Background
John Forbes Nash, Jr. (born June 13, 1928) is an American economist and mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting and military theory. Serving as a Senior Research Mathematician at Princeton University during the later part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.
Nash is the subject of the Hollywood movie A Beautiful Mind. The film, based rather loosely on the biography of the same name, focuses on Nash's mathematical genius and struggle with paranoid schizophrenia.
Early life
Nash was born on June 13, 1928 in Bluefield, West Virginia. His father, after whom he is named, was an electrical engineer for the Appalachian Electric Power Company. His mother, Margaret, had been a school teacher prior to marriage. Nash's parents pursued opportunities to supplement their son's education with encyclopaedias and even allowed him to take advanced mathematics courses at a local college while still in high school. Nash accepted a scholarship to Carnegie Institute of Technology (now Carnegie Mellon University) and graduated with a Master's Degree in only three years.
Post-graduate life
Nash's advisor and former Carnegie Tech professor, R.J. Duffin, wrote a letter of recommendation consisting of a single sentence: "This man is a genius." Nash was accepted by Harvard University, but the chairman of the mathematics department of Princeton, Solomon Lefschetz, offered him the John S. Kennedy fellowship, which was enough to convince Nash that Harvard valued him less. Thus he went to Princeton where he worked on his equilibrium theory. He earned a doctorate in 1950 with a 28 page dissertation on non-cooperative games. The thesis, which was written under the supervision of Albert W. Tucker, contained the definition and properties of what would later be called the "Nash Equilibrium". These studies led to four articles:
"Equilibrium Points in N-person Games", Proceedings of the National Academy of Sciences 36 (1950), 48–49. MR0031701
"The Bargaining Problem", Econometrica 18 (1950), 155–162. MR0035977
"Two-person Cooperative Games", Econometrica 21 (1953), 128–140. MR0053471
"Non-cooperative Games", Annals of Mathematics 54 (1951), 286–295.
Nash did ground-breaking work in the area of real algebraic geometry:
"Real algebraic manifolds", Annals of Mathematics 56 (1952), 405–421. MR0050928
See Proc. Internat. Congr. Math. (AMS, 1952, pp 516–517).
His most famous work in mathematics is the Nash embedding theorem, which shows that any abstract Riemannian manifold can be isometrically realized as a sub-manifold of Euclidean space. He made contributions to the theory of non-linear parabolic partial differential equations, and to singularity theory.
Personal life
As per Nash's biography, from 1951 onwards, he had a liaison with a nurse, named Eleanor Stier. They bore a child named John David Stier. Though Nash had thought of marrying her, he later decided against it and abandoned them.
In 1955, Nash went to the Massachusetts Institute of Technology as a C. L. E. Moore Instructor in the mathematics faculty. There, he met Alicia López-Harrison de Lardé (born January 1, 1933), a woman from El Salvador, whom he married in February 1957. She admitted Nash to a mental hospital in 1959 for schizophrenia; their son, John Charles Martin Nash, was born soon afterward, but remained nameless for a year because his mother felt that her husband should have a say in the name.
Nash won the Nobel Memorial Prize in Economic Sciences in 1994.
Schizophrenia
Nash began to show signs of extreme paranoia and his wife later described his behaviour as erratic, as he began speaking of characters who were putting him in danger. Nash seemed to believe that there was an organization chasing him, in which all men wore red ties. Nash mailed letters to embassies in Washington, D.C., declaring that they were establishing a government.
He was admitted to the McLean Hospital, April–May 1959, where he was diagnosed with paranoid schizophrenia. It is the most common type of schizophrenia in most parts of the world. The clinical picture is dominated by relatively stable, often paranoid, fixed beliefs that are either false, over-imaginative or unrealistic, usually accompanied by experiences of seemingly real perception of something not actually present—particularly auditory and perceptional disturbances, a lack of motivation for life, and mild clinical depression. Upon his release, Nash resigned from MIT, withdrew his pension, and went to Europe, unsuccessfully seeking political asylum in France and East Germany. He tried to renounce his U.S. citizenship. After a problematic stay in Paris and Geneva, he was arrested by the French police and deported back to the United States at the request of the U.S. government.
In 1961, Nash was committed to the New Jersey State Hospital at Trenton. Over the next nine years, he spent periods in psychiatric hospitals, where, aside from receiving anti-psychotic medications, he was administered insulin shock therapy.
Although he took prescribed medication, Nash wrote later that he only took it under pressure. After 1970 he was never committed to the hospital again and refused any medication. According to Nash, the film A Beautiful Mind inaccurately showed him taking new atypical anti-psychotics during this period. He attributed the depiction to the screenwriter (whose mother, he notes, was a psychiatrist), who was worried about encouraging people with the disorder to stop taking their medication. Others, however, have questioned whether the fabrication obscured a key question as to whether recovery from problems like Nash's can actually be hindered by such drugs, and Nash has said they are overrated and that the adverse effects are not given enough consideration once someone is considered mentally ill. According to Nasar, Nash recovered gradually with the passage of time. Encouraged by his then former wife, De Lardé, Nash worked in a communitarian setting where his eccentricities were accepted. De Lardé said of Nash, "it's just a question of living a quiet life".
Nash dates the start of what he terms "mental disturbances" to the early months of 1959 when his wife was pregnant. He has described a process of change "from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic' including seeing himself as a messenger or having a special function in some way, and with supporters and opponents and hidden schemers, and a feeling of being persecuted, and looking for signs representing divine revelation. Nash has suggested his delusional thinking was related to his unhappiness, and his striving to feel important and be recognized, and to his characteristic way of thinking such that "I wouldn't have had good scientific ideas if I had thought more normally." He has said, "If I felt completely pressureless I don't think I would have gone in this pattern". He does not see a categorical distinction between terms such as schizophrenia and bipolar disorder. Nash reports that he did not hear voices until around 1964, later engaging in a process of rejecting them. Nash reports that he was always taken to hospitals against his will, and only temporarily renounced his "dream-like delusional hypotheses" after being in a hospital long enough to decide to superficially conform, behave normally or experience "enforced rationality". Only gradually on his own did he "intellectually reject" some of the "delusionally influenced" and "politically-oriented" thinking as a waste of effort. However, by 1995, he felt that although he was "thinking rationally again in the style that is characteristic of scientists", he felt more limited.
