Alexander Grothendieck

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Alexander Grothendieck : biography

28 March 1928 –

While the issue of military funding was perhaps the most obvious explanation for Grothendieck’s departure from IHÉS, those who knew him say that the causes of the rupture ran deeper. Pierre Cartier, a visiteur de longue durée ("long-term guest") at the IHÉS, wrote a piece about Grothendieck for a special volume published on the occasion of the IHÉS’s fortieth anniversary. The Grothendieck Festschrift was a three-volume collection of research papers to mark his sixtieth birthday (falling in 1988), and published in 1990.The editors were Pierre Cartier, Luc Illusie, Nick Katz, Gérard Laumon, Yuri Manin, and Ken Ribet. A second edition has been printed (2007) by Birkhauser.

In it Cartier notes that, as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden. As Cartier puts it, Grothendieck came to find Bures-sur-Yvette "une cage dorée" ("a golden cage"). While Grothendieck was at the IHÉS, opposition to the Vietnam War was heating up, and Cartier suggests that this also reinforced Grothendieck’s distaste at having become a mandarin of the scientific world. In addition, after several years at the IHÉS Grothendieck seemed to cast about for new intellectual interests. By the late 1960s he had started to become interested in scientific areas outside of mathematics. David Ruelle, a physicist who joined the IHÉS faculty in 1964, said that Grothendieck came to talk to him a few times about physics. (In the 1970s Ruelle and the Dutch mathematician Floris Takens produced a new model for turbulence, and it was Ruelle who invented the concept of a strange attractor in a dynamical system.) Biology interested Grothendieck much more than physics, and he organized some seminars on biological topics. Allyn Jackson, March 1999, Noticed of the AMS pp. 329-337

After leaving the IHÉS, Grothendieck became a temporary professor at Collège de France for two years. A permanent position became open at the end of his tenure, but the application Grothendieck submitted made it clear that he had no plans to continue his mathematical research. The position was given to Jacques Tits.

He then went to Université de Montpellier, where he became increasingly estranged from the mathematical community. Around this time, he founded a group called Survivre (To Survive), which was dedicated to antimilitary and ecological issues. His mathematical career, for the most part, ended when he left the IHÉS.

Manuscripts written in the 1980s

While not publishing mathematical research in conventional ways during the 1980s, he produced several influential manuscripts with limited distribution, with both mathematical and biographical content.

La Longue Marche à travers la théorie de Galois [The Long March Through Galois Theory] is an approximately 1600-page handwritten manuscript produced by Grothendieck during the years 1980–1981, containing many of the ideas leading to the Esquisse d’un programme (see below, and also a more detailed entry), and in particular studying the Teichmüller theory.

In 1983 he wrote an extended manuscript (about 600 pages) entitled Pursuing Stacks, stimulated by correspondence with Ronald Brown, (see also and Tim Porter at University of Bangor in Wales), and starting with a letter addressed to Daniel Quillen. This letter and successive parts were distributed from Bangor (see External Links below): in an informal manner, as a kind of diary, Grothendieck explained and developed his ideas on the relationship between algebraic homotopy theory and algebraic geometry and prospects for a noncommutative theory of stacks. The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works, Les Dérivateurs. Written in 1991, this latter opus of about 2000 pages further developed the homotopical ideas begun in Pursuing Stacks. Much of this work anticipated the subsequent development of the motivic homotopy theory of Fabien Morel and V. Voevodsky in the mid-1990s.