John Forbes Nash Jr., known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential ge…
John Forbes Nash Jr., known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations ◦. He was born in Bluefield, West Virginia on June 13, 1928, and died in Monroe Township, New Jersey on May 23, 2015, at age 86 ◦. Nash earned a PhD in 1950 with a 28-page dissertation on noncooperative games, written under doctoral advisor Albert W. Tucker, which contained the definition and properties of the Nash equilibrium ◦. Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Prize in Economics, and in 2015, Louis Nirenberg and Nash were awarded the Abel Prize for their contributions to the field of partial differential equations ◦. In 1959, Nash began showing signs of mental illness and spent several years at psychiatric hospitals being treated for schizophrenia; after 1970, his condition slowly improved, allowing him to return to academic work by the mid-1980s ◦. Nash's paranoid thoughts began around 1958, and he spent most of the 1960s institutionalized ◦. He resigned from the M.I.T. faculty after 50 days under observation at McLean Hospital ◦.
Nash described his recovery as a deliberate intellectual act rather than a cure, stating that he gradually began to intellectually reject delusionally influenced lines of thinking, beginning with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort ◦. He wrote that rationality of thought imposes a limit on a person's concept of his relation to the cosmos, and that returning to rationality is not entirely a matter of joy ◦. Nash used Zarathustra to argue that madness can be generative, noting that without Zarathustra's "madness" he would necessarily have been only another of the millions or billions of human individuals who have lived and then been forgotten ◦. He rejected the framing of mental illness as pure suffering, stating that madness can be an escape and that in madness he thought he was the most important person in the world ◦. Late in life, he said that a hallucination is actually a wasted effort ◦. Nash framed his illness as a productive interruption, suggesting that the gap period of about 25 years of partially deluded thinking provided a sort of vacation and that his situation may be atypical ◦.
Nash's path through mathematics was shaped by elimination of what bored or constrained him: at Carnegie he reacted negatively to the regimentation of chemical engineering, then left chemistry because quantitative analysis was not a matter of how well one could think and understand or learn facts but of how well one could handle a pipette and perform a titration in the laboratory, before the mathematics faculty drew him into mathematics ◦. He recounted that his hospitalizations were coercive and that he resisted them, spending times of the order of five to eight months in hospitals in New Jersey always on an involuntary basis and always attempting a legal argument for release ◦. His hallucinations originated from the desire to be special ◦.
The Nash equilibrium is a position in a situation of competition or conflict in which both sides have selected a strategy, but where neither side can then independently change their strategy without ending up in a less desirable position; Nash proved mathematically that at least one such equilibrium exists in every situation of competition or conflict where the parties are unwilling or unable to communicate ◦. Nash framed his illness as a productive interruption, suggesting that the gap period of about 25 years of partially deluded thinking provided a sort of vacation ◦. When hospitalized long enough, he would renounce his delusional hypotheses and revert to thinking of himself as a human of more conventional circumstances and return to mathematical research ◦.
Nash made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations ◦. His 1950 PhD dissertation contained the definition and properties of the Nash equilibrium ◦. In the 1950s, Nash discovered and proved the Nash embedding theorems by solving a system of nonlinear partial differential equations arising in Riemannian geometry ◦. Ennio De Giorgi and Nash found, with separate methods, results whose De Giorgi–Nash theorem resolved Hilbert's nineteenth problem, an open problem for almost 60 years ◦. Even while hospitalized and delusional, Nash continued producing serious mathematics in lucid intervals, succeeding in doing some respectable mathematical research during interludes of enforced rationality ◦.
Nash's former professor Richard Duffin's letter of recommendation for Princeton stated only: 'He is a mathematical genius.' ◦ In his Nobel autobiography, he wrote that he would not really attempt to describe the long period of his change from scientific rationality into delusional thinking but rather avoid embarrassment by simply omitting to give the details of truly personal type ◦. Asked by his Harvard colleague George Mackey how a mathematician devoted to reason could believe extraterrestrials were sending him messages, Nash answered in a reasonable tone that the ideas he conceived about supernatural beings came to him in the same way as his mathematical ideas did, and for that reason he took them seriously ◦.
Nash was devoted to reason yet believed extraterrestrials were sending him messages because the ideas he conceived about supernatural beings came to him in the same way as his mathematical ideas did, and for that reason he took them seriously ◦. He wrote that rationality of thought imposes a limit on a person's concept of his relation to the cosmos, suggesting that returning to rationality is not entirely a matter of joy ◦. Nash stated that he would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia ◦. His hallucinations originated from the desire to be special, yet late in life he said that a hallucination is actually a wasted effort ◦. He believed he was being chased by a group of communists who wanted to overthrow the government ◦.
He reacted negatively to the regimentation of chemical engineering and left chemistry because quantitative analysis was not a matter of how well one could think and understand or learn facts but of how well one could handle a pipette and perform a titration in the laboratory, before the mathematics faculty drew him into mathematics ◦. He recounted that he spent times of the order of five to eight months in hospitals in New Jersey always on an involuntary basis and always attempted a legal argument for release ◦. He intellectually rejected politically-oriented thinking as essentially a hopeless waste of intellectual effort ◦. During interludes of enforced rationality, he succeeded in doing some respectable mathematical research ◦.
> 'He is a mathematical genius.' ◦
> 'Then gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort.' ◦
> 'So at the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However this is not entirely a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos.' ◦
> 'Because the ideas I conceived about supernatural beings came to me in the same way as my mathematical ideas did, and for that reason I took them seriously.' ◦
> 'People are always selling the idea that people with mental illness are suffering. I think madness can be an escape. If things are not so good, you maybe want to imagine something better. In madness, I thought I was the most important person in the world.' ◦
> '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.' ◦