GROTHENDIECK, ALEXANDRE

born March 28, 1928, Berlin, Ger. German-French mathematician who was awarded the Fields Medal in 1966 for his work in algebraic geometry. After studies at the University of Montpellier (France) and a year at the cole Normale Suprieure, Paris, Grothendieck received his doctorate from the University of Nancy (France) in 1953. After appointments at the University of So Paulo in Brazil and the University of Kansas and Harvard University, Cambridge, Mass., in the United States, he accepted a position at the Institute of Advanced Scientific Studies, Bures-sur-Yvette, France, in 1959. He left in 1970, eventually settling at the University of Montpellier, from which he retired in 1988. Grothendieck was awarded the Fields Medal at the International Congress of Mathematicians in Moscow in 1966. During the 19th and early 20th centuries there was an enormous growth in the area of algebraic geometry, largely through the tireless efforts of the Italian school. But a more abstract point of view emerged in the mid-20th century, and a great deal of the change is due to the work of Grothendieck, who was building on the work of Andr Weil, Jean-Pierre Serre, and Oscar Zariski. Although Grothendieck's early work was in functional analysis, he is renowned for his later work in algebraic geometry. Using category theory and ideas from topology, Grothendieck was able to expand enormously the field of algebraic geometry with ideas of great abstraction and depth. Grothendieck's publications include Produits tensoriels topologiques et espaces nuclaires (1955; Topological Tensor Products and Nuclear Spaces); with Jean A. Dieudonn, lments de gomtrie algbrique (1960; Elementary Algebraic Geometry); and Espaces vectoriels topologiques (1973; Topological Vector Spaces). A Festschrift containing articles in honour of Grothendieck's 60th birthday was published in 1990. Late in his career Grothendieck developed a strong interest in political action; his memoir, Rcoltes et semailles (1985; Reaping and Sowing), is largely concerned with subjects other than mathematics.