JOHN FORBES NASH: BIOGRAPHY, GAME THEORY AND OTHER CONTRIBUTIONS - CULTURE VOCABULARY - 2025

John Forbes Nash (1928 - 2015) was a prominent American mathematician, known for having developed his mathematical theory about games. For this theory he was awarded the Nobel Prize in Economic Sciences in 1994.

In addition, he made several contributions to differential geometry and the study of equations. Nash's work has been central to decision making within the complex systems found in everyday life. His theories are commonly used in various fields of economics.

Peter Badge / Typos1, via Wikimedia Commons

Beginning in 1959, Nash began to show signs of mental illness, for which he spent several years confined in a psychiatric hospital. After several tests and treatments, the experts concluded that it was a case of paranoid schizophrenia.

Since 1970, his schizophrenic condition has slowly improved, allowing him to return to academic work in the 1980s. The fight against his illness and his recovery motivated the German writer Sylvia Nasar to write the story of Nash, entitled A Beautiful Mind. In 2001 a movie was made with the same name.

Biography

First years and university studies

John Forbes Nash was born on June 13, 1928 in Bluefield, West Virginia, United States. His father, John Forbes Nash, was an engineer who worked at the Electric Power Company. His mother, Margaret Nash, had been a school teacher before they married.

He had a sister two years younger than him, named Martha Nash. Young John attended kindergarten and public school, although he also studied on his own with books from his parents and grandparents.

His parents sought to complete John's comprehensive education, leading him to take advanced math courses at a local college during his senior year of high school. He then attended Carnegie Mellon University, on a special scholarship, where he majored in chemical engineering.

However, on the recommendation of Professor John Lighton Synge, he swapped chemistry for mathematics. He graduated at the age of 19 and accepted a scholarship to study at Princeton University, where he did his graduate studies and specialized in mathematics.

Many professors rated Nash as one of the few mathematical geniuses of the day. For that reason, other universities offered him scholarships similar to Princeton. Still, Nash decided to stay in Princeton because of how close it was to home. In this institution he began to develop his theory of equilibrium.

Beginnings of mental illness

In 1951, he joined the faculty of the Massachusetts Institute of Technology, where he conducted his research on partial differential equations. In the late 1950s, she made the decision to resign, after severe episodes of mental illness that had not yet been properly diagnosed.

As part of the psychological illness, Nash began to believe that all the men wearing red ties were part of a communist conspiracy against him. In fact, he even sent letters to the embassy in Washington, United States, explaining what was happening.

The following year Eleanor Stier, a nurse from Massachusetts, began a love affair. Shortly after they were married, he left his wife after she became pregnant with their child.

In 1959, he tried to explain one of his mathematical hypotheses, but his presentation was completely incomprehensible to the audience. Immediately, he was admitted to McLean Hospital, where he stayed for a few months.

Eventually, he was diagnosed with paranoid schizophrenia. The disorder is often dominated by seemingly real experiences and some episodes of paranoia.

Paranoid schizophrenia

Since he learned of his wife's pregnancy, mental disorders began severely. Nash began to see himself as a "messenger."

Shortly after leaving his wife, he met Alicia Lardé, a woman with a degree in physics from the Massachusetts Institute of Technology. However, the woman had to deal with Nash's illness until the time of their divorce.

At the same time, he began to have a feeling of persecution and an intention to search for some divine symbolism or revelation. Basically, his thoughts were around false images and events that he created in his mind.

In 1961, he was admitted to the New Jersey State Hospital in Trenton. He spent nine years in psychiatric hospitals, where he received antipsychotic medications and various therapies. Nash commented that his delusional thinking was associated with his unhappiness and his desire to feel important and recognized.

Starting in 1964, he stopped hearing the voices in his head and started rejecting all kinds of help. Furthermore, he stated that he had been taken to hospitals against his will. After spending so much time in hospitals, he decided that he would face the problem and act normally.

Versions of Nash's story

The John Forbes Nash story has been attractive to writers and film producers around the world. Sylvia Nasar, a German writer, was inspired by the history of the mathematician to write the work entitled A Beautiful Mind, known in Spanish as A brilliant mind.

American screenwriter Akiva Goldsman adapted the story from Nasar's book to produce a film, which was released in 2001. The film was based primarily on Nasar's book, but it was not completely attached to reality.

Although the film tried to tell the story of the events as they happened, according to Nash's claims, the medications used in the film were incorrect. In addition, Nash showed concern in some parts of the script, as it seemed that people were encouraged to stop taking medication.

According to the film and Nasar's work, he was recovering from the disease as time went by, encouraged by his wife Alicia Lardé. In the real story, Nash and Lardé had divorced when his condition worsened, although after years they decided to resume the relationship again.

Subsequent work and recognition

In 1978, John Nash received the John von Neumann Prize for Theory after the discovery of non-cooperative equilibria, now called Nash Equilibria.

In 1994, he received the Nobel Prize in Economic Sciences along with other experts, as a result of his work on game theory. Between 1945 and 1996, he published a total of 23 scientific studies.

In addition, he developed a work on the role of money in society. She stated that people can be so motivated and controlled by money that sometimes they may not act rationally when money is involved. He criticized certain economic ideologies that allow the development of phenomena such as inflation.

During the 21st century, before his death, he received various recognitions and honorary degrees, among which were the Doctor of Science and Technology from Carnegie Mellon University and the degree in economics from the Federico II University of Naples; in addition to other universities in the United States, Europe and Asia.

Accident and death

Nash and Alicia were returning home to New Jersey after a visit to Norway, where Nash received the Abel Award. On the way from the airport to their home, the taxi in which the couple was traveling lost control, crashing into a railing. Both passengers were ejected from the car upon impact.

On May 23, 2015, Nash and his wife - with whom he had reconciled after a long breakup - died in the act of the car accident. According to state police, the couple were not wearing seat belts at the time of the accident. Nash died at the age of 86.

Games theory

Non-cooperative games

In 1950, Nash managed to finish a doctorate in which he gave a presentation explaining about the theory of non-cooperative games. Within his thesis he produced not only the explanation of non-cooperative games, but also the properties and elements detailed in his Theory of Equilibrium.

Non-cooperative games are based on a competition between individual players, where each of them is able to make decisions for their personal benefit.

The key for this theory to manifest is the absence of an external authority (or judge) who is in charge of enforcing the rules. In this type of game you try to predict the strategies and individual benefits of the players.

Instead, cooperative game theory focuses on predicting the joint actions of the groups and the collective outcomes. Non-cooperative games are responsible for analyzing the strategic negotiation that occurs within each team and more specifically each individual.

When an arbitrator is present to enforce an agreement, this agreement is outside the scope of non-cooperative theory. However, this theory allows sufficient assumptions to be made to end all strategies that players may adopt with respect to refereeing.

Nash equilibrium theory

The Nash equilibrium theory consists of a solution for non-cooperative games where two or more players are involved. In this theory, it is assumed that each player knows the strategies of the other players (of her team and the opponents).

As Nash explains, each player knows his opponent's strategy and has no benefit in changing his own. That is, even when a player knows the strategy of his rival, he does not alter the approach of his game. When this is the case for both players, what is called a Nash equilibrium is achieved.

This theory is used to determine possible outcomes in a game environment where two or more people are carrying out a decision-making process at the same time.

However, the Nash equilibrium has been used to determine the outcome of more serious situations, such as wars or armed confrontations.

Real example of equilibrium theory

At the 2014 soccer World Cup, Louis Van Gaal - a coach of the Dutch team at the time - applied the Nash equilibrium theory during the penalty shoot-out against Costa Rica. The application of this theory led to the Netherlands going undefeated to the next phase of the competition.

Van Gaal made a change of goalkeeper before the penalty shootout; at the last minute, he changed the starting goalkeeper for the substitute, Tim Krul (third goalkeeper of the call). Van Gaal had prepared Krul only for the definition of penalties.

Krul had a detailed report about the possible reactions of the meta rival. In addition, he studied the possible direction in which the Costa Ricans would collect penalties. To achieve this, a complete study of the opponent was conducted.

In addition, the fact that he had not worn out his physical performance was key to the result. Jasper Cillessen (the Dutch team's starting goalkeeper) had played all 90 minutes of the match plus 30 minutes of added time.

Van Gaal and the Dutch coaching staff had already decided to replace Cilessen in the event of the penalty shoot-out; They intentionally did not warn the starting goalkeeper to keep him focused on the match.

Other contributions

Real algebraic geometry

In 1952, John Nash tested various mathematical theories on real algebraic geometry, even establishing analytical mappings with graphs. Real geometry has been in charge of studying objects and structures that arise from physical or technological phenomena.

This concept involves the construction and development of structures to analyze certain objects. In addition, it discusses other computing methods, such as algorithms.

Nash inclusion theorem

One of his most important mathematical works is Nash's inclusion theorem. The mathematician's theorem can be explained through several examples, but one of the clearest is when folding a page of paper (without stretching), providing an inlay within the book.

In mathematics, an embed is an instance of one structure within another, such as groups and subgroups. In this sense, the folded page generates an inlay; that is, the page maintains the same arc length, even though it is moved within the book.

Advances in Evolutionary Psychology

Since John Nash became ill, he has suggested a set of hypotheses about mental illness. In fact, his illness was the engine for an advance on the points of view in evolutionary psychology, mainly in relation to human diversity.

References

1. John Forbes Nash, Wikipedia in English, (nd). Taken from wikipedia.org
2. John F. Nash Jr. Biographical, Website The Nobel Prize, (nd). Taken from nobelprize.org
3. Game Theory, Steven J. Brams and Morton D. Davis, (nd). Taken britannica.com
4. Not everything is luck: Holland uses a scientific theory for penalties, Portal iProfesional, (2014). Taken from iprofesional.com
5. Non-Cooperative Game Theory, Jorge Oviedo, (2005). Taken from mmce2005.unsl.edu.ar