John Nash was a mathematical genius who changed the face of game theory with his equilibrium theorem. Its influence, over the course of his life, spread into areas such as biology, economics and a multitude of others. From Princeton onward, Nash made a splash on the mathematical scene, but also struggled with schizophrenia throughout his life. He was able to overcome this obstacle through the use of his mind. This struggle in tandem with his talent marked him as a unique genius within the realm of math theory and history.
The mathematician John Nash is a fascinating figure who made strides both in the world of mathematics and in his personal struggle with schizophrenia. His life began on June 13, 1928 in the town of Bluefield, Virginia (Nasar, 1998, p. 30). His schizophrenia showed early on in school, cropping up in issues with socialization and being immature in comparison to his peers. But he made up for this with an insatiable, curious mind that loved to explore and test the things that he learned about (Nasar, 1998, p.31-32).
His first touch with mathematics occurred in his early teens when he read the book Men of Mathematics by E.T. Bell. This was the first step in his discovery of his own enjoyment of working to bend his mind around mathematical questions (Nasar, 1998, p. 34). As he continued on through school, Nash’s poor social skills continued to set him apart from his peers, but he developed used two defense mechanisms to buffer him: his mind and a layer of stout aloofness (Nasar, 1998, p. 38).
His collegiate work began at Carnegie Tech in Pittsburg Pennsylvania to major in electrical engineering. His skill in his math courses soon incited his professors to encourage him change his major to math. His social problems continued, setting him apart from the other students. He would gain more acceptance at Princeton, where his natural ability overshadowed his sometimes eccentric behavior (Nasar, 1998, p. 42).
It was during his time at Carnegie that Nash was exposed to the subject that would later be so infinitely influenced by his work at Princeton: economics. He chose this class, titled “International Economics,” as an added course. This one class provided the only exposure he would have in this area that later became part of his work with game theory and the problem of bargaining (Frangsmyr, 1994).
As Kuhn discusses in The Essential John Nash, at Princeton Nash had his own approach and was able to grow here in an environment filled with the greats. John von Neumann and Einstein were just two examples of the talented minds that he was exposed to. His eccentric behavior continued, as he would walk continually and stay away from class. Nash’s focus was on discovering the ultimate unsolved problem in math, and would involve himself in discussion with whoever might have information regarding one (Kuhn & Nasar, 2002, p. xvi).
He had early achievements at Princeton, one of which was his conception and making of a board game that he titled “Nash.” It became popular with the other students, who loved to play it. Its importance lay in a hint of what was to come in the future when he got enamored in game theory. He attended one of Princeton’s many seminars, and one given by Professor Albert Tucker on game theory caught his attention. It inspired Nash to take on a problem that was had been around in the realm of economics for a long time: the issue of bargaining (Kuhn & Nasar, 2002, p. xviii).
Nash attacked the problem of bargaining in a paper written while at Princeton. He outlined the idea that bargaining involves two people involved in a “game.” These two individuals approach the game using practical reasoning by working together so that both of them benefit from the outcome (1996, p. 155). Ultimately, the two involved use their individual skills at bargaining to reach a solution that also helps each individually (Nash, 1996, p.156).
Past work on bargaining had focused on competition between those trading goods, but this was not always the situation. The problem of accurately describing the behavior of the two individuals involved outside a situation of pure competition was met with a brick wall, until Nash (Nasar, 1998, p. 89). His idea as, as Nasar explains, took into account that those involved could work together to arrive at a solution and they would have alternative possible solutions as well (1998, p. 90).
His theory has been tested and established repeatedly over the decades, and has been found to be useful in business and economics, which is dependent on the interplay between those involved (Kotler, 1980, p. 540; Webster, 1979, p. 62-63 as referenced in Nelsin & Greenhalgh, 1986, p. 3).
His paper led him to gain attention from the RAND Corporation, which was an Air Force supported “think tank” full of scientists and other personnel that did math for the military. The work involved issues such as the performance of weapons, targeting for bombs and interaction of parties in a conflict (or war). Nash joined this group in 1950 (Nasar, 1998, p.104-105). His eccentric behavior was still present here, such as walking the hallways of the building endlessly. This did not take away from his aura as a talented mathematician (113). Sylvia Nasar sums up his status at this time in the math community in her 2002 lecture at MIT: I learned that by the time John Nash was thirty years old he was already a celebrity in the rarified world of mathematics. He was a brilliant student at Princeton in the late forties and a rising star here at MIT in the 1950’s.
During his time at MIT, Nash worked as an instructor from 1951 to 1959. He did work with “differential geometry,” finding the solution to a past problem and related areas. This was also a key time in his life, as two major shifts occurred. The first was meeting and marrying his wife, Alicia. The second involved the gradual alteration in his thinking, as Kuhn quoted him, “Now I must arrive at the time of my change from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as “schizophrenic” or “paranoid schizophrenic (2002, p. 9).”
In 1959, Nash had to be put into the hospital for observation after his condition had become more serious. He left MIT and spent the next few years in and out of hospitals for the same reason, without his consent, for treatment (Kuhn & Nasar, 2002, p.10). As John Nash aged into the 1970’s, he made a return to Princeton. He became a well known figure to students who would wander the campus, working math solutions on blackboards around Fine Hall, and received the nickname of “the Phantom (Nasar, 1998, p. 332-333).”
As the years progressed and he aged, his schizophrenia became more manageable and he was able to Nash’s mind, was over time able to find a middle ground where he could return his thinking to a more rational viewpoint, and put aside many of his “delusions (Kuhn & Nasar, 2002, p.10). He began a return to life of an active mathematician, and by the 1980’s his writing on various problems began to pop up in journals and other literature again. The journals his work appeared in dealt primarily with the realm of economics, which his earlier ideas had worked such as enormous influence on (Nasar, 1998, p. 353-354).
John Nash’s ultimate achievement was winning the Nobel Prize in economics in 1994. Nash’s work with game theory, bargaining and his equilibrium had forged a huge change in the world of economics. His work is taught in universities, governments use it in making policy in a number of areas and it can be applied to numerous situations to find solutions. It has and continues to affect many arenas in the public sector (Nasar, 1998, p. 374-375).
Nash’s contributions are shadowed and enhanced by his schizophrenia. He was inhibited by it during a good portion of this life, but at was able to overcome it of his own accord. During this struggle, his research was able to forge great change in many avenues. This is part of what makes his life so interesting and astounding at the same time.
John Nash summed up his future goals after winning the Nobel Prize by saying: Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future.
References:
- Frangsmyr, Tore. (ed.). (1994). Les prix nobel: The nobel prizes 1994.
- Stockholm:Nobel Foundation. Retrieved 29 May 2010 from http://nobel prize.org/nobel_prizes/economics/laureates/1994/nash-autobio.html
- Kuhn, Harold W. & Nasar, Sylvia (eds.). (2002). The essential john nash.
- Princeton: Princeton University Press. Retrieved 27 May 2010 from http://www.google.com/books?id=IvOjnugbg7AC&printsec=frontcover&dq=John+Nash&cd=2#v=onepage&q&f=false
- Nasar, Sylvia. (1998). A beautiful mind: The life of mathematical genius and nobel laureate john nash. New York: Touchstone.
- Nasar, Sylvia (2002). A beautiful mind: Genius, madness, reawakening dr. Sylvia nasar. [lecture video recording]. MIT. Retrieved 29 May 2010 from https://mitworld.mit.edu/video/39/
- Nash, John F. (1996). Essays on game theory. Northampton: Edward Elgar Publishing, Inc.
- Nelsin, Scott A. & Greenhalgh, Leonard. (1986). The ability of nash’s theory of cooperative games to predict the outcome of negotiations: A dyad-level test. Management Science, 32, p. 480-498.
