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John Nash — the brilliant ‘madman’
TO BE SURE, John F. Nash Jr is neither the only nor the first mathematician who made breakthroughs in the area of game theory. That is why he had to share his 1994 Nobel Prize in Economics with John C. Harsanyi of the US and Reinhard Selten of Germany.
However, because the story of his personal life resembles a piece of fiction, he is known far better than any other game theorist. Below, Sci-tech World presents excerpts from his autobigraphical sketch, which was written at the time of the award and later published in the book series Les Prix Nobel/Nobel Lectures:
“My beginning as a legally recognized individual occurred on June 13, 1928 in Bluefield, West Virginia, in the Bluefield Sanitarium, a hospital that no longer exists... . By the time I was a student in high school I was reading the classic ‘Men of Mathematics’ by E.T. Bell and I remember succeeding in proving the classic Fermat theorem about an integer multiplied by itself p times where p is a prime.
“Regarding the circumstances of my studies at Carnegie (now Carnegie Mellon University), I was lucky to be there on a full scholarship, called the George Westinghouse Scholarship. But after one semester as a chemical engineering student I reacted negatively to the regimentation of courses... and shifted to chemistry instead. But, I shifted again and became officially a student of mathematics. And in the end I had learned and progressed so much in mathematics that they gave me an MS in addition to my BS when I graduated.
“As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to ‘Non-Cooperative Games’, also to make a nice discovery relating to manifolds and real algebraic varieties.
“While I was on the academic sabbatical of 1956-1957 I also entered into marriage. Alicia had graduated as a physics major from MIT where we had met and she had a job in the New York City area in 1956-1957... .
“The mental disturbances originated in the early months of 1959 at a time when Alicia happened to be pregnant. And as a consequence I resigned my position as a faculty member at MIT and, ultimately, after spending 50 days under ‘observation’ at the McLean Hospital, travelled to Europe and attempted to gain status there as a refugee.
“I later spent 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. And it did happen that when I had been long enough hospitalized that I would finally renounce my delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances and return to mathematical research.
“In these interludes of, as it were, enforced rationality, I did succeed in doing some respectable mathematical research... . But after my return to the dream-like delusional hypotheses in the later 60’s I became a person of delusionally influenced thinking but of relatively moderate behaviour and thus tended to avoid hospitalization and the direct attention of psychiatrists.
“Thus further time passed. 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... .
“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.”
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