questions, relevant for locally convex spaces. Grothendieck introduced new mathematical methods that enabled him to solve all of these problems within a few months. In Nancy, he wrote his dissertation under those two professors on functional analysis, from 1950 to 1953. At this time he was a leading expert in the theory of topological vector spaces. In 1953 he moved to the University of São Paulo in Brazil, where he immigrated by means of a Nansen passport, given that he had refused to take French nationality (as that would have entailed military service against his convictions). He stayed in São Paulo (apart from a lengthy visit in France from October 1953 - March 1954) until the end of 1954. His published work from the time spent in Brazil is still in the theory of topological vector spaces; it is there that he completed his last major work on that topic (on "metric" theory of Banach spaces). Grothendieck moved to Lawrence, Kansas at the beginning of 1955, and there he set his old subject aside in order to work in algebraic topology and homological algebra, and increasingly in algebraic geometry. It was in Lawrence that Grothendieck developed his theory of Abelian categories and the reformulation of sheaf cohomology based on them, leading to the very influential "Tôhoku paper". In 1957 he was invited to visit Harvard by Oscar Zariski, but the offer fell through when he refused to sign a pledge promising not to work to overthrow the United States government--a position that, he was warned, might have landed him in prison. The prospect of prison did not worry him, so long as he could have access to books. Comparing Grothendieck during his Nancy years to the École Normale Supérieure–trained students at that time (Pierre Samuel, Roger Godement, René Thom, Jacques Dixmier, Jean Cerf, Yvonne Bruhat, Jean-Pierre Serre, and Bernard Malgrange), Leila Schneps said: His first works on topological vector spaces in 1953 have been successfully applied to physics and computer science, culminating in a relation between Grothendieck inequality and the Einstein-Podolsky-Rosen paradox in quantum physics. IHÉS years In 1958, Grothendieck was installed at the Institut des hautes études scientifiques (IHÉS), a new privately funded research institute that, in effect, had been created for Jean Dieudonné and Grothendieck. Grothendieck attracted attention by an intense and highly productive activity of seminars there (de facto working groups drafting into foundational work some of