the problem of negotiation (April 1950) and "Non-cooperative games with two players" (January 1953) .

During the summer of 1950, John Nash worked for the Rand Corporation in Santa Monica, California, where he returned for shorter periods in 1952 and 1954. In 1950-1951, Nash taught calculus at Princeton, studied and managed to "slop down" military service. During this time, he proved the Nash theorem on regular embeddings, which is one of the most important in differential geometry on manifolds. From 1951-1952 John became a research assistant at the Massachusetts Institute of Technology in Cambridge, Massachusetts.

At the Massachusetts Institute of Technology, John Nash met Alicia Lard, a student from El Salvador, whom he married in February 1957. Their son, John Charles Martin (born May 20, 1959), remained nameless for a year, because Alicia, since John Nash was in a psychiatric clinic, did not want to name the child herself. Following in his parents' footsteps, John became a mathematician, but like his father, he was diagnosed with paranoid schizophrenia. John Nash had another son, John David (born June 19, 1953) with Eleanor Steer, but he wanted nothing to do with them. Recognized as bisexual, Nash had relationships with men during this period.

Although Alicia and John divorced in 1963, they remarried in 1970. But according to Nash's biography, Sylvia Nazar, they lived "like two distant relatives under the same roof" until John Nash won the Nobel Prize in 1994 , then they resumed their relationship and married on June 1, 2001.

In 1958, John Nash began to show the first signs of his mental illness. He became paranoid and was admitted to McLean Hospital in April-May 1959, where he was diagnosed with paranoid schizophrenia. After a problematic stay in Paris and Geneva, Nash returned to Princeton in 1960. He wandered through psychiatric hospitals until 1970 and did research at Brandeis University from 1965 to 1967. Between 1966 and 1996, John Nash did not publish a single scientific paper. In 1978 he was awarded the John von Neumann Prize for "Equilibrium analysis in the theory of non-cooperative games".

The psychological state of John Nash slowly but gradually improved. His interest in mathematical problems is gradually returning, and with it his ability to think logically. In addition, he became interested in programming. 1990s his genius returned. In 1994, John Nash received the Nobel Prize in Economics as a result of his work on game theory at Princeton.

Nash published 23 scientific papers between 1945 and 1996, plus his autobiography Les Prix Nobel (1994).

A film called A Beautiful Mind starring Russell Crowe, released in December 2001 and directed by Ron Howard, showed some events from the biography of John Nash. It, (tentatively) based on the 1999 biography of the same name by Sylvia Nazar, won 4 Oscars in 2002. However, in this film, many events from John's life are embellished or even untruthful, as is the case in many film adaptations to create a greater effect on the audience. Unlike in the film, Nash's manifestations of schizophrenia did not consist of deciphering newspapers for spies. In fact, it seemed to John that encrypted messages from aliens periodically appeared in the newspapers, which only he could decipher. But all this is nonsense. In the film, John Nash is not cured of schizophrenia, which in turn is incurable. In real life, everything is much more interesting. For thirty years, Nash was in various psychological clinics, from which he periodically escaped, but at one point, John was mysteriously cured. How this happened is still a mystery...

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 schizophrenic mathematician, 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.

A brilliant mind was involved in a battle with itself and with its own illusions. Mathematician was forcibly placed in a clinic, after which Nash tried to escape from the country to Europe. History knew examples when the "treatment" of mental patients led to the loss of their mental abilities and talent, and Nash was afraid to repeat the fate of Hemingway. But in Europe he was arrested and returned to his homeland.

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. 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 who have 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

John Nash died immediately after he, along with his colleague Louis Nirenberg, received the Abel Prize, which in the world of mathematics is considered an analogue of the Nobel Prize. Together with his wife, the 86-year-old mathematician returned to the United States from Norway, where this prestigious award is traditionally presented. Upon arrival at home, John Nash and his 82-year-old wife took a taxi, the path of which ran through the New Jersey toll road. For example, it was on it that the protagonist of the series "The Sopranos" Tony rode in the screensaver.

According to the police who arrived at the scene of the tragedy, the taxi driver, in which the Nash spouses were traveling, lost control while trying to overtake another car and, as a result, crashed into a fence. Neither Nash nor his wife were wearing their seatbelts and were thrown out of the car.

Both died on the spot, and the taxi driver was taken to the hospital with non-life-threatening injuries. No charges were brought against him.

The life of a genius

John Nash was born in West Virginia in 1928. At school, Nash did not show much interest in mathematics, but teachers remembered him for his constant craving for reading, his virtuoso game of chess, and the ability to whistle all the works of Bach from memory. The future genius came to mathematics at the age of 13, when he was able to prove Fermat's little theorem.

After receiving his bachelor's and master's degrees from the Carnegie Institute of Technology, he abandoned his intention to follow in his father's footsteps and become an engineer. In 1947, John Nash entered the university, simultaneously rejecting the idea of ​​​​becoming a chemist. And less than two years later, at the age of 21, the mathematician wrote a dissertation on game theory, for which he later received the Nobel Prize.

When he entered the doctoral program at Princeton University, he had a rather short letter in his hand that read: "This man is a genius."

In 1950, the scientist published a paper on the theory of non-cooperative games. The proposed Nash equilibrium turned out to be a simple and effective means of mathematical analysis of various situations, ranging from corporate competition to decision-making in the field of legislation.

According to his theory, there are games in which no player can increase the payoff unilaterally. All participants in the game either win or lose.

In some cases, they use strategies that create a stable balance, called the Nash equilibrium. The classic example that explains this balance is the negotiations between the trade union and the employer, which can lead to both a mutually beneficial agreement and a loss-making strike for all parties.

In 1994, the scientist became a Nobel laureate in economics, sharing the prize with Reinhard Selten and John C. Harsanyi, who largely influenced the decision. It is known that not all of its members approved the candidacy of Nash, who suffers from a serious mental disorder. Moreover, the mathematician was even denied the opportunity to give the traditional Nobel lecture for all laureates, believing that he would not cope with the honorable task.

“I dare not say that mathematics and madness are directly related, but many great mathematicians suffered from schizophrenia, mental disorders and delirium,” the mathematician himself later recalled.

A few days before his death, John Nash received the Abel Prize for his contribution to the theory of non-linear differential equations.

sickness and love

In 1957, John Nash married Alicia Lard, a physics student he met at MIT. Shortly after his marriage, Nash began to show the first symptoms of schizophrenia. So, he considered people with red ties to be members of the Communist Party who organized a conspiracy against him. For a while, the scientist's relatives managed to hide what was happening from others. However, in 1959, Nash still lost his job at the Massachusetts Institute of Technology.

On the offer to become the dean of the Faculty of Mathematics, he said that he was not going to waste time on stupid things and intended to become the emperor of Antarctica.

The trick was the last straw, after which the professor was placed in a psychiatric clinic McLean Hospital. There he was diagnosed with paranoid schizophrenia. After the mathematician underwent treatment and was discharged from the hospital, Nash and his family left for Europe. However, after some time he was deported back to the United States, refusing to grant political asylum.

Sometimes Nash wandered around Princeton and wrote strange formulas on blackboards that didn't make any sense.

Unable to bear this, in 1962 Alicia divorced her husband, but did not leave him. In 2001, the couple got married again.

For many years, Nash's life was a series of flare-ups between taking antipsychotic drugs and trying to return to science. It was not until the mid-1980s that Nash recovered from his illness and was able to resume his studies in mathematics.

“I recovered on my own, without medication. At some point, I just took it and decided not to think about the disease, ”John Nash himself recalled this.

"Mind games"

In 1998, the scientist's biography A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash, written by American journalist Sylvia Nazar, appeared on the shelves of bookstores. An instant bestseller, the book caught the attention of the director. And in 2001, a film of the same name was shot on it with a genius mathematician suffering from schizophrenia and his wife.

The tape received four Oscars, in particular in the categories "Best Film" and "Best Director's Work". After Nash's death became known, Russell Crowe wrote in his

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 chemical engineering department. 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 began teaching at the Massachusetts Institute of Technology. While at university, Nash developed the iteration method, later improved by Jürgen Moser, which is 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 year's sabbatical from the Institute for Advanced Study at Princeton. During this period he lived in New York, collaborated with the Richard Courant Institute for Applied Mathematics at the University of New York.

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

In 1961, at the urging of his relatives, he was sent to Trenton State Hospital in New Jersey for treatment. After completing the course of therapy, he traveled extensively in Europe, doing individual research.

By the 1990s, Nash's mental state 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 his analysis of equilibrium in the theory of non-cooperative games". Nash shared the award with the Hungarian economist John C. Harsanyi and the German mathematician Reinhard Selten.

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

In 1999, for his 1956 embedding theorem, together with Michael D. Crandall, he received the Steele 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 died in a car accident in New Jersey. According to preliminary data, the dead were not fastened.

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