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 in the screensaver that I went the protagonist TV series "The Sopranos" Tony.
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 the teachers remembered constant thrust to reading, a 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 hands 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 mathematical analysis 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 nonlinear 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 nonsense 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 get back to scientific activity. 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
Sometimes the line between genius and mental disorders seems completely invisible. The examples of many great people confirm this sad truth. The eminent mathematician John Nash, winner of the 1994 Nobel Prize in Economics, has long struggled with paranoid schizophrenia...
In 2001, A Beautiful Mind was released in the United States, based on the book of the same name by Sylvia Nazar. This film is about tragic fate John Nash, shocked the public and the American Academy of Motion Picture Arts, which awarded the film several Oscars. And the fees of this picture amounted to 312 million dollars.
The famous actor Russell Crowe, who played the role of a mathematician, played his image so convincingly that it seemed that all the passions and complex life collisions of John Nash came to life on the screen. But real story the math was even more tragic than it appears in the movie...
John Forbes Nash Jr. was born on June 13, 1928 in West Virginia to an electrical engineer and former school teacher. It is interesting that, like many future geniuses, he studied at school rather averagely, and did not like mathematics at all. In his autobiography, he said that his unusual abilities were revealed after he read Eric T. Bell's book "Great Mathematicians" at the age of 14. And the teenager's abilities turned out to be truly phenomenal: "After reading this book, I was able to prove Fermat's little theorem myself, without outside help."
After graduating from high school, Nash initially intended to follow in his father's footsteps and become an electrical engineer. But instead, he enrolled at Carnegie Polytechnic Institute and took up chemistry. However, this science did not interest the young genius at all, and he became interested in economics.
In 1948, Nash graduated and went to Princeton University with a short letter of recommendation from his professor, Richard Duffin. There was only one line in this letter: "This man is a genius!"...
Game time
Princeton in the late forties and early fifties was a special place. For example, Albert Einstein worked there. John von Neumann and Oskar Morgenstern, scientists who published the landmark book Game Theory and Economic Behavior in the mid-forties, also had a Princeton residence permit.
Game theory has become for American science a kind of key to solving a wide variety of problems: from microeconomics to strategy. foreign policy USA.
However, while declaring the enormous potential of the theoretical concept, within which almost any social phenomenon can be represented as the interaction of two players acting according to certain rules, Neumann and Morgenstern could not explain how it can be applied to everyday life.
Nash figured out how to fill that gap. His dissertation, which consisted of only 27 pages, was devoted to cooperative and non-cooperative games, as well as the equilibrium of their strategies. He defended it at the age of 22 and in fact received the Nobel Prize for it 45 years later.
One of the main achievements of Nash is the formulation of the "Nash equilibrium": in each game there is a certain set of strategies of its participants, in which none of them can change their behavior in order to be more successful if the other participants do not change their strategies. In other words, it is disadvantageous for the players to abandon this balance, because otherwise they will only make the situation worse.
At the same time, Nash assumed that any game, in essence, can be reduced to a non-cooperative one - the players act on their own, without agreeing. However, such a game does not assume that opponents are initially aimed at the logic of "make or break". They can pursue a dual goal - to benefit both for themselves and for all participants in the game. It is in the state of "Nash equilibrium" that the most successful combination of personal and collective benefits is possible.
Thanks to this point, game theory has gained new life- Morgenstern and Neumann tried to deal with the games, the result of which is the absolute loss of one of the parties: ousting a competitor from the market or winning the war. Nash showed that it is wiser to look for a common benefit.
In addition, the scientist developed the "bargaining theory" - a mathematical model of the interaction of participants with initially unequal knowledge, and therefore - able to build behavior patterns in different ways. Over time, the "bidding theory" formed the basis of modern strategies for conducting auctions, making deals, where the interested party itself determines the amount of information that the "partner" in the game should know.
In the film, Nash's discovery was illustrated with an episode of five pretty girls. If all Nash's friends rushed to the most beautiful of them (that is, they began to play each for themselves), then, firstly, pushing each other aside, they would not achieve her, and secondly, turning their backs on her friends, they would rejected by them too, because no one wants to be a "consolation prize." "Nash Equilibrium" offered them another option - to start courting each girl individually, as a result of which, almost everyone got what they wanted.
In the scientific world, John Nash's theory is usually presented through another striking example - the Prisoner's Dilemma problem, which was invented by Nash's teacher Albert W. Tucker. The task is as follows: John and Jack are thieves who got caught by the police after committing a robbery. They are put in separate cells and offered to confess. They have two options for behavior - confess or deny everything. If one confesses, and the other is silent, then the first is released, and the second receives 10 years in prison. If they both confess, then each of them will have to serve five years. If both are silent, then each faces 1 year in prison for illegal possession of weapons. It is important that neither of them knows which path the other has chosen.
How should they do it? From the point of view of the "Nash equilibrium", John and Jack must both remain silent, in which case, each of them is guaranteed to receive a minimum term.
Such a state of balance can be found, according to experts in game theory, in any area of human life. But the game approach did not take root right away - and for several reasons.
It turned out that the "Nash equilibrium" is an excellent analytical tool for working with simple situations of interaction between two objects. However, the more complex the situation becomes, the more sets of strategies that satisfy the criterion of "Nash equilibrium" in it. Which one will the players choose? Nash did not answer this.
The theory of games was also not attractive because it "undermined" the foundations of classical capitalism, where the main commandment was "my interests are above all." Concern for the achievement of a collective goal hinted at a planned economy, which in the 1950s during the witch hunts could not be approved. It is curious that the theory of games would not have hurt the Soviet economy either - experts say that it could have prevented such a global, but completely unjustified project as the construction of the BAM.
In addition, the mathematician's belief that players make decisions in isolation also turned out to be an abstraction - at least in the field of microeconomics. The seller and the buyer, competitors - always have the opportunity to enter into negotiations in order to agree on a joint optimal model of behavior.
Schizophrenia
But back to life path Nash. Thanks to his developments, John Nash ended up in the laboratories of the RAND Corporation, the largest US think tank during the Cold War. Americans now openly admit that game theory and the notion of balance, which implies that destroying the enemy is not the best goal, helped keep the "degree of war" from rising.
After RAND, Nash taught briefly at the Massachusetts Institute of Technology, climbing the academic ladder fairly quickly. There he met Alicia Larde, a promising young physicist who eventually became his wife.
John and Alicia are newlyweds
Nash had little interest in economics and other real-world problems, moving more and more into the realm of abstract mathematics. Riemann spaces interested him much more than the use of "Nash equilibrium". He has written some brilliant papers on some of the toughest problems in math - differential equations, differential geometry, and more. He was destined for a great future. In 1957, Fortune magazine named Nash the Outstanding New Generation Mathematician. Nash's colleagues joked that if the Nobel Prizes were awarded to mathematicians, he could become their laureate more than once.
It would seem that everything was going great, Alicia was expecting a baby, and Nash, at the age of 30, was supposed to become one of the youngest professors - already Princeton. However, the mathematician reacted to the message about this in a completely different way than those around him expected. "I cannot take this post," he said, "the throne of the Emperor of Antarctica awaits me." Nash was hospitalized with a diagnosis of paranoid schizophrenia.
For the next 30 years, he did not write a single article. Many believed that Nash had died. Those more in the know whispered that he had been lobotomized. Nash lost everything - his job, his friends, his family. AT real life Alicia could not stand this burden and in 1963 divorced John
However, he was not up to it, he fled to Europe, considered himself the savior of the world, blamed the communists and Jews for his troubles, raved, was treated and could not leave the world of illusions. Medicines didn't help.
After divorcing his wife, Nash moved into his mother's house. However, she died in 1970. Then Nash called Alicia and asked to be taken in. To everyone's surprise, she agreed (they had recently remarried). They settled near Princeton. Nash went for walks around the campus of the university, entering classrooms and leaving mysterious mathematical formulas and messages to nowhere on the boards. For this, the students nicknamed him "Phantom".
Return
However, in the early 1990s, Nash gradually began to return to the real world. His statements have found logic. He began to operate with meaningful mathematical expressions. He began to learn how to work with a computer and made friends with some students. Doctors attributed this amazing remission to age-related changes in his body. Nash himself says that he got better because he learned to separate the illusion from the real world. This does not mean that he recovered - he learned to live with the disease. "Intellectually I refused it," he wrote in his autobiography.
When the Swedish Academy of Sciences recognized his merits in the field of game theory, Nash took this news quite calmly, however, a limited range of emotions - salient feature schizophrenics. He was more interested in the fact that he would finally be able to support his family on his own. After all, besides him, Alicia also has their son, a talented young man who also fell ill with schizophrenia.
Nash received the Nobel Prize in 1994 for "a pioneer in equilibrium analysis in non-cooperative game theory". After that, Princeton decided to give him an office and gave him the opportunity to teach students. Nash claims that, regardless of age and health, he is ready to take new mathematical heights.
John Nash and Paul Krugman (Nobel Laureate)
Nash's case lives on and...
Where are Nash's discoveries applied today?
Having experienced a boom in the seventies and eighties, game theory has taken a strong position in some branches of social knowledge. Experiments in which the Nash team at one time recorded the behavior of the players in the early fifties were regarded as a failure. Today they formed the basis of "experimental economics". "Nash equilibrium" is actively used in the analysis of oligopolies: the behavior of a small number of competitors in a particular market sector.
In addition, in the West, game theory is actively used when issuing licenses for broadcasting or communications: the issuing authority mathematically calculates the most optimal variant of frequency distribution.
In the same way, a successful auctioneer determines what information about the lots can be provided to specific buyers in order to obtain optimal income. With the theory of games successfully work in jurisprudence, social psychology, sports and politics. For the latter, a characteristic example of the existence of a "Nash equilibrium" is the institutionalization of the concept of "opposition".
However, game theory has found its application not only in the social sciences. Modern evolutionary theory would not be possible without the concept of "Nash equilibrium", which mathematically explains why wolves never eat all hares (because otherwise they will starve to death in a generation) and why animals with defects contribute to the gene pool of their species (because that in this case the species can acquire new useful characteristics).
Now Nash is not expected to make grandiose discoveries. It doesn't seem to matter anymore, because he managed to do two of the most important things in his life: he became a recognized genius in his youth and defeated an incurable disease in his old age.
Letter from John Nash to the NSA, 1955
The US National Security Agency has declassified the amazing letters that the famous mathematician John Nash sent them in 1955.
John Nash proposed a completely revolutionary idea for those times: to use the theory of computational complexity in cryptography. If you read the letter dated January 18, 1955, you will admire how prophetic Nash's analysis of computational complexity and cryptographic strength turned out to be. It is on these principles that modern cryptography is based. The first work in this area was published only in 1975.
At one time, the authorities showed no interest in the work of an eccentric professor of mathematics. Or, which is also possible, they used Nash's ideas without him knowing.
In his letter, John Nash develops Claude Shannon's 1949 idea of communication theory in secret systems without mentioning it, but goes much further. He proposes to base the security of cryptosystems on computational complexity, exactly on the principle that, in 1975, two decades later, formed the basis of modern cryptography. Nash goes on to clearly describe the difference between polynomial time and exponential time, which is the basis of computational complexity theory. This principle was first described in 1965, although Gödel's famous letter to von Neumann of 1956 refers to it, but not in relation to cryptography.
John Nash:
“So the logical way to classify encryption processes would be by the way in which the difficulty of calculating the key increases with the length of the key. It is exponential at best, and at worst probably at least a relatively small power of ar2 and ar3, in substitution ciphers.”
Elsewhere, he seems to be talking about a one-way function, although such terms, of course, did not exist then:
“My general hypothesis is as follows: for almost all fairly complex types of encryption, especially where instructions given by different parts of the key act on the complex interaction of instructions with each other in determining their effect on the final encryption result, the average complexity of calculating the key grows exponentially with key length.
The mathematician is well aware of the importance of his hypothesis for practical cryptography, because the use of new methods will put an end to the eternal "game" of cryptographers and code breakers.
“The importance of this general hypothesis, if we assume its truth, is easily seen. It means that it becomes quite likely to create ciphers that will be virtually unbreakable. As the complexity of the cipher increases, the cipher-breaking game between skillful teams, etc., will become history.”
Actually, that's how it happened.
It is also interesting that John Nash is open about using methods whose theoretical basis he cannot prove (P = NP). Moreover, he explicitly says in the letter that he "does not expect his proof", which is unusual for a mathematician.
Scanned copies of John Nash's handwritten letters
Interesting facts about the film
- The director's spot was originally assigned to Robert Redford.
- John Nash could have been played by Tom Cruise.
- The bed scene between the characters Crowe and Connelly was cut from the final version of the picture.
- John Nash (played by Russell Crowe in the film) was brought on set to help the actors play their roles more authentically. Russell Crowe later admitted that he was fascinated by John's hand movements and tried to do the same during filming.
- Salma Hayek was invited to play the role of Alicia Lard.
- The Harvard scenes were actually filmed at Manhattan College.
- For the right to film the life of John Nash, two applicants-producers fought. Brian Grazer won the argument, and Scott Rudin was the loser.
- Professor Dave Byer became the main consultant of the picture and even got into the frame. It is his hands that draw complex formulas on the windows.
- Despite the fact that the picture is a kind of biography of the life of John Nash, some details of the life of the great mathematician were deliberately omitted:
- 1) John has been married several times;
- 2) in his youth, John was bisexual - had close relationships with both women and men;
- 3) John had an illegitimate child.
- John Nash really received the Nobel Prize, but not alone, but together with colleagues - Reinhard Selten and the Hungarian Janos Harsanyi. Moreover, another Hungarian, Janos Newman, became the founder of Game Theory. Nash distinguished himself by being able to apply the provisions of "game theory" in the business world.
- Robert Redford was offered to direct the film, but he was not satisfied with the filming schedule.
- When Nash first sees Parker, he refers to him as "big brother" (an allusion to Orwell's 1984). Another reference to Orwell comes later, when we see the number on the door of Nash's office - 101.
- The manuscript that young John Nash shows to his curator, Professor Helinger, is a genuine copy of an article published in the journal Econometrica under the heading "The Dealing Problem."
- The screenwriter of the film, Akiva Goldsman, had considerable experience in dealing with mentally ill people: when he was a doctor, he personally developed methods for restoring the mental health of children and adults.
- The Mathematics Curator of the film was Dave Bayer, a professor at Barnard College — it was with his hand that Russell Crowe “brings out” tricky formulas on the blackboard. "Wise formulas" on closer examination are just a meaningless set of Greek letters, arrows and mathematical signs. Apparently, the professor was paid a salary in vain.
- Unlike his on-screen counterpart, who was distinguished by rare devotion to his "half", the real John Nash was married several times in his life, and at the age of twenty he adopted an illegitimate child.
- In the film, Jennifer Connelly plays the wife of Russell Crowe. In real life, her husband is Paul Bettany, who plays Crowe's friend.
“I can’t say that I understand this disease,” the scientist said in an interview with the film, “but I don’t think anyone understands this.”
“In my madness, I thought that I was assigned a very important role, and that I was chosen to convey alien messages to people. In the same way, the prophet Mohammed called himself the messenger of Allah. I think this is the standard wording,” the scientist said.
“The Nobel Prize opened for me the recognition of the world ... I became an honorary member of various scientific societies and organizations ... It is clear to me that all this would not have happened if it were not for her,” he added self-critically.
Quotes by John Nash
But Newton was right!
Yes, the old man had sound ideas
“If we all go up to the blonde, we will block each other’s paths, and none of us will get it.” We'll go to her friends and they'll turn their backs on us because nobody wants to feel second-rate. What if neither of us approaches the blonde? ... We will not interfere with each other and will not offend other girls. This is the only way to win.
Tell me, is he real?
- Yes.
— Do you see him?
- Yes Yes.
“I am wary of new people.
“I don't know what I should say to have sex with you. But let's assume that I've already said all this and go directly to it.
I believed in numbers and terms, equations and logic, common sense… But having spent my life in such research, I don’t know what logic is, what common sense determines… I have come a long way through physics, metaphysics, illusion… and back. And I made the most important of my discoveries - the main discovery of my life: logical foundations can only be revealed in the mysterious equations of love.
Good scientific ideas wouldn't come to my mind if I thought like normal people. D. Nash
Childhood of a genius
On June 13, 1928, a completely ordinary boy, John Forbes Nash, was born in West Virginia. His father (John Nash Sr.) worked as an electrical engineer. Mother (Virginia Martin) taught English at school.
Little John studied average, and he did not like mathematics. It was very boring to be taught at school. He liked to conduct chemical experiments in his room and read a lot. Eric T. Bell's book "Great Mathematicians", which the boy read at the age of 14, made him "fall in love" with the "queen of all sciences." He independently and without any difficulty was able to prove Fermat's little theorem. So the mathematical genius of John Forbes Nash first made itself known. Life promised the guy a bright future.
Nash study
An unexpectedly revealed talent as a mathematician helped Nash (among the 10 lucky ones) to 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 he chose mathematics. Nash graduated from his master's course in 1948 and immediately entered the 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 very 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 completed his thesis on non-cooperative games. It contained the properties and definition of what would later be called "Nash equilibrium". After 44 years, the scientist received the Nobel Prize thanks to the main provisions of the dissertation.
Work
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 in calculus courses (Princeton). During this period of time, he proved the Nash 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 (Massachusetts Institute of Technology).
It was difficult for the great scientist to get along in working 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 collegiate decision (Nash agreed with him) that the scientist did not give the solemn speech because of his poor health.
The dissertation for which the prize was awarded was written in 1949, before the onset of the illness. It only had 27 pages. At that time John Nash's dissertation was not appreciated, and in the 70s game theory became the basis of modern experimental economics.
Scientific achievements of John Nash
Applied mathematics has one of the sections - 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 is the derived equilibrium formula. It describes a game strategy in which no participant can increase the payoff if he changes his mind unilaterally. For example, a workers' rally (demanding higher social benefits) may end with an agreement between the parties or a putsch. For mutual benefit, the two parties must use an ideal strategy. The scientist made a mathematical justification for combinations of collective and personal benefits, the concepts of competition. He also developed the "bidding theory", which was the basis of modern strategies for various transactions (auctions, etc.).
The scientific research of John Nash after research in the field of game theory did not stop. Scientists believe that even the people of science cannot understand the works that the mathematician wrote after his first discovery, they are too difficult for their perception.
Personal life of John Nash
John Nash's first love is nurse Leonor Steer, who was 5 years older than him. In relations with this woman, the selfishness of the scientist was fully manifested. After Leonor became pregnant, John did not give the child his last name, refused custody of him and financial support. As a result, John (Nash's eldest son) spent almost all of his childhood in the orphanage.
The mathematician's second attempt to arrange personal life became Alicia Lard, a physics student from El Salvador, whom he met in Massachusetts. In 1957 they got married, 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, because of which the newborn remained without a name for a whole year, since Alicia herself did not want to name the child, and her father (John Nash) was being treated in a psychiatric hospital.
Later, the son of scientific parents, following in their footsteps, became a mathematician.
genius schizophrenia
The great mathematician fell ill with schizophrenia at the blossoming age of 30, after marrying Alicia, who was only 26 at the time. Initially, Nash's wife made attempts to hide the terrible disease from colleagues and friends. She wanted to save her husband's career. But after a few months of his inappropriate behavior, Alicia had to forcibly put her husband in 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 work.
And John Nash's disease 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 the 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 being discharged, the former colleagues of the mathematician wanted to help him by offering him a job as a researcher, but John went to Europe alone. Only cryptic 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 a severe illness from his father.
Mathematicians (colleagues of Nash) offered to help the scientist. They got him a job and found a good psychiatrist who prescribed strong antipsychotics for John. Nash began to feel much better and stopped taking the pills. He was afraid that the drugs would harm his activity as a thinker. And in vain. The symptoms of schizophrenia recurred.
In 1970, Alicia re-adopted her schizophrenic husband, who was already retired. Nash continued to go to Princeton and wrote down more than strange formulas on the blackboard. The students gave him the nickname "Phantom".
In 1980, Nash's disease, much to the surprise of psychiatrists, began to recede. This was because John had rediscovered his favorite math and learned to ignore his schizophrenia.
In 2001, the couple, after a long cohabitation, re-legalized family relationships. Alicia, throughout her life with Nash and his long illness, insisted that her husband be treated, and always supported him.
“Now I think sensibly,” the scientist wrote, “but this does not give me the feeling of happiness that any convalescent should experience. A sound mind limits the scientist’s ideas about his connection with space.
Some sayings of John Nash
I think if you want to get rid of a mental illness, then you should, without relying on anyone, set yourself a serious goal yourself. Psychiatrists want to stay in business.
At times I thought differently than everyone else, did not follow the norm, but I am sure that there is a connection between creative thinking and abnormality.
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 in spite of everything, the more than 30-year war against schizophrenia was crowned with a significant success - he was awarded the Nobel Prize in Economics in 1994. Now Nash is one of the most revered and famous mathematicians in the world.
Based on his biography, an Oscar-winning Feature Film"Mind Games", 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".
If an unusual incident happened to you, you saw a strange creature or an incomprehensible phenomenon, you had an unusual dream, you saw a UFO in the sky or became a victim of alien abduction, you can send us your story and it will be published on our website ===> .
Everyone knows the life story of this man mainly thanks to movie "A Beautiful Mind". However, the real genius mathematician John Nash differed in many ways from the character portrayed on screen by Russell Crowe. It was an amazing life for an amazing person.
John Forbes Nash was the most ordinary American teenager who did not demonstrate exceptional success in any school subject, including mathematics. His life was turned upside down by the book The Mathematicians, written by the American popularizer of science Eric Temple Bell, which fell into his hands. This happened in 1942. John Nash was 14 at the time.
Actor Russell Crowe in A Beautiful Mind (2002)
Law of balance
Mathematics for quite a long time remained for Nash more of a favorite pastime than a vocation. After school, he entered the Carnegie Polytechnic Institute, where he first studied chemistry, then tried to find himself in the field of international economics. But in the end he decided that numbers, formulas and theorems attracted him the most in the world.
In 1947, he went to continue his education at the legendary Princeton University. In his pocket he had a letter of recommendation from the institute professor Richard Duffin: “I recommend Mr. John Nash, who applied for admission to Princeton. Mr. Nash is 19 years old and graduated from Carnegie Polytechnic Institute in June. He is a math genius."
At Princeton, Nash was introduced to "game theory" - mathematical method finding the best strategy. Already in 1949, a 21-year-old student submitted his dissertation to the Academic Council.
The concept of negotiation he formulated in the 1950s (mathematicians call it “Nash equilibrium”) seems to be extremely simple. In short, it boils down to the fact that during negotiations (whether political, economic or domestic) both parties must take into account the interests of each other.
Young John Nash
If negotiators strive to cooperate, and not to harm each other, then all participants will ultimately benefit, and the overall effectiveness of negotiations will increase significantly.
It doesn't seem like such a difficult idea. But, being translated by Nash into the language of mathematical formulas, she was able to arrange a real revolution in the world economy. Previously, it was possible to respect the interests of the other side by referring to ethical or moral principles. Now, from a scientific point of view, the “Nash equilibrium” has demonstrated all the inefficiency and harm of wild capitalism, when everyone sought to “drown” a competitor by any means.
The Art of Encryption
In the early 1950s, John Nash was invited to freelance for the RAND Corporation, an organization that worked for the US government and US intelligence agencies on national security issues. What exactly John Nash was working on at this time is still a secret.
But, given that these were the years of the Cold War, most likely he had to somehow come into contact with the topic of protection from the “red threat”. At the same time, Nash taught at the Massachusetts Institute of Technology.
More recently, it became known that in 1955, John Nash sent several letters to the US National Security Agency.
In them, he described in detail invented by him new approach to cryptography. Simplifying as much as possible, Nash's method boiled down to the fact that the longer the key to the cipher, the more difficult it is to break this cipher.
“The importance of this general hypothesis, assuming its truth, is easily seen,” wrote Nash. - It means that it becomes quite likely to create ciphers that will be virtually unbreakable. As the complexity of the cipher increases, the cipher-breaking game between skillful teams, etc., will become history.”
cryptography methods, similar topics, which Nash proposed, began to be used only in the mid-1970s.
So the mathematician was ahead of his time by at least 20 years. But then, in the 1950s, the letters went into the archives of the NSA, were strictly classified and were not actually used.
The fact is that Nash has already managed to gain a scandalous reputation as an eccentric, prone to incomprehensible antics and living in his own strange world. In general, many scientists who are too immersed in science are famous for such features.
But with Nash, it sometimes took on very strange forms. For the same reason, RAND quickly refused to cooperate with him.
Nevertheless, in 1950 until 1959, John Nash's life, one might say, went uphill. In 1957, he married the beautiful Alicia Lard. A year later, the influential Fortune magazine named him "the rising star of the new mathematics." But it soon became clear that his problems were something more than just distraction and eccentricity.
Struggling with schizophrenia
US legislation at that time was not distinguished by excessive liberalism, and therefore the mad scientist was soon placed for compulsory treatment in one of the Boston psychiatric clinics. To get out of there, he had to resort to the help of a lawyer.
Frightened and sick, John Nash left America and rushed around Europe for about a year, trying to get political asylum in several countries. However, the American government could not allow a person to emigrate who, albeit briefly, had access to classified information. Therefore, Nash was arrested in France and returned to the US.
There the disease came upon him. new force. He spoke of himself in the third person, constantly pestering his acquaintances with phone calls, during which he confusingly and incoherently talked about numerology, then about international politics, then again about aliens.
In this state, he could neither work nor conduct a normal family life. Followed by new courses of treatment, which did not give any result. As a result, Alicia, with pain in her soul, divorced her insane husband and raised their son alone. It seemed that nothing could save this brilliant mind from complete disintegration.
Luckily Nash was not abandoned by his friends. They even helped him find a job at Princeton. There, Nash received the respectfully fearful nickname Phantom from students. For days on end, he wandered the corridors of the university, muttering something under his breath and periodically scribbling blackboards in classrooms with chains of absolutely incomprehensible formulas.
But over time, the disease began to recede. By the 1980s, Nash had almost completely recovered. His wife returned to him, and hallucinations and obsessions receded.
“Now I think quite rationally, like any scientist,” Nash said of himself. “I won’t say that it gives me the joy that anyone who recovers from a physical illness experiences. Rational thinking limits man's ideas about his connection with the cosmos.
John Nash could forever remain a little-known madman who put forward several
interesting theories, if in 1994 world recognition had not fallen upon him. The Nobel Committee awarded him a prize in economics.
For the very ideas about balance and negotiation tactics that he put forward as a very young man. Due to illness, Nash was unable to give the laureate's traditional lecture in Stockholm. But his authority as a mathematician since that time has become indisputable. The power of the mind turned out to be stronger than the stupefaction of reason.
His amazing fate attracted the attention of Hollywood screenwriters, and in 2001 the film A Beautiful Mind was released with Russell Crowe in leading role. The creators of the picture tactfully circumvented many facts of unfair treatment of the scientist by the American authorities. And instead of hunting for aliens, Nash was credited with spy mania.
The hallucinations, which in reality were only auditory, were portrayed as visual in the film. But, despite all these inaccuracies, the film earned a lot of positive ratings and received four Oscars and a Golden Globe. Nash himself, as far as is known, treated him with restraint and positive.
In 2015, John Nash was awarded the Nobel Prize in Mathematics. The American became the only person in the world to receive both this and the Nobel Prize. Alas, after just a month, the life of a genius was cut short as a result of a banal traffic accident.
Viktor Banev
John Forbes Nash Jr., the brilliant Princeton mathematician whose life inspired the Oscar-winning film A Beautiful Mind, died over the weekend along with his wife, Alicia.
The police found that a taxi driver who lost control was responsible for the death of the 86-year-old scientist and his 82-year-old wife. The driver of a Ford Crown Victoria tried to overtake another car on the left side and crashed into the guardrail. The accident happened on the New Jersey Turnpike. New Jersey State Police spokesman Gregory Williams told NJ.com that the couple were apparently not wearing seat belts. John and Alicia were thrown out of the cab by the impact and died on the spot. The driver survived and was taken to hospital with minor injuries.
Just a few days earlier, John Nash received the Abel Prize from the hands of King Harald V of Norway - it is called the mathematical “Nobel Prize”. The $800,000 prize was awarded to Nash and his colleague Louis Nierenbehr, recognized giants of 20th-century mathematics, for "innovative contributions to the theory of non-linear partial differential equations in the field of geometric analysis." As noted, each of the scientists worked on his own, but the mathematicians had a great influence on each other, and the results of the work were far ahead of their time. Nirenberg and the Nash family flew in together from Oslo, said goodbye at the airport, and departed in a taxi. John and Alicia died on the way to their home in a suburb of Princeton.
As you know, the Nobel Prize is not awarded to mathematicians. However, John Nash nevertheless became her winner in the category "Economics" for his analysis of equilibrium in the theory of non-cooperative games.
There is an opinion in the mathematical community that John Nash became famous thanks to the simplest of his works, while many of his developments are still incomprehensible to his colleagues.
He is known to a wide circle thanks to the biopic A Beautiful Mind, in which the role of Nash was played by Russell Crowe. The film, which became the discovery of 2001, told the whole world that for most of his life the mathematical genius struggled with schizophrenia and remained a patient in psychiatric clinics for a long time. As is often the case, everything in life was more complicated, more tragic, and more surprising than in the movies.
Math Maker
John Forbes Nash Jr. was born June 13, 1928 in Bluefield, West Virginia to a strict Protestant family. His father was an electrical engineer and his mother was a teacher. in English and Latin. 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 technology. However, the vocation found him by itself.
When Nash was 14 years old, he read Eric T. Bell's Math Makers. Having learned what he had read, he managed to prove Fermat's little theorem himself, without outside help. And soon he turned his room into a real laboratory, where he surrounded himself with books and conducted various experiments.
In 1945, John entered the Carnegie Polytechnic Institute in Pittsburgh and was going to become an engineer, like his father. He tried to study chemistry, but abandoned the idea. The course of economics also did not seem exciting to him. As a result, the gifted student fell deeply in love with mathematics and seriously took up number theory and Diophantine equations. And then he tackled the "negotiation problem" that John von Neumann had left unresolved in his Game Theory and Economic Behavior.
By the time he entered Princeton, John Nash had a bachelor's and a master's degree, and the institute teacher Richard Duffin provided him with a letter of recommendation, which consisted of just one line: "This guy is a genius." At Princeton, in 1949, at the age of 21, Nash completed his thesis on game theory, which would be awarded the Nobel Prize in Economics 40 years later. He developed the foundations of the scientific method, which had a particular impact on the development of the world economy. Until 1953, he published four papers with deep analysis of non-zero-sum games. The situation he modeled would later be called the Nash equilibrium.
Shot from the movie "A Beautiful Mind"
An example of such a balance can be, for example, the negotiations between trade unions and company management to increase wages. Such negotiations can end either in a long strike and losses for both parties, or in a mutually beneficial agreement. Moreover, such an agreement cannot be violated by any of the parties, since violation will lead to losses.
The scientist was unable to obtain political asylum in Europe and was persecuted by the State Department
From the 1950s, Nash worked at the Massachusetts Institute of Technology in Cambridge and wrote a number of papers on real algebraic geometry and the theory of Riemannian manifolds. At the same time, he proved the Nash theorem on regular embeddings, which became one of the most important in differential geometry on manifolds.
Shot from the movie "A Beautiful Mind"
Nash was a recognized genius, but he did not develop relationships with his colleagues. His works mathematically substantiated Karl Marx's theory of surplus value. At the time of the witch hunt, such views in the United States seemed heretical. Therefore, when Nash's girlfriend, nurse Eleanor Stier, gave birth to a child, Nash refused to give him his name and provide any financial support - in order to protect mother and child from the persecution of the McCartney Commission.
BecomeUnder the pressure of circumstances, the mathematician leaves for California, to the RAND Corporation, which was engaged in analytical and strategic developments for the US government. The corporation was known as a haven for dissidents, and Nash quickly became one of the leading experts in the field of Cold War warfare, using the best practices in game theory. However, he failed to get along in RAND. The scientist was fired after the police arrested him for indecent behavior.
Shortly thereafter, Nash met Alicia Lard, a student from El Salvador, and they married in 1957. Everything went well, the couple was expecting a child, Fortune magazine named Nash a rising American star in new mathematics. He received an invitation to become one of the youngest professors at Princeton. However, the mathematician reacted to the invitation in a very strange way. “I cannot take this post. The throne of the Emperor of Antarctica awaits me.”
For several months, Alicia, frightened by the symptoms of schizophrenia, tried to hide her husband's condition from his colleagues and friends. However, in the end, John had to be forcibly hospitalized in a private psychiatric clinic in the suburbs of Boston. He was diagnosed with paranoid schizophrenia.
After breaking out of the clinic with the help of a lawyer, Nash leaves for Europe. Alicia left her newborn son with her mother and followed her husband. Nash constantly talked about the persecution, about alien messages that only he could decipher. The scientist tried to obtain political refugee status in France, Switzerland and the GDR and renounce American citizenship. However, under pressure from the US State Department, these countries refused to shelter the couple. Now it is known that Nash was really being monitored, his appeals to the embassies of different countries were blocked. After some time, the mathematician was arrested by the French police and deported to the United States. Together with Alicia, he settled in Princeton, she found a job. But John's condition worsened, he was afraid of everything, spoke of himself in the third person, wrote meaningless letters and told former colleagues about numerology and politics.
30 "dark" years ended with an inexplicable return to reality
In 1961, Alicia, John's mother, and his sister, after much hesitation, decided to admit John to Trenton State Hospital in New Jersey for risky and brutal insulin therapy. After being discharged, colleagues tried to get him a job, but John again left for Europe, this time alone. Alicia soon divorced him.
Shot from the movie "A Beautiful Mind"
Until 1970, Nash wandered through psychiatric hospitals and occasionally lived with his mother. One of the psychiatrists prescribed him the latest drugs, which gave him a visible improvement. But John refused to drink them, fearing side effects.
For thirty "dark" years, Nash did not write a single article. There were rumors in the scientific world about his untimely death, about the transferred lobotomy. And he himself considered himself the savior of the Universe and wandered in the world of illusions, blaming communists and mysterious enemies for his troubles.
After the death of his mother, he again turned to Alicia and asked for shelter. To everyone's surprise, she agreed. So John was back at Princeton. Sometimes he walked around the university and left mysterious formulas and messages to nowhere on the boards in the audience. The students nicknamed him the Ghost.
The movie A Beautiful Mind tells how Nash never recovered from schizophrenia - it's simply impossible - but learned to live with the disease. In reality, his return to the real world in the early 1990s remained unexplained. He again began to reason logically, operate with mathematical expressions, mastered the computer. Doctors said that age-related changes contributed to this. John himself is sure that he himself has learned to separate illusions from reality. And again engaged in science.
Nash spoke out against "dirty" money and refuted Adam Smith
In 1994, when Nash was awarded the Nobel Prize, the committee denied him the right to give the traditional laureate lecture, fearing for his fortune. However, subsequent years showed that the genius did not lose the sharpness of the mind.
“I remained in captivity of the disease long enough to finally give up my delusional hypotheses and return to thinking of myself as an ordinary person in order to again engage in mathematical research,” Nash wrote in his autobiography. In 2011, she and Alicia got married again.
Nash was again given an office at Princeton, and he did mathematics for the rest of his life. From time to time he was invited to give lectures in different countries. In 2013, the professor visited Kyrgyzstan and gave a lecture in Bishkek on ideal money.
Shot from the movie "A Beautiful Mind"
“When we talk about money, we immediately think about how to spend it faster and have fun. We do not perceive money as a radio that can convey valuable and important information. If we take advantage of the possibilities of money, invest it in education or in something else, then the money will double and enrich us, ”said the scientist.
Nash has been critical of capitalist policies that equate good and dirty money. “You can’t assume that dirty money is better than honestly earned money. The new government of Japan adhered to such a policy and is now disentangling Negative consequences. Japan wanted to lower the prices of exported goods, wanted to artificially maintain the exchange rate of the national currency. The cost of goods fell, exports really revived. But in Japan itself, prices have risen, the exchange rate has fallen, inflation is pestering the economy, ”he recalled.
John Nash advocated the creation of a world financial organization like the International Monetary Fund, which will allow you to take and give loans not in money, but in goods.
The theories developed by Nash refuted the idea of Adam Smith "every man for himself" and had a serious impact on the formation of the world economy. His developments are actively used in the analysis of oligopoly - the behavior of a small number of competitors in certain sectors of the economy. In addition, his game theory works successfully in jurisprudence, social psychology, sports and politics.
