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... Vladimir Voevodsky and his collaborators have provided us with a very interesting candidate-category of motives: a category (of sheaves relative to an extraordinarily fine Grothendieck-style topology on the category of schemes) which in some intuitive sense softens algebraic geometry so as to allow for a good notion of homotopy in an algebro-geometric setup and is sufficiently directly connected to concrete algebraic geometry to have already yielded some extraordinary applications. The quest for a full theory of motives is a potent driving force in complex analysis, algebraic geometry, automorphic representation theory, the study of L functions, and arithmetic. It will continue to be so throughout the current century.
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Number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!
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In the history of the concept of number, number has been adjective (three cows, three monads) and noun (three, pure and simple), and now.... number seems to be more like a verb (to triple).
Barry Mazur
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Nobody ever did anything very foolish except from some strong principle.
William Lamb, 2nd Viscount Melbourne
Barry Mazur
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Born:
December 19, 1937
(age 86)
Bio:
Barry Charles Mazur is an American mathematician and a Gerhard Gade University Professor at Harvard University.
Known for:
Prime Numbers and the Riemann Hypothesis (2015)
Imagining Numbers (2003)
Kolyvagin systems (2004)
Barry Mazur on Wikipedia
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