Alexander Grothendieck (born 28 March 1928 in Berlin, Germany; died 13 November 2014 in St Girons, Ariège) is considered to be one of the greatest mathematicians of the 20th century. He is most famous for his revolutionary advances in algebraic geometry, but he has also made major contributions to algebraic topology, number theory, category theory, Galois theory ("new" math), 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. He declined the latter prize on ethical grounds in an open letter to the media.
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.[1][2][3] 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 is the subject of many stories and some misleading rumors concerning his work habits and politics, his confrontations with other mathematicians and the French authorities, his withdrawal from mathematics at age 42, his retirement, and his subsequent lengthy writings.