1957. It appeared in print in a paper written by Armand Borel with Serre. This result was his first work in algebraic geometry. Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in Claude Chevalley's seminar. He outlined his programme in his talk at the 1958 International Congress of Mathematicians. His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed generic points, which led to the theory of schemes. Grothendieck also pioneered the systematic use of nilpotents. As 'functions' these can take only the value 0, but they carry infinitesimal information, in purely algebraic settings. His theory of schemes has become established as the best universal foundation for this field, because of its expressiveness as well as its technical depth. In that setting one can use birational geometry, techniques from number theory, Galois theory, commutative algebra, and close analogues of the methods of algebraic topology, all in an integrated way. Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. 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. His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules. Although lauded as "the Einstein of mathematics", his work also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems. EGA, SGA, FGA The bulk of Grothendieck's published work is collected in the monumental, yet incomplete, Éléments de géométrie algébrique (EGA) and Séminaire de géométrie algébrique (SGA). The collection, Fondements de la Géometrie Algébrique (FGA), which gathers together talks given in the Séminaire Bourbaki, also contains important material. Grothendieck's work includes the invention of the étale and l-adic cohomology theories, which explain an observation made by André Weil that argued for a connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers. Weil had realized that to prove such a connection, one needed a new cohomology