Brilliant mind

The "brilliant mind" is considered one of the most influential mathematicians of the 20th century. Do you know how his theories changed science?

Just days after he was awarded the prestigious Abel Prize for his contribution to mathematics in Norway, John Nash (86) and his wife Alicia (82) tragically lost their lives on May 23, 2015 in a car accident while returning from a trip from this Nordic country. The tragedy happened when the driver of the taxi, in which the married couple Nash was, lost control of the vehicle and hit the protective fence.

John Forbes Nash Jr. is one of the most influential mathematicians of the second half of the 20th century. The Nobel Prize in Economics was awarded to him for his contribution to the development of this field within the framework of Game Theory, Nash Equilibrium. However, some mathematicians believe that Nash's contribution in the field of differential geometry and partial differential equations is even more significant.

Nash equilibrium is one of the most commonly used theoretical concepts in economics. In Game Theory, it represents a solution for the case of so-called non-cooperative games. Although he did not receive the award until 1994, he developed his theory when he was only 22 years old.

The capricious character and work of this famous mathematician have inspired not only mathematicians and economists around the world, but also Hollywood artists. The central theme of the Oscar-winning Hollywood film Brilliant Mind is the life of this Nobel laureate and his decades-long struggle with a severe form of paranoid schizophrenia.

John Nash has not always been famous. This radiant mind has been in the shadow of a severe mental illness for many years. Until the awarding of the Nobel Prize in Economics in 1994, he was almost unknown to the general public. The inner circle of the scientific community and students from Princeton, who often saw him walking alone on the university campus, knew about him. At the time of the award ceremony, he was in very poor financial condition, which was a consequence of a long struggle with the disease.

He was born on June 13, 1928 in West Virginia. Although he first studied engineering, it soon became clear that his affinities were more geared toward pure mathematics. His immeasurable mathematical talent was also recognized by his mentors and directed him this way. In 1948, Nash received a scholarship to Princeton, and only two years later he developed his famous theory.

The brilliance of his mind brought him to MIT, but also to one of the most famous think-tank military organizations called the RAND Corporation. During the first half of the 1950s, Nash worked as an expert consultant in this corporation, developing a series of games that served to predict the strategies of American military enemies. In the late fifties, he was hospitalized with serious symptoms of schizophrenia.

The fight against the disease was very long and difficult. Although the method of electric shocks has long been abandoned, unfortunately, in those years it was very popular to treat severe mental illnesses with this extremely aggressive method. As he himself often stated, he was in psychiatric institutions several times against his will. Since the early 1970s, John Nash has been slowly recovering, although the struggle continues, but then he officially stops taking antipsychotics.

Game Theory

Game theory was originally designed to analyze poker as a game in which each player tried to figure out which moves his opponent would make. In that sense, game theory had the task of mathematically showing which moves were best for each player.

Alisha Nash was a graduate student at MIT, when she met John Nash, in the 1950s. Shortly after she became pregnant, Nash ended up in a psychiatric hospital for the first time. All the weeks that followed a really difficult mental state led to the couple divorcing after only a few years, back in 1963. However, Alisha continued to take care of John despite the divorce. In addition to psychological support, she helped him financially in moments when he was without income, unable to take care of himself. The couple officially remarried in 2001.

However, the application of game theory is just beginning here. One much more serious "game" was very current in those years in the world. In the early 1950s, at a time when Nash was a consultant to the RAND Corporation, the Cold War and fear of starting a nuclear war between East and West prompted politicians, the military and scientists to turn to game theory to devise new strategies for assessing opponents. The strategies, which were extremely important for our survival on the planet, mathematically predicted which moves the Soviets would take in response to the moves on the American side. The message was crystal clear and stated that America would always have more nuclear weapons, if the Soviets decided to attack. At the heart of this game lay personal interest, doubt and fear. In a way, these not-so-popular human traits prevented nuclear war.

While working for RAND Corporation, Nash developed several games. One of the most famous is "See you, sucker!", which in the first version bore an even sharper name "F ** k you, buddy". The only way to defeat an opponent in this game is to betray him mercilessly. Nash wanted to apply his game, at the center of which is a distrustful, suspicious individual, not only to the twisted relations that prevailed during the Cold War between East and West, but to society as a whole. However, at that time, no one understood that the basis of his ideas was a view of the world that was a consequence of paranoia and huge distrust of people.

With the help of a series of equations known as Nash's equilibrium, Nash showed that in a system at the heart of which lies the individual's distrust and personal interests, balance can always be achieved so that individuals' desires are in perfect balance with each other. The prisoner's dilemma, for which Nash is very famous, represents a conflict between the option of two actors of the game helping each other and their selfish, personal interest.

The prisoner's dilemma

The prisoner's dilemma is an example of a decision-making process. Imagine two prisoners, whom the police suspect committed the same crime, but are still looking for evidence. Police are separating the suspects and offering them a settlement. If they betray each other, the traitor is released, while the other serves a full sentence of 3 years. If they both betray the other, each gets 2 years. If both are silent, each gets 1 year.

Our balance in this case means that each person should make the optimal choice, according to the given choice of the other person. However, since there is no rational way to predict how the other side will react, Nash's equations have shown that it is always a better option to betray another player. In this particular case, the "traitor" is released at best, and gets 2 years in prison at worst.

Game theorists have used Nash’s equilibrium to analyze the outcome of strategic negotiations and situations where several decision makers are at stake. Its equations allow you to predict what will happen if several people or institutions make decisions at the same time and when their decisions depend on the decisions of other players.

The simplest interpretation of Nesh's ideas is that the results of different decisions cannot be predicted if decisions in isolation are analyzed. Instead, the decision-making process of all actors must be taken into account. In this regard, Nash's equations were used to analyze war situations and other conflict situations. Also, Nash’s balance was used to assess the extent to which people with different preferences could cooperate and whether they would take risks to achieve a profit for all team players. They were also used in banking systems, when organizing auctions, regulating traffic jams, and even for the rules of penalties that are applied in sports.