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The uncertain lurks everywhere – even in mamatics. 1999 Vladimir Voevodsky discovered in a lecture a mistake in one of his own works. Three years later he won field medal for same work, Nobel Prize in mamatics. But it remained a severe personal blow for him.
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“From 1993 on, several groups of mamaticians had reviewed and used my work in seminars,” he later noted. No one has discovered error. “This was obviously no coincidence: it was a technical argument from an author who was familiar, an argument that is difficult to verify and that looks exactly like arguments that are known to be correct. This kind of thing is hardly checked to last detail. ” Untenable as he found.
In fact, gaps and mistakes in mamatics are not individual cases: history of science is full of evidence that sometimes only years later proves to be false. Voevodsky made this an extremist. He fought for a whole new mamatical culture.
Evidence has always been considered as explanations of mamatical contexts, as means of communicating mamatics, and usually y work. “Evidence is what Littlewood and I call ‘ fuel ‘,” wrote, for example, mamatician Godfrey Hardy, who has written important work on numerical ory with his friend John Littlewood. In year 1929 probably noticed. “Evidence is rhetorical blossoms intended to stimulate psyche, pictures on blackboard in lecture, machines to stimulate imagination of students,” Hardy continued.
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That was true a hundred years ago, when evidence still fit on a blackboard. But how stimulating can be a proof that is five hundred pages thick and a human life costs at work just to understand it? At Hardy’s set of “machine”, Voevodsky probably would have shrugged, getting red cheeks in keyword “psyche.” Because mamatician spoke cautiously, sometimes quite hesitantly. But behind his quiet way, a mighty energy hid. He wanted to use m to change math.
Wojewodskis Vision: Machines should form core of a new mamatical culture. Evidence would have to be electronically signed, available on central servers, “because it’s crucial that you know what you’re talking about,” as he put it. The signature would help to clean up misunderstandings. Above all, however, evidence should be written so clearly that computers can read. This compels author to slowness, to work in small steps, to formulate in computer language – but it creates clarity. Because computer is incorruptible, human psyche is not.
More than once in his life, Voevodsky has experienced in his own body how inscrutable and unreliable brain works. Especially in years 2006 and 2007, re were longer phases in which hallucinations and mystical experiences of mamatical work were held. But he always managed to return to science.
