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Alexander Grothendieck (born 28 March 1928) is a French mathematician. He is known principally for his revolutionary advances in algebraic geometry, and also for major contributions to number theory, category theory and homological algebra, and his early achievements in functional analysis. He was awarded the Fields Medal in 1966.
He is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. Indeed, the increasing abstraction and formalization of pure mathematics over the 20th century is due in part to his influence. Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. He retired in 1988 and within a few years became reclusive.
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Mathematical achievements
Grothendieck's early mathematical work was done in functional analysis between 1949 and 1953 working on his doctoral thesis in Nancy, supervised by Jean Dieudonné and Laurent Schwartz. His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of L^{p} spaces in studying linear maps between topological vector spaces. In a few years, he had turned himself into a leading authority on this area of functional analysis — to the extent that Dieudonné compares his impact in this field to that of Banach.^{[1]}
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