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Other mathematics[ edit ] Nash did groundbreaking work in the area of real algebraic geometry: Nash, John Forbes Mikhail Leonidovich Gromov writes about Nash's work: Nash was solving classical mathematical problems, difficult problems, something that nobody else was able to do, not even to imagine how to do it.
Judging from the classical perspective, what Nash has achieved in his papers is as impossible as the story of his life He learned that an Italian mathematician, Ennio de Giorgihad published a proof just months before Nash achieved his.
Each took different routes to get to their solutions. The two mathematicians met each other at the Courant Institute of Mathematical Sciences of New York University during the summer of It has been speculated that if only one had solved the problem, he would have been given the Fields Medal for the proof.
Nash seemed to believe that all men who wore red ties were part of a communist conspiracy against him; Nash mailed letters to embassies in Washington, D.
Originally intended to present proof of the Riemann hypothesisthe lecture was incomprehensible. Colleagues in the audience immediately realized that something was wrong.
There, he was diagnosed with paranoid schizophrenia. According to the Diagnostic and Statistical Manual of Mental Disordersor DSM, a person suffering from the disorder is typically dominated by relatively stable, often paranoid, fixed beliefs that are either false, over-imaginative or unrealistic, and usually accompanied by experiences of seemingly real perception of something not actually present.
Further signs are marked particularly by auditory and perceptional disturbances, a lack of motivation for life, and mild clinical depression. Afterhe was never committed to a hospital again, and he refused any further medication.
According to Nash, the film A Beautiful Mind inaccurately implied he was taking what were the new atypical antipsychotics of the time period. He attributed the depiction to the screenwriter who was worried about the film encouraging people with the disorder to stop taking their medication.
He 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'". Only gradually on his own did he "intellectually reject" some of the "delusionally influenced" and "politically oriented" thinking as a waste of effort.
Byhowever, even though he was "thinking rationally again in the style that is characteristic of scientists," he said he felt more limited. I 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.Example, sample of a problem statement.
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