On May 23, 1994, at the Nobel Prize ceremony held in Stockholm, Sweden, a man of literature and thin body attracted the attention of people, when he stood up to receive the Nobel Prize in economics, elegantly bowed down, many people in their hearts filled with emotion, finally waiting for this day.

This man is the great mathematician John Forbes Nash Jr., a legend who wandered a lifetime between genius and madmen. If everyone thinks his name isn't so familiar, then the 2001 American film "Beautiful Heart", which was released and won four Oscars, may evoke more memories.

Although many believe that Nash had been crazy for more than thirty years, after he became a normal person in the eyes of people, he published an autobiography, he said he had never actually been crazy, but only saw two worlds at the same time, and he called the process of "healing" and had nothing to do with human use of drugs.

Genius is born

On June 13, 1928, Nash was born in Brookfield, Virginia. His father was a well-educated electronic engineer and his mother was a teacher. The family lived a warm life. However, Nash's personality was less isolated and less willing to play with children of the same age, he preferred to buried himself in a bunch of books, looking for happiness in books.

Although Nash later became a mathematician, he was always charged with mathematics teachers as a child, saying that he had problems with mathematics, did not log in and liked to solve problems with some strange methods. When he came to high school, this situation became more remarkable, often teachers wrote a blackboard calculation process, and Nash did it in a few simple steps, making teachers pretty embarrassed. At that time, Nash's over-human talent had been shown, he received the full "George Westinghouse Scholarship" at high school, entered the Carnegie Technology College, which was later the predecessor of the renowned Carnegie Mellon University, and continued to study.

In fact, Nash initially wanted to study chemistry, because he liked the strange experiments, and at the age of 12 built a small laboratory at his own home. So, he entered the chemical engineering department at the university. But in his first year, he was dissatisfied with the institutionalization of the profession and the lack of mathematical rigor in the course. Nash said in his autobiography that the profession measures a person's talent "not by how strong his thinking ability is, but by whether he can handle the tubes and digest in the laboratory."

In the second year of the university, the university expanded its faculty, and several outstanding researchers joined it. They were physicists John Singh, Richard Daven, and mathematicians Raul Bot and Alexander Weinstein. Talented people always regretted, and they immediately discovered Nash's talent and successfully led him from the field of chemistry to the field of mathematics.

In 1948, Nash's junior year, he was already accepted to Harvard, Princeton, Chicago, and the University of Michigan. Princeton is particularly enthusiastic about Nash, who they know must be a rare wizard. Why is it? Because the letter of recommendation written by Nash's thesis supervisor only contained this sentence: "Mr. Nash is 19 years old and will graduate in June. He is a mathematical genius." Finally, at the invitation of Princeton's mathematics department head Lefschetz, at the advice of Mr. Carnegie, and for the face of Princeton's generous scholarship, Nash entered Princeton in 1948. I would like to add here that Nash studied at Carnegie for three years and graduated with a master's degree in mathematics. He went to Princeton to study for a doctorate.

The peak moment.

Princeton was a place where the masters gathered, where Einstein, Von Neumann and Obenheimer taught. Though Nash was just a student, he dared to talk to the masters. And he never went to class because he thought the knowledge he received in the class would restrict his thinking, so his life at Princeton was often his own study and thinking.

The game theory was a newly established discipline of mathematics at the time. Von Neumann and economist Oscar Morganstein published the book The Game and Economic Behavior Theory in 1944, which inspired the discipline. However, Von Neumann and Morganstein only analyzed the so-called "zero-sum game", mainly referring to the possibility of mutual benefit when both sides play, and the benefit of one side inevitably leads to the loss of the other, so that the sum of the outcomes of the two sides is always zero. But in the real world, most interactions are more complex, and the interests of the parties are not winning or losing, but the possibility of mutual benefit.

At that time, Von Neumann was already busy and wanted to meet him in advance, and such an appointment should still be. But Nash went straight into Von Neumann's office and began to talk about his thoughts. Per because it seemed too crazy in Von Neumann's eyes, so not waiting for Nash to finish his speech, Von Neumann interrupted him, jumped to the conclusion not yet explained in Nash's argument, and suddenly said: "It was insignificant, you know, it was just a pointless thesis."

Nash's heart was a little confused after being dismissed by von Neumann. But gold always has to shine. Nash's doctoral supervisor, Albert Tucker, saw the value of Nash's views. He guided Nash to write his paper and personally wrote his letter of recommendation to the National Academy of Sciences. Levsets, head of the Department of Mathematics, submitted the manuscript directly to the Academy of Sciences. The paper was published in the Bulletin of the Academy of Sciences on November 26, 1949 and caused an immediate sensation. Nash not only got his doctorate with this theory, but even established his position as a master of game theory.

Nash¡¯s theory is the ¡°Nash equilibrium¡± which is now commonly found in economics textbooks, and where does it matter?

The classical prisoner situation is as follows: Police arrest two suspects, A and B, but there is not enough evidence to accuse the two of them of guilt.

If a person pleads guilty and testifies against the other party (the related term is called "betraying" the other party), but the other party remains silent, the person will be released immediately, and the silent person will be sentenced to 10 years in prison.
If both of them remain silent (the terms refer to each other as ¡°co-operating¡±), they are equally sentenced to six months in prison.
If both persons accuse each other (e.g. betray each other), they are equally sentenced to five years in prison.

So A.B. is at the same time in a situation of silence or confession of guilt. From the table, of course, neither of the two believes that guilt is the most beneficial for the whole. However, B.B. cannot communicate, they are all seeking the greatest benefit for themselves. So, in the end, this situation occurs:
If the other person is silent and I confess guilt, I will be released, so I choose to confess guilt.
If the other party pleads guilty to accuse me, I will also accuse the other party to get a lower sentence, so it will also choose to confess guilt.

So in the end, the two chose to confess guilt, and this ending is called "Nash balance" and also called "non-cooperative balance".

The Nash Balance not only laid the mathematical foundation for the theory of equation, but was also widely used in business. In the years that followed, Nash also made some breakthroughs in algebraic theory, Riemannian geometry, polarisation and elliptical equations, and won the Fields Prize for the Highest Prize in Mathematics in 1958.

In addition to his academic achievements, Nash¡¯s marriage was also envious at the time. During his teaching at MIT, Nash¡¯s handsome appearance and extraordinary talent attracted the attention of a beautiful female student, Alicia Lopez-Harrison de Lardé, who was not only beautiful but also very intelligent. At the time of her admission, only 16 girls were hired by MIT, and she was one of them. In 1957, they married.

All this seemed so beautiful to the outside, that Nash was at the height of his life.H, things didn¡¯t go in the direction everyone expected, and Nash¡¯s life was a turning point in 1958.

The Ghost of Princeton.

In the winter of 1958, Nash had already got a tenure position at MIT, but his actions suddenly became more and more incredible. He thinks he can decrypt secret messages sent by aliens from newspapers. He also believes that everything in the world can be expressed in a mathematical formula.

By the way, Nash at that time was studying the core principles of "encryption and decryption". In 2011, the National Security Agency declassified the letters written by Nash in the 1950s. Found in a letter, Nash proposes a new encryption decryption machine. In the letter, Nash pioneered many modern cryptographic concepts based on computer complexity, which is quite shocking.

However, before Nash studied in depth and published these ideas, his grotesque behavior had convinced everyone that he was really crazy. Before his child with Alicia was born, he was forced into a mental hospital by his wife, and Nash insisted that he was not crazy.

When he first entered the hospital, Nash was sent to the McKinley Hospital, where doctors treated schizophrenia as a mental illness and gave psychological advice on a full day basis. His colleague, Donald Newman, came to see him, and Nash regretted that he could not leave the hospital if he did not become a normal person in the worldly eye. So, after 50 days of hospitalization, Nash managed to return to normal out of the hospital. Thus, Nash¡¯s ¡°madness¡± seemed to be controllable in his own opinion, as long as he hid those things that people didn¡¯t believe and didn¡¯t want to see.

The second time he was admitted to hospital, Nash was sent to Trenton Mental Hospital, a public hospital, and forced to undergo insulin coma treatment. Nash recalled, "They gave you injections to make you like an animal, so that they could treat you like an animal." Six months later, Nash, who became "humble and polite", was discharged from the hospital again.

At this time, Nash couldn't let go of his wife Alicia's forced sending him to a mental hospital, and his wife couldn't bear Nash's repeated wandering between normal and madness, so they divorced in 1963.

After having had an experience at the Trenton Psychiatric Hospital, Nash rejected all drug treatments, which he thought would make him feel delayed and unable to think about mathematics. In Nash¡¯s view, mathematics is the only thing that matters to him.

When Nash was in the hospital, a friend visited him and asked him, ¡°You claim that aliens are talking to you, but how can you, as a rational mathematician, believe these nonsense of aliens?¡±Nash replied, ¡°Mathematical inventions come into my mind like aliens, and I believe that aliens exist, as I believe in mathematics.¡±

In the days that followed, Nash¡¯s old-time colleagues earned him a research job in Princeton, so in the 1970s and 1980s, Princeton¡¯s students often saw a thin and silent middle-aged man who wandered around the campus in red running shoes, occasionally writing deep math propositions on blackboards, he was called ¡°Princeton¡¯s ghost,¡± he was Nash.

Newborn

However, just when people thought that genius Nash was gone forever, a miracle appeared. In the late 1980s, Nash gradually recovered. When people asked how he came back to his senses without drugs, Nash said, "As long as I want to". He said that he had never been crazy, but experienced 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 didn't have a so-called recovery, but he was able to know what kind of himself to show the world. And what he had always believed in his mind was the information from aliens, and it would always be a mystery.

In 2001, Nash¡¯s life story was adapted to the movie ¡°Beautiful Mind¡±, which caused shock when it was released.In the same year, he was also concerned about taking care of his ex-wife, Erisia, and getting married again.

In 2015, he won the Abel Prize from the Norwegian Academy of Science and Letters, becoming the only scholar in history to win both the Nobel Prize and the Abel Prize.

However, on May 23, 2015, the couple returned to the United States after receiving the prize, but suffered a major car accident on their way home in New Jersey.The couple were thrown out of the car and died on the spot.