Alexander Grothendieck

Alexander Grothendieck was a German-born French mathematician who became the central figure in a sweeping reconstruction of algebraic geometry, the branch of mathematics that studies geometric shapes defined by polynomial equations, during the 1950s and 1960s. Working largely at the Institut des Hautes Etudes Scientifiques outside Paris, Grothendieck rebuilt the field around new, far more general and abstract foundations, most notably the theory of schemes, along with extensive use of sheaf theory, homological algebra and category theory, tools that let mathematicians unify and vastly extend earlier, more restricted approaches to geometric objects. This reconstruction, carried out through an enormous, largely collaborative body of published work, transformed algebraic geometry into one of the most powerful and unifying branches of modern mathematics and directly enabled major later results by other mathematicians in number theory and geometry. Grothendieck was awarded the Fields Medal, mathematics' most prestigious prize, in 1966 for his contributions to algebraic geometry. In his later life Grothendieck became known as much for his political activism, particularly opposition to military funding of scientific research and the Vietnam War, as for his mathematics, and he eventually withdrew from the mathematical community into decades of increasing seclusion in rural France.