**Alexander Grothendieck** was a German mathematician and Fields medal winner. He made important contributions in topology, algebra and logic.

- His parents were Alexander Schapiro (1890-1942) and Johanna Grothendieck (1900-1957).
- Alexander Schapiro was a Russian Jew, born in Novozybkov, a town near the point where Russia, White Russia, and Ukraine met.
- Eventually, in 1921, he escaped to live for a while in Berlin and then in Paris under the name Alexander Tanaroff.
- Although Alexander Schapiro was hiding his Jewish origins by using the name Tanaroff, he still considered that Berlin was too dangerous a place for a Jew and he returned to Paris in May 1933.
- After the defeat of the Republicans in early 1939, Alexander and Hanka returned to France where Hanka began working in Nîmes.
- A professor of Grothendieck's assured him that a certain Lebesgue had resolved the last outstanding problems in mathematics, but that his work would be too difficult to teach.
- Alone, with almost no hints, Grothendieck rediscovered a very general version of the Lebesgue integral.
- He had been taught by Élie Cartan and he advised Grothendieck to go to Paris and work with Cartan.
- Grothendieck followed that advice and, after graduating from Montpellier with his licence, he spent the year 1948-49 at the École Normale Supérieure in Paris.
- Grothendieck was now rubbing shoulders with the leading mathematicians of the day who were also attending Henri Cartan's seminar including Claude Chevalley, Jean Delsarte, Jean Dieudonné, Roger Godement, Laurent Schwartz, and André Weil.
- One of Grothendieck's fellow students was Jean-Pierre Serre.
- Since Grothendieck was at this time more interested in topological vector spaces than he was in algebraic topology, André Weil and Henri Cartan both advised him to go to Nancy where there was a strong team including Jean Dieudonné, Jean Delsarte, Roger Godement and Laurent Schwartz.
- It provided a wonderful environment for the young Grothendieck.
- We therefore proposed them to Grothendieck, and the result turned out to exceed our most sanguine expectations.
- recalled that after Grothendieck wrote his thesis he asserted that he was no longer interested in topological vector spaces.
- Grothendieck's second thesis was on sheaf theory, and this work may have planted the seeds for his interest in algebraic geometry, where he was to do his greatest work.
- After Grothendieck's thesis defense, which took place in Paris, Malgrange recalled that he, Grothendieck, and Henri Cartan piled into a taxicab to go to lunch at the home of Laurent Schwartz.
- "In the taxi Cartan explained to Grothendieck some wrong things Grothendieck had said about sheaf theory," Malgrange recalled.
- Grothendieck spent the years 1953-55 at the University of São Paulo and then he spent the following year at the University of Kansas.
- During this period Grothendieck had been supported by the Centre National de la Recherche Scientifique, the support beginning in 1950.
- Grothendieck's Séminaire de Géométrie Algébrique Ⓣ(Algebraic geometry seminar) established the IHES as a world centre of algebraic geometry, and him as its driving force.
- During this period Grothendieck's work provided unifying themes in geometry, number theory, topology and complex analysis.
- Luc Illusie began attending Grothendieck's seminar at the Institut des Hautes Études Scientifiques in 1964.
- Valentin Poénaru also knew Grothendieck during these years.
- In looking back at this period, one marvels at the generosity with which Grothendieck shared his ideas with colleagues and students, the energy he and his collaborators devoted to meticulous redaction, the excitement with which they set out to explore a new land.
- He introduced the idea of K-theory (the Grothendieck groups and rings).
- The "Tohoko paper" referred to in this citation is about abelian categories, sheaves of modules, resolutions, derived functors, and the Grothendieck spectral sequence.
- Now Grothendieck was always strongly pacifist in his views and he had campaigned against the military built-up of the 1960s.
- At the Congress, Léon Motchane, director of IHES, received the Fields Medal on Grothendieck's behalf.
- Grothendieck made no public statement about the reasons for not going to Moscow but he declared himself a citizen of the world and requested United Nations citizenship.
- Grothendieck tried to persuade all the professors to resign in protest but the others refused to follow his example.
- Grothendieck's letter of resignation was dated 25 May 1970.
- However, Grothendieck had other problems for he wrote that at this time he was suffering a "spiritual stagnation".
- In contrast to his acceptance of the 1966 Fields Medal, Grothendieck declined the Crafoord Prize in 1988.
- Between 1980 and 1990, Grothendieck wrote literally thousands of pages some containing his mathematical thoughts and others containing non-mathematical meditations.
- Let us end with some quotations from Grothendieck's correspondence with Ronnie Brown at Bangor.

Born 28 March 1928, Berlin, Germany. Died 13 November 2014, Saint-Girons, France.

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Bourbaki, Prize Fields Medal, Origin Germany, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive