John Nash became widely known throughout the world thanks to the movie "Mind Games." This is an amazingly moving, charged with faith in the power of human genius, life-affirming film. This is a biography film, a shock film, a discovery film. He introduces the viewer into the world of the future, where the mind works real miracles. The 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. 27 pages of Nash's doctoral dissertation had such an impact on society and the economy as 21 pages of Einstein's doctoral dissertation on theoretical physics.
The theory of Adam Smith, which traditionally follows the development of a liberal bourgeois society, in comparison with how John Nash explores it, looks pale, without giving a clear explanation to many modern phenomena. The above theories are related in the same way that two-dimensional geometry is only a subset of three-dimensional.
Initiation
John was born on 06/13/1928 in Bluefield (West Virginia). He was not a “nerd” at school, he studied secondary. By nature - closed, selfish.
Imagine that the future mathematician (differential geometry and game theory) did not like this subject at school. At this stage, everything in it was suspiciously average. It was as if his intellect was sleeping and waiting for a jolt. And he did come.
At the age of 14, the teenager fell into the hands of the book "Creators of Mathematics" by his compatriot Eric Bell, a mathematician and author of science fiction. The book very reliably told about the life of the 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 before that the completely average "gray" schoolboy John Nash takes up the impossible and suddenly proves Fermat's little theorem for those around him. The last circumstance says little to non-specialists. But believe me, it was a miracle. What can it be compared with? Perhaps, as if an amateur provincial actor turned up a chance, and he played Hamlet perfectly in the capital.
Polytechnical Institute
His father (his son dubbed his first and last name) was an educated person, worked as an electronic engineer in a commercial company. After proving Fermat's theorem, it became clear to the parent that John Nash Jr. would become a scientist.
Several brilliant research papers opened the guy’s doors to the fairly prestigious Carnegie Polytechnic Institute, where the young man first chose chemistry, then the international economy and finally established himself in the desire to become a mathematician. His diplomas, bachelor's and master's degrees corresponded to the specialty “Theoretical and Applied Mathematics”.
About how his institute teachers appreciated, says the recommendation issued by educator Richard Duffin for admission to Princeton University. Let us cite her text completely and literally: “This guy is a genius!”
Princeton University
And yet, thanks not to a recommendation, but to brilliantly passed exams, John Nash entered the university. His biography at the time creates the impression that fate really led him. How did this manifest?
He, which he did not know, had only nine years to go, when madness for thirty years would cover him with a dark veil of paranoid schizophrenia from the outside world, erase him from society, destroy his family, and deprive him of work and home.
The young man did not know all this, nor did he know where the thin line separates genius and madness. He enthusiastically greeted the presentation of the new science of game theory, the brainchild of economists Oscar Morgenstern and John von Neumann, and immediately took off his brain brainstorming. 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 did the young almost doctor of sciences know that in 45 years John Nash's theory would be awarded the Nobel Prize? It will take society almost half a century to understand: it was a breakthrough!
Work
Very early, in 1950–1953, a period of creative maturity begins with a 22–25-year-old scientist. He writes several fundamental works on the so-called game theory with a nonzero sum. 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: the Massachusetts Institute of Technology, located in Cambridge. Then luck smiles at him: contact with the RENT propentagon corporation. He tastes what unlimited financing of the Cold War is, becoming one of the leading American experts in its conduct.
What is game theory
The contribution of game theory to the modern regulation of society is difficult to overestimate. What is a society in terms of macroeconomics? The interaction of many players. For example, aggregated: business, state, households. Even at this macro level, it is clear that each of them pursues its own strategy.
Businesses are potentially inclined to overstate their profits (tarnishing households) and minimize taxes (underpaying to the state).
It is beneficial for the state to raise taxes (suppressing small and medium-sized businesses) and reduce the level of social protection (depriving support of unprotected sections of society).
Households are comfortable with overstated social support from the state and minimum prices for services and goods produced by the business.
How to make these Swans, Cancer and Pike together and dynamically drag a cart whose name is society? This is determined by game theory.
The brainchild of John Nash - tasks with a nonzero sum
The above class of problems, when the gain of one of the parties is equal to the loss of the other, is called tasks with zero sum. Both Morgenstern and Neumann were able to calculate it. However, we recall that for this class of tasks, John Nash created the toolkit and conceptual apparatus.
But the brilliant mathematician did not stop on this model; he justified a more subtle class of problems (with a nonzero sum). For example, the conflict between the administration and the trade unions, pushing the requirement to raise wages.
By fueling the situation through a long strike, both sides will suffer losses. If both the unions and the administration use the ideal strategy, both will benefit. This situation is called non-cooperative equilibrium, or Nash equilibrium. (Such tasks include diplomatic problems, trade wars.)
A highly competitive modern society demonstrates a truly endless range of interactions between various entities. Moreover, almost all of them lend themselves to mathematical analysis as problems with a nonzero sum.
Personal life
Until the end of the 50s, future Nobel laureate John Nash climbed the scientific and career ladder, so to speak, jumping through three steps. The main thing for him was ideas, not people. Cold and cynical, he reacted to his fellow MIT colleague, Eleanor Stier. He was not touched by the fact that the woman bore him a child. He simply did not acknowledge his paternity. By the way, Nash had no friends in any team among his work colleagues. He was eccentric and strange, lived in a world of formulas invented by himself. All his attention was devoted to one thing - the development of ideal strategies.
Needless to say, the leading Cold War technologist, thirty-year-old John Nash, flourished. A photo of him during these years is very similar to the picture of actor Russell Crowe who played him. Brunette with an intelligent face and a thoughtful look. Fortune Magazine prophesies glory and fame for him. In February 1957, he marries Alicia Lard, their son Martin appears two years later. However, at this seemingly highest point of career take-off and personal well-being, John began to show symptoms of paranoid schizophrenia.
Disease
Further, for John Nash, a real nightmare began: harsh insulin therapy at Trenton State Hospital, dismissal from work, divorce after three years of illness with desperate Alicia Lard, wandering around insane asylums.
In the 60s he felt better, and Eleanor Stier gave a homeless scientist a roof over his head, he spent time in conversations with his first son. It seemed to Nash that he was recovering, and he stopped taking antipsychotic drugs. The disease has returned.
Then, in the 70s, Alicia Lard gave him shelter. Colleagues gave him a job.
The path to recovery
At this point, he realized that he was living in an illusory, deformed schizophrenia and paranoia world, and began to fight the disease. But he was not a doctor, but a scientist. Therefore, his weapon was not medical methods, but a game theory developed by himself. Scientifically fought with paranoia John Nash. A film with Russell Crowe in the role of a genius clearly showed this. He fought the disease around the clock, uncompromisingly, like an opponent in the game, ahead of the initiative, minimizing his chances, limiting the choice of moves, depriving the initiative. As a result of this most important party in his life, genius defeated madness: he achieved constant absolute minimization of an incurable disease.
Finally, in 1990, the physicians issued a long-awaited verdict: John Nash recovered. We must pay tribute to the scientific world of the United States, we have not forgotten the genius, because all these more than fifty years they used the tools developed by Nash. In 1994, he became a Nobel Prize laureate (for his student dissertation, written at the age of 21!). In 2001, Nash again tied the knot with Alicia Lard. Today, a well-known scientist continues his research activities at his Princeton office. He is interested in non-linear strategies for using computers.
Output
This American genius is a surprisingly solid person, his whole life is a proof of game theory. His destiny came together and triumph, and love, and madness, and the victory of the intellect over paranoia. To analyze the surrounding reality, John Nash invariably uses the scientific tools developed by himself.
The scientist's genius can be very clearly characterized by the phrase Umberto Eco (novel “Foucault's Pendulum”) that a genius always plays on one component. However, his game is unique and unique. Because when he plays it, then all other components are involved.