### John Forbes Nash Jr.

John Forbes Nash Jr. was one of the most influential mathematicians of the second half of the 20th century. He was awarded the Nobel Memorial Prize in Economic Sciences for the contribution that his work, the Nash equilibrium, made to the development of Game theory. However, some mathematicians believe that Nash’s contribution to the fields of differential geometry and partial differential equations is even more significant.

John Forbes Nash Jr. (born in West Virginia on June 13, 1928) was an American mathematician who made contributions to game theory, differential geometry, and the study of partial differential equations. He graduated from the Carnegie Institute of Technology, and earned his PhD at Princeton University, where he worked as a research mathematician. **He received the *** Nobel Memorial Prize in Economic Sciences in 1994 for pioneering equilibrium analysis in the framework of non-cooperative game theory,* which is considered one of the most important achievements of the past century. It could be argued that the Nash equilibrium is as important as the discovery of DNA. Nash started exhibiting symptoms of schizophrenia in 1959, and consequently had to spend several months in McLean Hospital, after which he returned to Princeton, where he became known as “The Phantom of Fine Hall” and stopped taking his medications of his own accord. He associated his madness with his living on an “ultralogical” plane. Author Sylvia Nasar wrote a novel called

*based on his life, which was later adapted into a scenario for the Hollywood movie of the same name and was very successful with both audiences and critics. He became famous around the world among experts and laymen alike, and his life and work have fascinated people everywhere ever since.*

**“A Beautiful Mind”**But John Nash has not always been famous. This beautiful mind spent many years in the shadow of severe mental illness. Until 1994, when he received his Nobel Prize, he was almost unknown to the general public. Only a narrow circle within the scientific community and the Princeton students were aware of him, and they often saw him strolling around the university campus on his own. At the time he received the Nobel Prize, he was in a very poor financial situation as a consequence of his long struggle with the illness.

The brilliancy of his mind took him to MIT, as well as to one of the infamous think tank military organizations — the RAND Corporation. During the early 1950s, Nash worked as an expert consultant in this corporation, developing a string of games serving to predict the strategies of the US military’s enemies. At the end of the 1950s, he was hospitalized due to serious symptoms of schizophrenia.

His struggle with this illness was very long and hard. Even though electroshock therapy has long been abandoned, treating severe mental illnesses using this extremely aggressive method was unfortunately very common at the time. As he often stated himself, Nash was admitted to psychiatric hospitals several times against his will. From the beginning of the 1970s, he slowly started recovering, and, even though he was still in the middle of an on-going struggle, he stopped taking his antipsychotic medications.

Nash equilibrium – Game theory

The equilibrium concept within game theory is modeled after the so-called prisoner's dilemma, the most famous and the most referenced strategic game, which Nash researched based on “Theory of Games and Economic Behavior”, a book written by John von Neumann and Oskar Morgenstern in 1944. This problem is tightly connected with economics in the sense of exploring and finding rational strategies in situations when the result depends not only on one’s own strategy and the “market conditions”, but also on the strategy that the other players with the same goals have chosen. The prisoner’s dilemma is a game in which two people arrested for committing a certain crime are interrogated separately so that neither prisoner can hear what the other has said. Each prisoner has a chance to cooperate with the other prisoner by refusing to provide the police with the necessary information, or he/she can come into a conflict with the other prisoner, i.e. accuse him/her and obtain a certain kind of immunity. The game is designed in such a way that the prisoners are awarded or punished based on their statements, and there are numerous possible variations of their actions. The logic behind this dilemma can be implemented in many different situations. An example can be found in marketing: if there is no advertising, two companies can share the market. If both companies advertise their products, they can share the market, but generate smaller profits (due to advertising expenses). However, if only one of the companies advertises its product, that company will attract more customers, and therefore generate a bigger profit. The principle can also be applied in modeling numerous situations in economics and politics: making decisions on whether to join a union, or about participation in free trade. In practice, there are usually more than two players, which makes the analysis more complex.

Game theorists have used the Nash equilibrium to analyze the outcome of strategic negotiations or situations including several decision makers. Nash’s equations enable us to predict what will happen if several people or institutions make decisions simultaneously and if their decisions depend on the decisions of other players.

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John Nash had a successful private life as well. He met his wife Alicia while she was a physics student. At the time, not many women studied “male sciences”. They got married in 1957. In 1963, they got divorced due to his deteriorated mental health, but were remarried in 2001.

He received the Nobel Memorial Prize in Economic Sciences in 1994.

A Beautiful Mind

This emotional drama directed by Ron Howard tells the life story of a true genius, the eccentric John Nash, exactly as it was recorded. It begins with his success at university which leads to his widely recognized scientific research, as well as to his secret work in which he spends his nights decoding secret Soviet messages in the American press for the US government secret services. He manages to keep the balance between the real and the imaginary, since Nash’s mental condition produces numerous, often very extensive and realistic hallucinations up to the point where differentiating between reality and illusion is quite difficult.

In May, 2015, the famous mathematician and Nobel Prize winner tragically lost his life in a car accident together with his wife at the age of 86.

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