Alexander Grothendieck (born March 28, 1928 in Berlin, Germany) is one of the most influential mathematicians of the twentieth century, known principally for his revolutionary advances in algebraic geometry, but also for major contributions to algebraic topology, number theory, category theory, Galois theory, descent theory, commutative homological algebra and functional analysis. He was awarded the Fields Medal in 1966, and was co-awarded the Crafoord Prize with Pierre Deligne in 1988, but Grothendieck declined it. He is noted for his mastery of abstract approaches to mathematics, and his perfectionism in matters of formulation and presentation. In particular, he demonstrated the ability to derive concrete results using only very general methods. 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, on French mathematics and the Zariski school at Harvard University. He retired in 1988 and within a few years became reclusive.

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