If you think his name is a bit strange, we might as well recall an American movie "A Beautiful Mind". The film was released on 200 1 and won four Academy Awards, and Nash is the prototype of the hero in this film.
Many people think that Nash was crazy for more than 30 years and was later cured by the hospital. In fact, just after people thought Nash was back to normal, he published an autobiography. In his autobiography, he said that he had never been crazy for so many years, but he saw two worlds at the same time. He saw things that ordinary people could not see, which made people feel that his performance was different!
His so-called healing process has nothing to do with the drugs people gave him. So what kind of incredible experience does it have?
1928 June 13, Nash was born in bloomfield, Virginia, USA. My father is a well-educated electronic engineer, my mother is a teacher, and my family lives a warm life. But Nash was withdrawn from childhood and didn't want to play with children of his own age. He prefers to bury himself in reading and find happiness from books.
In fact, it seems that many geniuses in natural science have some of these characteristics. Although Nash later became a mathematician, when he was young, he was always complained by his math teacher that he had problems with math, didn't play by common sense, and liked to solve problems in some strange ways. In middle school, this situation is even more prominent.
Teachers often write down the dense calculus process on the blackboard, and Nash can do it in just a few simple steps, which makes the teacher particularly embarrassed. But it also allowed him to show this extraordinary talent. In my senior year, I got a full scholarship from George Westinghouse and entered Carnegie Institute of Technology for further study.
This college is the predecessor of the later famous Carnegie Mellon University. In fact, Nash wanted to learn chemistry at first because he liked those strange experiments very much. /kloc-when he was 0/2 years old, he set up a small laboratory in his home, so he entered the department of chemical engineering in college. However, in his first year here, he was dissatisfied with the institutionalization of this major and the lack of rigorous and sexy mathematics in the course.
Nash later wrote in his autobiography that this major measures a person's talent not by how strong his thinking ability is, but by whether he can handle straws and titrations in the laboratory.
In the second year, the school expanded the teaching staff, and more than a dozen outstanding researchers joined in. They are physicists john singh and Richard Dafen, and mathematicians Raul Bott and Alexander Weinstein. Talented people always appreciate each other. They discovered Nash's talent at once and successfully guided him from the field of chemistry to the field of mathematics.
1948, junior year of Nash. He has been admitted to several universities, including Harvard, Princeton, Chicago and the University of Michigan. Among them, Princeton University is particularly enthusiastic about Nash. They know Nash must be a rare wizard. Why?
Because there is only one sentence in the recommendation letter written by Nash's thesis supervisor, Mr. Nash 19 years old, graduated in June. He is a genius in mathematics. Finally, at the invitation of Lefschetz, head of the Department of Mathematics at Princeton, and at Carnegie's suggestion, Nash entered Princeton with a score of 1948. Let me add here that Nash studied at Carnegie for three years and graduated with a master's degree in mathematics. He went to Princeton University to study for a doctorate.
Princeton is a place where masters gather. Einstein, von Neumann and Oppenheimer all taught here at that time. Although Nash is only a student, he dares to challenge the master. He never goes to class because he thinks that what he receives in class will bind his mind.
So in his life at Princeton University, he often does his own research and thinks for himself. Nash is also quite arrogant. When he is discussing problems with others, he even suddenly gets up and leaves. Because he really thinks that the other person's thinking really can't keep up with himself.
At that time, game theory was a newly established subject in the Department of Mathematics. Von Neumann and economist Oscar Morgenstein published Game Theory and Economic Behavior in 1944, which injected vitality into this subject. However, Von Neumann and Morgenstein only analyzed the so-called zero-sum game, which mainly means that when the two sides play, the pride of one side will inevitably cause the loss of the other side, so the sum of the results of the confrontation between the two sides will always be zero.
But in the real world, most interactions are often more complicated, and the interests of all parties are either win or lose, and sometimes there is the possibility of mutual benefit. Nash was keenly aware of this, so he went to von Neumann and explained his thoughts to him. At this time, von Neumann was famous all over the world and busy. Anyone who wants to see him must make an appointment in advance, and out of courtesy, he should do the same.
What about Nash? So I went straight into von Neumann's office and started talking about my ideas. Perhaps, such behavior is too arrogant in von Neumann's eyes, so before Nash finished, von Neumann interrupted him and said that what Nash mentioned was irrelevant. Von Neumann also said, you know, this is just a fixed point theorem. Nash was rebuffed, a little confused.
However, gold always shines, but Albert Tucker, Nash's doctoral supervisor, saw the value of Nash's point of view. He instructed Nash to write his thesis and personally wrote a letter of recommendation to the National Academy of Sciences. Lev Shetz, head of the Department of Mathematics, submitted the manuscript directly to the Academy of Sciences. This paper was finally published in the first issue of the Proceedings of the National Academy of Sciences. 1949165438+1October 26th, which immediately caused a sensation.
Nash not only graduated as a doctoral student in this theory, but also established his position as a master of game theory. Nash's theory is the Nash equilibrium that often appears in economics textbooks. So why is this theory so important?
Here we are going to talk about the most famous case in the game world, the prisoner's dilemma. The classic prisoner's dilemma has a fixed condition. The police arrested two suspects, A and B, but because there was not enough evidence to accuse them of guilt, the police chose to imprison the suspects separately and meet them separately to provide the same choice for both sides.
1. If a person pleads guilty and testifies against the other party, the relevant clause is betrayal, and the other party keeps silent, then the person who pleads guilty and accuses the other party will be released immediately, and the silent person will be sentenced to ten years' imprisonment.
2. If both of them keep silent, the relevant term is called mutual cooperation, then they will also be sentenced to six months' imprisonment.
Third, if these two people report to each other, that is, betray each other, then these two people are also sentenced to five years in prison. The silence of both parties at the same time is actually the dilemma of pleading guilty. Of course, it is in the best interest of both of them not to plead guilty as a whole. However, Party A and Party B can't communicate with each other, and both will seek the best interests for themselves, so this will eventually happen.
First, if the other party is silent, I will be released if I plead guilty, so I will choose to plead guilty. Second, if the other party pleads guilty and accuses me, I will also accuse the other party, so that I can get a lighter sentence, so I will still choose to plead guilty. So in the end, both of them chose to plead guilty. This ending is called Nash equilibrium, which is also called non-cooperative equilibrium.
Nash equilibrium not only lays the mathematical foundation of game theory, but also is widely used in business. In the following years, Nash also made some breakthroughs in algebraic cluster theory, Riemannian geometry, parabolic and elliptic equations. 1958, he almost won the Fields Prize, the highest prize for mathematicians. In the same year, he was named the most outstanding figure among a new generation of talented mathematicians by American Fortune magazine.
In addition to academic performance, Nash's marriage was also enviable at that time. At that time, Nash was teaching at MIT. His handsome and tall appearance and extraordinary talent attracted the attention of Alicia, a beautiful female student. Alicia is not only beautiful, but also very clever. In my freshman year, MIT only recruited 16 girls, and Alicia was one of them.
They got married on 1957, and Alicia got pregnant on 1958. All this is so beautiful to outsiders, and Nash has reached the peak of his life. However, things did not develop in the direction expected by everyone. 1958 was a turning point in Nash's life.
1In the winter of 958, Nash got tenure at MIT, but his behavior suddenly became more and more incredible. He thinks he can decrypt the secret information sent by aliens from the newspaper. He also believes that everything in the world can be expressed by a mathematical formula. By the way, Nash was studying the core principles of encryption and decryption in this period, and in 20 1 1 year, the National Security Agency of the United States decrypted Nash's letters written in 1950, and it was found that Nash proposed a new encryption and decryption machine in a letter.
In the letter, Nash creatively encountered many modern cryptography concepts based on computer complexity, which was quite shocking. However, before Nash studied deeply enough to express these ideas, his strange behavior made everyone think he was crazy. Before the birth of his child with Alicia, he was forcibly sent to a mental hospital by his wife, and Nash insisted that he was not crazy.
When Nash was admitted to the hospital for the first time, he was sent to McLean Hospital, which specializes in treating the upper class. Doctors there regard schizophrenia as a mental illness and have to do psychological counseling all day. When his colleague Donald Newman came to visit him, Nash lamented that he could not leave the hospital unless he became a normal person in the eyes of the secular world.
So, after 50 days in hospital, Nash returned to normal smoothly and was discharged from the hospital. In this way, maybe Nash's so-called madness is controllable in his own view. As long as he hides things that people don't believe and behaviors that they don't want to see.
On his second admission, Nash was taken to Trenton Psychiatric Hospital, a public hospital. Nash recalled that he was forced to receive insulin coma treatment. They give you injections to make you look like an animal, so they can treat you like an animal. Nash, who became humble and polite again after half a year, was discharged from the hospital again. At this time, Nash couldn't let go of his wife Alicia, who was forcibly sent to a mental hospital, and her wife couldn't stand his repeated wandering between normal and crazy.
So the two divorced on 1963, and Nash began to refuse all medical treatment after his experience in clanton mental hospital. He thinks it will make him feel dull and unable to think about mathematics. In Nash's view, mathematics is the only thing he thinks is important.
Nash believes that the purest mathematics is not rationality, but inspiration. Reason is just a way to communicate with this inspiration. When Nash was in hospital, a friend went to visit him and asked him, you claimed that aliens were talking to you, but how could you, a rational mathematician, believe such nonsense?
Nash replied that the creation of mathematics came into my mind like an alien. I believe in aliens as much as I believe in mathematics. He also wrote such a sentence in his notebook, rational thinking blocked the closeness between man and the universe.
In the following days, Nash's former colleagues found him a job as a researcher at Princeton. Therefore, in the 1970s and 1980s, Princeton students often saw a thin, taciturn middle-aged man wandering around the campus in red running shoes and occasionally writing profound mathematical propositions on the blackboard. It is called the ghost of Princeton, and he is Nash.
However, just when people thought that the genius Nash was gone forever, a miracle appeared.
In the late 1980s, Nash gradually recovered. When people asked him how he woke up without taking medicine, he said, as long as I want to.
He said that he had never been crazy, but he was experiencing two worlds at the same time, and when one day he decided to live in this real world, he relied on his strong willpower and logical ability to make himself rational. In fact, until 1994, when Nash accepted the Nobel Prize in Economics, the seemingly gentle scholar still had no so-called recovery, but he knew what he should show the world.
What is the information from aliens that he has always believed in his mind is always a mystery.
200 1 Nash's life story was adapted into the film A Beautiful Mind, which caused a sensation as soon as it was released. In the same year, she remarried her divorced ex-wife, Alicia, who always cared for herself. 20 15 won the Abel Prize from the Norwegian Society of Science and Literature, becoming the only scholar in history who has both Nobel Prize and Abel Prize.
On May 23rd, 20 15, just as the couple were about to return to the United States after winning the lottery, they had a serious car accident on their way home by taxi in New Jersey. The couple were thrown out of the car and died on the spot. A generation of genius has thus finished his legendary life.