Good scientific ideas would not come to me if I thought like normal people. D. Nash
Childhood of a genius
On June 13, 1928, a completely ordinary boy was born in West Virginia - John Forbes Nash. His father (John Nash Sr.) worked as an electrical engineer. Mother (Virginia Martin) taught English at school.
Little John was an average student, and he didn’t like mathematics. It was taught very boringly at school. He loved to conduct chemical experiments in his room and read a lot. Eric T. Bell's book "Great Mathematicians", which the boy read at age 14, made him "fall in love" with the "queen of all sciences." He was able to prove Fermat's little theorem independently and without any difficulty. This is how the mathematical genius of John Forbes Nash first announced himself. Life promised the guy a bright future.
Nash's studies
The unexpected talent of a mathematician helped Nash (among 10 lucky ones) receive a prestigious scholarship to study at the university. In 1945, the young man entered the Carnegie Polytechnic Institute. At first, he tried to study either international economics or chemistry, but chose mathematics. Nash completed his master's course in 1948 and immediately entered graduate school at Princeton University. The young man's institute teacher, R. Duffin, wrote him a letter of recommendation. It contained one line: “This man is a genius!” (This man is a genius).
John rarely attended classes and tried to distance himself from what others were doing. He believed that this did not contribute to his originality as a researcher. This turned out to be true. In 1949, Nash defended his dissertation on non-cooperative games. It contained the properties and definition of what would later be called the “Nash equilibrium.” After 44 years, the scientist received the Nobel Prize thanks to the main provisions of the dissertation.
Job
John Nash began his career at the RAND Corporation (Santa Monica, California), where he worked in the summer of 1950, as well as in 1952 and 1954.
In 1950 - 1951, the young man taught calculus courses (Princeton). During this period of time he proved Nash's theorem (on regular embeddings). It is one of the main ones in differential geometry.
In 1951 – 1952 John works as a research assistant at Cambridge (MIT).
It was difficult for the great scientist to get along in work groups. Ever since his student days, he was known as an eccentric, isolated, arrogant, emotionally cold person (which even then indicated a schizoid character organization). Colleagues and fellow students, to put it mildly, did not like John Nash for his selfishness and isolation.
Great Scientist Awards
In 1994, John Forbes Nash, at the age of 66, received the Nobel Prize in Economics. The Nobel Committee made a collegial decision (Nash agreed with him) that the scientist would not give a ceremonial speech due to his poor health.
The dissertation for which the prize was awarded was written in 1949, even before the onset of the illness. It was only 27 pages. John Nash's thesis was not appreciated at the time, but in the 70s game theory became the basis of modern experimental economics.
Scientific achievements of John Nash
Applied mathematics has one of its branches – game theory, which studies optimal strategies in games. This theory is widely used in social sciences, economics, the study of political and social interactions.
Nash's biggest discovery was the equilibrium formula he derived. It describes a gaming strategy in which no participant can increase their winnings if they change their decision unilaterally. For example, a workers' meeting (demanding an increase in social benefits) may end in an agreement between the parties or a putsch. For mutual benefit, the two parties must use an ideal strategy. The scientist made a mathematical substantiation of the combinations of collective and personal benefits, the concepts of competition. He also developed the “bidding theory,” which was the basis for modern strategies for various transactions (auctions, etc.).
John Nash's scientific research did not stop after research in the field of game theory. Scientists believe that even people of science cannot understand the works that the mathematician wrote after his first discovery; they are very difficult for them to perceive.
Personal life of John Nash
John Nash's first love was nurse Leonor Steer, who was 5 years older than him. In his relationship with this woman, the scientist’s selfishness was fully revealed. After Leonor became pregnant, John did not give the child his last name and refused custody and financial support. As a result, John (Nash's eldest son) spent almost his entire childhood in the orphanage.
The mathematician’s second attempt to arrange his personal life was Alicia Lard, a physics student from El Salvador, whom he met in Massachusetts. They married in 1957, and in 1959 the young couple had a son, John Charles Martin. At the same time, the scientist began to show the first signs of schizophrenia, which is why the newborn remained without a name for a whole year, since Alicia herself did not want to give a name to the child, and the father (John Nash) was being treated in a psychiatric hospital.
Later, the son of learned parents, following in their footsteps, became a mathematician.
Brilliant schizophrenia
The great mathematician fell ill with schizophrenia at the prime age of 30, after his wedding to Alicia, who was only 26 at the time. At first, Nash’s wife made attempts to hide the terrible illness from her colleagues and friends. She wanted to save her husband's career. But after a few months of his inappropriate behavior, Alicia had to forcibly admit her husband to a private psychiatric hospital. There he was given a disappointing diagnosis of paranoid schizophrenia.
After John Nash was discharged, he decided to leave his homeland and went to Europe. The wife, leaving her little son with her mother, followed him and persuaded her husband to return to America. In Princeton, where they settled, Alicia found a job.
And John Nash's illness progressed. He spoke about himself in the third person, was constantly afraid of something, called former employees, wrote some meaningless letters.
In 1959, the scientist lost his job. In 1961, John's family made a hard-won decision to place Nash in a mental hospital in New Jersey. There he underwent a very risky and harsh treatment - a course of insulin therapy.
After his discharge, the mathematician’s former colleagues wanted to help him by offering him a job as a researcher, but John went to Europe alone. Only mysterious messages came home from him.
After 3 years of torment, in 1962 Alicia decided to divorce her husband. She raised her son alone, with the help of her mother. Unfortunately, the son inherited his father's serious illness.
Mathematicians (Nash's colleagues) offered to help the scientist. They gave him a job and found a good psychiatrist who prescribed John strong antipsychotic medications. Nash began to feel much better and stopped taking the pills. He was afraid that the medications would harm his work as a thinker. And in vain. Symptoms of schizophrenia recurred.
In 1970, Alicia again accepted her schizophrenic husband, who was already a pensioner. Nash continued to go to Princeton and wrote down more than strange formulas on the blackboard. Students gave him the nickname "phantom".
In 1980, Nash's illness began to recede, much to the surprise of psychiatrists. This happened because John returned to his favorite mathematics and learned to ignore his schizophrenia.
In 2001, the couple, after a long cohabitation, re-legitimized family relationships. Alicia spends her entire life with Nash and his long illness insisted that her husband undergo treatment and always supported him.
“Now I think sensibly,” the scientist wrote, “but this does not give me the feeling of happiness that any person recovering should experience. A sound mind limits the scientist’s ideas about his connection with the cosmos.
Some Sayings of John Nash
I think if you want to get rid of mental illness, then we must, without relying on anyone, set a serious goal for ourselves. Psychiatrists want to stay in business.
At times I thought differently than everyone else and did not follow the norm, but I am sure that there is a connection between creative thinking and abnormality.
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.
The life of a great man could have ended tragically, but against all odds, the more than 30-year war against schizophrenia was crowned with significant success - he was awarded the Nobel Prize in Economics in 1994. Nash is now one of the most revered and famous mathematicians in the world.
Based on his biography, the Oscar-winning feature film “A Beautiful Mind” was made, which was recognized as the best in 2001. The film makes you look differently at people who have a history of the mysterious name of the disease “schizophrenia.”
John Forbes Nash Jr., the brilliant Princeton University mathematician whose life was the basis for the Oscar-winning film “A Beautiful Mind,” died over the weekend along with his wife Alicia.
The police established that a taxi driver who lost control was to blame 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 vehicle on the left side and crashed into a guardrail. The accident occurred on the New Jersey Turnpike. New Jersey State Police spokesman Gregory Williams said in a comment to NJ.com that it appears the couple was not wearing seat belts. John and Alicia were thrown out of the taxi 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 Nierenber, acknowledged giants of 20th-century mathematics, for “pioneering contributions to the theory of nonlinear differential equations with partial derivatives 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 long ahead of their time. Nirenberg and the Nash couple flew in from Oslo together, said goodbye at the airport and parted ways in a taxi. John and Alicia died on the way to their home in the suburbs of Princeton.
As you know, the Nobel Prize is not awarded to mathematicians. However, John Nash still became its laureate in the “Economics” category for his analysis of equilibrium in the theory of non-cooperative games.
In the mathematical community, there is an opinion that John Nash became famous thanks to the simplest of his works, while many of his developments are still inaccessible to the understanding of his colleagues.
He is widely known for his biopic A Beautiful Mind, in which Russell Crowe played the role of Nash. The film, which became a discovery in 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 often happens, in life everything was more complicated, more tragic, and more surprising than in the movies.
Creator of mathematics
John Forbes Nash Jr. was born on June 13, 1928, in Bluefield, West Virginia, into a strict Protestant family. His father was an electrical engineer and his mother was a teacher. in English and Latin. Little John did not do well at school, and did not like mathematics - it was taught too boringly. In a small provincial town, he grew up far from scientific communities and high technologies. However, the calling found him on its own.
When Nash was 14 years old, he read Eric T. Bell's book, The Makers of Mathematics. Having mastered what he had read, he was able to prove Fermat’s little theorem himself, without outside help. And soon he turned his room into a real laboratory, where he covered himself with books and conducted various experiments.
In 1945, John entered the Carnegie Polytechnic Institute in Pittsburgh and planned to become an engineer, like his father. He tried to study chemistry, but abandoned the idea. He didn't find the economics course interesting either. As a result, the gifted student fell deeply in love with mathematics and seriously took up number theory and Diophantine equations. And then he took on the “bargaining problem” that John von Neumann had left unsolved in his Game Theory and Economic Behavior.
By the time he entered Princeton, John Nash had earned a bachelor's and master's degree, and his institute teacher, Richard Duffin, provided him with a letter of recommendation consisting of just one line: “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 basics scientific method, which had a special impact on the development of the world economy. Before 1953, he published four papers with in-depth analysis of non-zero-sum games. The situation he modeled would later be called “Nash equilibrium.”
Still from the movie “A Beautiful Mind”
An example of such a balance can be, for example, negotiations between trade unions and company management about increasing 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 either party, 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 Nash's theorem on regular embeddings, which became one of the most important in differential geometry on manifolds.
Still from the movie “A Beautiful Mind”
Nash was a recognized genius, but his relationships with his colleagues did not work out. His works mathematically substantiated Karl Marx's theory of surplus value. During 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 or provide any financial support - in order to protect mother and child from persecution by the McCartney Commission.
become Under pressure from circumstances, the mathematician moved to 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 developments in game theory. However, he failed to get along at RAND. The scientist was fired after police arrested him for indecent behavior.
Shortly thereafter, Nash met El Salvadoran student Alicia Lard, and they married in 1957. Everything was going 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 the youngest professors at Princeton. However, the mathematician reacted to the invitation very strangely. “I cannot take this position. 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.
Having escaped 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 persecution, about messages from aliens 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 asylum to the couple. It is now known that Nash was indeed under surveillance, and his appeals to the embassies of various countries were blocked. Some time later, the mathematician was arrested by the French police and deported to the United States. He settled in Princeton with Alicia, and she found a job. But John's condition worsened, he was afraid of everything, spoke about 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 cruel insulin therapy. After his discharge, his colleagues tried to get him a job, but John went to Europe again, this time alone. Soon Alicia divorced him.
Still from the movie “A Beautiful Mind”
Until 1970, Nash wandered around psychiatric hospitals and periodically lived with his mother. One of the psychiatrists prescribed him the latest medications, which gave a visible improvement. But John refused to take 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 and about the lobotomy he suffered. And he himself considered himself the savior of the Universe and wandered in a world of illusions, blaming communists and mysterious enemies for his troubles.
After his mother's death, he turned to Alicia again and asked for shelter. To everyone's surprise, she agreed. So John ended up back in Princeton. Sometimes he walked around the university and left mysterious formulas and messages to nowhere on the boards in the classroom. The students nicknamed him the Ghost.
The film A Beautiful Mind reveals that Nash was never cured of schizophrenia - it is simply impossible - but 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, and mastered the computer. Doctors said that age-related changes contributed to this. John himself is confident that he himself has learned to separate illusions from reality. And he took up science again.
Nash railed against "dirty" money and rebutted Adam Smith
In 1994, when Nash was awarded the Nobel Prize, the committee denied him the right to give the traditional laureate lecture out of concern for his fortune. However, subsequent years showed that the genius had not lost his sharpness of mind.
“I remained in the grip of illness long enough to finally abandon my delusional hypotheses and return to thinking of myself as an ordinary person and once again take up mathematical research,” Nash wrote in his autobiography. In 2011, he and Alicia got married again.
Nash was again given an office at Princeton, and he studied 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 on ideal money in Bishkek.
Still 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 something else, then the money will double and enrich us,” the scientist said.
Nash was critical of capitalist policies that equate good money with dirty money. “You cannot assume that dirty money is better than honestly earned money. The new Japanese government adhered to this policy and is now dealing with the negative consequences. Japan wanted to reduce the prices of exported goods and wanted to artificially maintain the exchange rate of the national currency. The cost of goods has dropped and exports have really picked up. But in Japan itself, prices have risen, the exchange rate has fallen, and inflation is plaguing the economy,” he recalled.
John Nash advocated the creation of a global financial organization similar to the International currency board, which will allow you to take and give loans not in money, but in goods.
The theories developed by Nash refuted Adam Smith's "every man for himself" idea and had a major impact on shaping the world economy. His work is 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 important events his life. Mathematician Quotes, Photo and video.
Years of life of John Nash:
born June 13, 1928, died May 23, 2015
Epitaph
“Both delusions and insights;
A prisoner of fantasy, a 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 could imagine that this was possible in reality. And yet that’s exactly what happened. The great mathematician who fought the disease and defeated it was named 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 brilliant prospects were opening up before him. After 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 seemed to have 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 found itself in a battle with itself and its own illusions. The mathematician was forcibly placed in a clinic, after which Nash tried to escape the country to Europe. History has known examples when the “treatment” of mental patients led to the loss of their mental abilities and talent, and Nash was afraid of repeating the fate of Hemingway. But in Europe he was arrested and returned to his homeland.
At that time (as, in principle, today) universal effective techniques There was no cure for schizophrenia. The only chance for Nash was to work on himself - and just work. Friends helped him get into a university, where he could continue his scientific work. And, to the surprise of those around her, the disease began to recede. Although Nash himself admitted that phantoms and obsessions did not disappear from his mind: he simply learned to fence himself off from them.
It is unknown how the mathematician’s life would have turned out if not for his wife. One day, with a small son in her arms and an uncontrollable husband, she made what she later considered a mistake by filing for divorce. Later, Alicia Nash repented of her action and took her husband back just when Nash, who had returned from Europe, had nowhere else to go in the whole world. After this, the couple lived together for 45 years. They died on the same day - in a car accident. Nash was 86 years old when this happened.
Life line
June 13, 1928 Date of birth of John Forbes Nash Jr.
1949 Thesis on game theory.
1950-1953 Four original studies of non-zero-sum games and the discovery of the Nash equilibrium principle.
1951 Applying to work 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 Placement in a clinic in New Jersey.
1962 Divorce.
1970 Restoring the relationship with my 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. McLean Clinic in the suburbs of Boston, where Nash was admitted with a diagnosis of paranoid schizophrenia.
6. Trenton Hospital in New Jersey, where Nash was admitted in 1961.
7. graduate School management at St. Petersburg State University, where Nash made a presentation at international conference"Game Theory and Control" in 2008
Episodes of life
Nash was not a very good student at school and did not like mathematics at all.
For admission to the university, the institute teacher of the future great mathematician made a recommendation for him. 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 winner in the world of the Nobel Prize 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 always sell the idea that those with mental illness suffer. I think madness can be a release. If things are not going well, you may want to imagine something better.”
“Some things tend to moderate with age. Schizophrenia is something from this series.”
A story about meeting John Nash for the film A Beautiful Mind
Condolences
“Stunned... My heart goes out to John and Alicia. An amazing union. Beautiful minds, beautiful hearts."
Russell Crowe, actor, performer of the role of Nash in the film “A Beautiful Mind”
"I honestly believe that there weren't many great ideas in economics in the twentieth century and perhaps its balance is among the top 10."
Harold W. Kuhn, professor of mathematics at Princeton, 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 great adversity.”
Christopher L. Eisgruber, President of Princeton
John Nash became widely known throughout the world thanks to the film A Beautiful Mind. This is an amazingly touching, life-affirming film, charged with faith in the power of human genius. It is He who introduces the viewer to the world of the future, where the mind works real miracles. A piercing interweaving of madness and genius in its unity and struggle. The Oscars collection is evidence of this. The game theory created by this mathematician turned the foundations of corporate business upside down. The 27 pages of Nash's doctoral dissertation had the same impact on society and economics as the 21 pages of Einstein's doctoral dissertation on theoretical physics.
Adam Smith's theory, which traditionally follows the development of liberal bourgeois society, in comparison with the way John Nash studies it, looks pale, not giving a clear explanation for many modern phenomena. The above theories are related in the same way that two-dimensional geometry is only a subset of three-dimensional geometry.
Initiation
John was born on June 13, 1928 in Bluefield, West Virginia. At school I was not a “nerd”; I was an average student. By nature - closed, selfish.
Imagine, a future mathematician (differential geometry and game theory) did not like this subject at school. At this stage, everything about him was suspiciously average. It was as if his intellect was sleeping and waiting for a jolt. And yet he came.
At the age of 14, the teenager came across the book “Creators of Mathematics” by his compatriot Eric Bell, a mathematician and author. The book very reliably told about the lives of great mathematicians, about their motivation and contribution to progress.
What happened when he read the book? Who knows... However, it was like an initiation, after which the previously quite average “gray” schoolboy John Nash takes on the impossible and suddenly proves Fermat’s little theorem for those around him. To non-specialists, this last circumstance means little. But believe me, it was a miracle. What can it be compared to? Perhaps, it was as if a chance came along for the amateur provincial actor, and he played Hamlet superbly in the capital.
Polytechnical Institute
His father (the son duplicated his first and last name) was an educated man, worked as an electronics engineer in commercial company. After proving Fermat's theorem, it became quite obvious to the parent that John Nash Jr. would become a scientist.
Several brilliant research papers opened the door wide for the guy to the rather prestigious Carnegie Polytechnic Institute, where the young man first chose chemistry, then international economics, and finally became convinced of his desire to become a mathematician. The master's degrees he received corresponded to the specialty “Theoretical and Applied Mathematics.”
The recommendation given to him by teacher Richard Duffin for admission to the Institute speaks about how much his institute teachers valued him. Let us quote its text in full and verbatim: “This guy is a genius!”
Princeton University
What he didn’t know, he had only nine years left until the point when madness would cover him with a dark veil of paranoid schizophrenia from the outside world for thirty years, erase him from society, destroy his family, deprive him of his job and home.
The young man did not know all this, just as he did not know where the fine line was that separated genius and madness. He enthusiastically greeted the presentation of the new science of game theory, the brainchild of economists Oskar Morgenstern and John, and immediately began brainstorming headlong. The twenty-year-old genius managed to independently develop the fundamental tools of game theory, and at the age of 21 he completed work on the corresponding doctoral dissertation.
How could the young almost doctor of science know that 45 years later John Nash’s theory would be awarded the Nobel Prize? It will take almost half a century for society to understand: this was a breakthrough!
Job
Very early, in 1950-1953, the period of creative maturity begins for the 22-25 year old scientist. He writes several fundamental works on the so-called theory of non-zero-sum games. What it is? You will find the comment later in this article.
John Nash is a famous and successful mathematician. His place of work is very prestigious: located in Cambridge. Then luck smiles on him: contact with the Pro-Pentagon RAND Corporation. He tastes the unlimited funding of the Cold War, becoming one of America's leading experts on its conduct.
What is game theory
The contribution of game theory to modern regulation of social life is difficult to overestimate. What is society from a macroeconomics point of view? Interaction of many players. For example, aggregated: business, government, households. Even at this macro level, it is clear that each of them is pursuing its own strategy.
Businesses potentially tend to inflate their profits (squeezing out households) and minimize taxes (underpaying the government).
It is beneficial for the state to inflate taxes (suppressing small and medium business) and reduce the level of social protection (depriving vulnerable groups of society of support).
Households are comfortable with excessive social support from the state and minimal prices for services and goods produced by business.
How can we get these Swan, Cancer and Pike to work together and dynamically pull the cart whose name is society? This is determined by game theory.
The brainchild of John Nash - non-zero sum problems
The above class of problems, when the gain of one of the parties is equal to the loss of the other, are called zero-sum problems. Both Morgenstern and Neumann knew how to calculate it. However, let us recall that for this class of problems John Nash created the tools and conceptual apparatus.
But the brilliant mathematician did not stop at this model; he substantiated a more subtle class of problems (with a non-zero sum). For example, a conflict between the administration and trade unions putting forward demands for higher wages.
By escalating the situation through a long strike, both sides will suffer losses. If both trade unions and management use the ideal strategy, both will benefit. This situation is called non-cooperative equilibrium, or Nash equilibrium. (Tasks of this kind include diplomatic problems and trade wars.)
Modern highly competitive society demonstrates a truly endless range of interactions between various subjects. Moreover, almost all of them lend themselves mathematical analysis as non-zero sum problems.
Personal life
Until the end of the 50s the future Nobel laureate John Nash climbed the scientific and career ladder, so to speak, jumping three steps. The main thing for him was ideas, not people. He treated his MIT colleague Eleanor Stier, who fell in love with him, coldly and cynically. He was not touched by the fact that the woman gave birth to his child. He simply did not acknowledge his paternity. By the way, Nash had no friends among his work colleagues. He was eccentric and strange, living in a world of self-invented formulas. All his attention was devoted to one thing - developing ideal strategies.
Needless to say, the leading Cold War technologist, thirty-year-old John Nash, was thriving. His photo during these years is very similar to the photo of the actor who played him, Russell Crowe. A brunette with an intelligent face and a thoughtful look. Fortune magazine predicts fame and glory for him. In February 1957, he married Alicia Lard, and two years later they had a son, Martin. However, in this it would seem highest point As his career took off and his personal well-being began, John began to show symptoms of paranoid schizophrenia.
Disease
In the 60s, he felt better, and Eleanor Stier gave the homeless scientist a roof over his head, and he spent time talking with his first son. Nash seemed to be improving and stopped taking his antipsychotic medications. The disease has returned.
Then, in the 70s, Alicia Lard gave him shelter. Colleagues gave him a job.
The road to recovery
At this point, he realized that he was living in an illusory world, deformed by schizophrenia and paranoia, and began to fight the disease. But he was not a doctor, but a scientist. Therefore, his weapon was not medical methods, but the game theory he himself developed. John Nash fought scientifically and consistently against paranoia. The film with Russell Crowe as a genius clearly showed this. He fought the disease around the clock, uncompromisingly, as with an opponent in the game, ahead of the initiative, minimizing his chances, limiting the choice of moves, depriving him of the initiative. As a result of this most important game in his life, the genius defeated madness: he achieved the constant absolute minimization of an incurable disease.
Finally, in 1990, doctors delivered the long-awaited verdict: John Nash recovered. We must pay tribute to the scientific world of the United States; they did not forget the genius, because all these more than fifty years they used the tools developed by Nash. In 1994, he won the Nobel Prize (for his student dissertation, written at the age of 21!). In 2001, Nash again tied the knot with Alicia Lard. Today the famous scientist continues scientific activity in his Princeton office. He is interested in nonlinear strategies for using computers.
Conclusion
This American genius is an amazingly complete person, his whole life is proof of game theory. In his fate, triumph, love, madness, and the victory of intellect over paranoia came together. To analyze the surrounding reality, John Nash invariably uses scientific tools developed by himself.
The genius of a scientist can be very clearly characterized by Umberto Eco’s phrase (novel “Foucault’s Pendulum”) that a genius always plays on one component. However, his game is inimitable and unique. Because when he plays it, all the other components are involved.
Last weekend, the media spread the news about the death of the iconic 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 crazy scientist from the film “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 raised in strictness, but he was not good at the exact sciences at all - a mathematician adult life, Nash didn't like math as a child(they taught it in a very boring and uninteresting way). 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 myself, without outside help.”
Student years
However, he began his student studies - again - not with mathematics, but with chemistry, having taken a corresponding course at the Carnegie Polytechnic Institute (now it is the private Carnegie Mallon University). Then he took a course in international economics. And only then I decided to take up mathematics after all. In 1948, he graduated with two degrees (bachelor's and master's) and entered Princeton. His letter of recommendation from teacher Richard Duffin consisted of a single line: “This man is a genius!”
How game theory developed
Exactly At Princeton, John Nash is introduced to game theory., presented by J. von Neumann and Oskar Morgenstern. What he read impressed him so much that at the age of 20, Nash formulated the foundations of the scientific method, which would later be used by representatives of economic science around the world. In 1949, at the age of 21, he wrote an entire dissertation on game theory. 45 years later it would bring him the Nobel Prize.
Game theory is a mathematical method for learning strategies for anyone gameplay. At first, mathematicians studied comparatively simple games, like “tic-tac-toe” or chess, and then moved on to games with 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 it was the turn of “games on a global scale” - divorces, economic processes, technical progress. Each of the parties in each case has its own strategy, peculiarities of thinking and capabilities that it uses in a given situation.
If 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 over 3 years in the 50s of the twentieth century, Nash published four works with 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, leading to a stable long-term equilibrium of interests and capabilities. 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
In 1951, John Nash began teaching at MIT. His selfishness and arrogance did not really please his colleagues at the university, but math skills were so stunning 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 his mother, Elianor Steer.
Despite some scandal, Nash was very successful as a person during these years: RAND Corporation begins working 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 called “America's rising star in the new mathematics” according to Fortune magazine. His wife was pregnant when Nash suddenly developed symptoms of schizophrenia. She is 26, he is 30, his career is at its peak and the wife, fearing that her husband would lose his prestigious job and authority, carefully hid the symptoms of her husband’s illness. However, in just a couple of months, Nash has become so out of control that Alicia Lard admits him to a private psychiatric clinic. The diagnosis is no consolation - “paranoid schizophrenia”, the doctors will write on Nash’s chart.
After a short 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 return him to the States. Upon returning to the United States, Alicia goes to work at Princeton, but Nash's symptoms prevent them from living a normal life. Panic attacks, constant conversations about oneself in the third person, meaningless postcards and calls to former colleagues, hours-long monologues about politics and numerology - this is what the life together of Lard and Nash turns into.
In 1959, a mathematician loses his job., and in 1961, the joint advice of Alicia, Nash's mother and sister decides to place John in Trenton Hospital, where he is treated with huge doses of insulin. The treatment doesn't help much, and when his colleagues offer him a job as a researcher at Princeton, he refuses and leaves for Europe. There is practically no communication with him, except for confusing and strange letters. In 1962, his wife filed for divorce and raised their son on her own. Only later does it turn out that the son inherited his father’s illness and also suffers from schizophrenia.
Colleagues in mathematicians decide not to abandon Nash during a difficult period, they get him a job and even find a psychiatrist who provides drug therapy. The scientist's condition improves, he even begins to meet with the mother of his first child and with his first-born son, John David, whom he had previously not wanted to recognize and support financially.
However, the drugs make Nash less efficient, and he stops taking them, fearing for his acuity of perception and thinking. Symptoms return.
Return of the 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 in 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 blackboards in the classrooms. Students call him “Phantom” behind his back. In the 80s of the last century, symptoms suddenly receded. Nash himself claimed that he simply learned to ignore her and began to study mathematics again. In his autobiography, he wrote about this period that his condition did not cause much joy (unlike ordinary convalescents), because “sound thinking limits a person’s understanding of his connection with the cosmos.”
Death
John Nash's life ended as suddenly and strangely as it had lasted. On May 23, 2015, the 86-year-old scientist died in a car accident along 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 it flew off to the side of the road and crashed into a wall.
Nobel Prize and cinema
A prestigious scientific award found Nash in old age. In 1994, when he was 66 years old, Nash received the Nobel Prize for his contributions to game theory. In 2001, he got back together with his wife Alicia, remarried her and returned to the office in Princeton. During the same period, his life and work became the property of the silver screen: Russell Crowe played a mathematician with schizophrenia in the film A Beautiful Mind.