Game theorist John Nash

John Nash became widely known throughout the world thanks to the movie "Mind Games". It is surprisingly touching, charged with faith in the power of human genius, a life-affirming film. This is a film-biography, a film-shock, a film-discovery. He introduces the viewer into the world of the future, where the mind creates real miracles. A piercing weave of insanity and genius in its unity and struggle. The "Oscars" collection is a testament to this. The theory of games, created by this mathematician, turned the foundations of corporate business on its head. 27 pages of Nash's doctoral thesis had such an impact on society and economics, like the 21 page of Einstein's doctoral dissertation on theoretical physics.

The Adam Smith theory, which traditionally follows the development of liberal bourgeois society, compares with how John Nash explores it, looks pale, without giving a clear explanation to many contemporary phenomena. The above theories relate just as a two-dimensional geometry is only a subset of a three-dimensional one.

Initiation

John was born on June 13, 1928 in Blyufilde (state of West Virginia). At school he was not a "botanist", he studied medium. By nature - closed, selfish.

Imagine, the future mathematician (differential geometry and game theory) did not like this subject in school. At this stage, everything in it was suspiciously average. As if his intellect was asleep and was waiting for a push. And that all the same has come.

At the age of 14 a teenager got into the hands the book "The Creators of Mathematics" by his compatriot Eric Bell, a mathematician and author of science fiction. The book very reliably told about the life of great mathematicians, about their motivation and contribution to progress.

What happened when you read the book? Who knows ... However, it was like an initiation, after which, before that, the quite average "gray" schoolboy John Nash undertook the impossible and suddenly proves Fermat's small theorem to those around him. The latter does not say much to the non-specialists. But believe me, it was a miracle. With what it can be compared? Perhaps, with the fact that an amateur provincial actor turned up an opportunity, and he played Hamlet magnificently in the capital.

Polytechnical Institute

His father (the son duplicated his name and surname) was an educated person, he worked as an electronic engineer in a commercial company. Parent after the proof of Fermat's theorem it became quite obvious that John Nash Jr. will become a scientist.

A few brilliant research papers widely opened the door to a fairly prestigious Carnegie Polytechnic Institute, where the young man first chose chemistry, then the international economy, and finally became established in the desire to become a mathematician. Received diplomas, bachelor's and master's degrees, corresponded to the specialty "Theoretical and Applied Mathematics".

About how he appreciated his institute teachers, says a recommendation issued to him by the teacher Richard Duffin for admission to Princeton University. Let's quote her text completely and verbatim: "This guy is a genius!"

Princeton University

And yet, thanks not to the recommendation, but to brilliantly passed exams, John Nash entered the university. His biography at the time creates the impression that his fate really led him. How was this manifested?

He, whom he did not know, was only nine years old before the line, when madness for thirty years would cover him with a dark veil of paranoid schizophrenia from the outside world, strike him out of society, destroy his family, and deprive him of work and home.

The young man did not know all this, just as he did not know where the fine line separating genius and insanity passes. He enthusiastically met the presentation of a new science of game theory, the brainchild of economists Oscar Morgenstern and John von Neumann, and immediately took up his head brainstorming. Twenty-year-old genius managed to independently develop a fundamental tool for game theory, and at the age of 21 he completed work on the corresponding doctoral thesis.

Where did the young almost doctor of science know that in 45 years the theory of John Nash would be evaluated by the Nobel Prize? The society will need almost half a century to understand: it was a breakthrough!

Job

Very early, in 1950-1953, a 22-25-year-old scientist begins a period of creative maturity. He writes several fundamental works on the so-called game theory with nonzero sum. What it is? The commentary will be found later in this article.

John Nash is a famous and successful mathematician. The place of his work is very prestigious: Massachusetts Institute of Technology, located in Cambridge. Then he smiles luck: contact with the proponentan corporation RAND. He tastes what is unlimited funding for the Cold War, becoming one of the leading American experts in its conduct.

What is game theory

The contribution of game theory to modern regulation of society's life is difficult to overestimate. What is society in terms of macroeconomics? 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.

Business is potentially inclined to overstate its profits (clamping households) and to minimize taxes (underpaying the state).

It is advantageous for the state to overcharge taxes (suppressing small and medium businesses) and to reduce the level of social protection (depriving support of unprotected strata of society).

Households are comfortable with overestimated social support from the state and the minimum prices of services and goods produced by the business.

How can you make these Swans, Cancers and Pike together and dynamically drag the cart, the name of which is society? This is determined by the theory of games.

John Nash brainchild - problems with non-zero sum

The above class of problems, when the gain of one of the parties is equal to the loss of the other, is called zero-sum tasks. He was able to count both Morgenstern and Neiman. However, we recall that for this class of problems, John Nash created the tools 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 trade unions, which put forward a demand for higher wages.

Staling the situation through a long strike, both sides will suffer losses. If you use the same trade union and administration, the ideal strategy, and those and others will benefit. This situation is called the non-cooperative equilibrium, or Nash equilibrium. (Such tasks include diplomatic problems, trade wars.)

A modern highly competitive society demonstrates a truly endless spectrum of interactions between different actors. Moreover, almost all of them are amenable to mathematical analysis as problems with a nonzero sum.

Personal life

Until the end of the 50's, the future Nobel laureate John Nash climbed the scientific and career ladder, so to speak, jumping through three steps. The main thing for him were ideas, not people. Coldly and cynically, he reacted to his beloved colleague at MIT Eleanor Steer. Nor did he feel that a woman had given him a child. He simply did not recognize his paternity. By the way, Nash had no friends in any of the colleagues among his colleagues. He was eccentric and strange, he lived in a world of invented by himself formulas. All his attention was devoted to one thing: the development of ideal strategies.

Needless to say, the leading technologist of the Cold War, the thirty-year-old John Nash, flourished. His photo in these years is very much like a shot of his actor Russell Crowe. Brunet with an intelligent face and a pensive look. Fortune magazine predicts fame and fame for him. In February 1957, he married Alicia Lard, they have two years later, the son of Martin. However, in this seemingly highest point of career advancement and personal well-being, John began to show symptoms of paranoid schizophrenia.

Disease

Further for John Nash, a real nightmare began: severe insulin therapy at Trenton State Hospital, dismissal from work, divorce after three years of illness with desperate Alicia Lard, wandering around crazy homes.

In the sixties, he felt better, and Eleanor Stier gave the homeless scientist a roof over his head, he spent time talking with his first son. Nash thought he was recovering, and he stopped taking antipsychotic medications. The disease returned.

Then, in the 70's, Alicia Lard gave him shelter. Colleagues gave him work.

Path to recovery

At this point, he realized that he lives 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 weapons were not medical methods, but the game theory he developed himself. John Nash consistently fought with paranoia in a scientific manner. The film with Russell Crowe as a genius clearly showed this. He fought the disease around the clock, uncompromisingly, as with the opponent in the game, ahead of the initiative, minimizing his chances, limiting the choice of moves, depriving initiative. As a result of this most important party in his life, genius conquered madness: he achieved a constant absolute minimization of the incurable disease.

Finally, in 1990, the doctors issued a long-awaited verdict: John Nash recovered. It is necessary to pay tribute to the learned world of the United States, the genius is not forgotten, because all these more than fifty years they have used the tool developed by Nash. In 1994, he became a Nobel Prize laureate (for his student thesis written at the age of 21!). In 2001, Nash again linked himself by marriage to Alicia Lard. Today, the renowned scientist continues his scientific work in his Princeton office. He is interested in nonlinear strategies for the use of computers.

Conclusion

This American genius is an amazingly integral person, his whole life is a proof of the theory of games. In his destiny came together and triumph, and love, and insanity, and the victory of the intellect over paranoia. For the analysis of the surrounding reality, John Nash invariably uses his own scientific tools developed by him.

The genius of the scientist can be very clearly characterized by the phrase Umberto Eco (the novel "Foucault's Pendulum") that a genius always plays on one component. However, his game is unique and unique. Because when he plays it, all other components are involved.