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Biographies: Alexander Grothendieck

life around 1970, after having discovered the partly military funding of IHES (see pp. xii and xiii of SGA1, Springer Lecture Notes 224). He returned to academia a few years later as a professor at the University of Montpellier, where he stayed until his retirement in 1988. His criticisms of the scientific community are also contained in a letter written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.



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 theorie de Galois (roughly The Long Walk Through Galois Theory) is an approximately 1600-page handwritten manuscript produced by Grothendieck during the years 1980-1981 and contains many of the ideas leading to the Esquisse d'un Programme (see below) and in particular studies the Teichmüller theory.

In 1983 he wrote a huge extended manuscript (about 600 pages) titled Pursuing Stacks, 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 F. Morel and V. Voevodsky in the mid 1990s.

His Esquisse d'un programme (1984) is a proposal for a position at the Centre National de la Recherche Scientifique, which he held from 1984 to his retirement in 1988. Ideas from it have proved influential, and have been developed by others, in particular in a new field emerging as anabelian geometry. In La Clef des Songes he explains how the reality of dreams convinced him of God's existence.

The 2000-page autobiographical manuscript Récoltes et Semailles (1986) is now partly available on the internet in the French original, and an English translation is underway (these parts of Récoltes et Semailles are already translated to Russian and published in Moscow).

Disappearance
In 1991, he left his home and disappeared. He is said to now live in the South of France and to entertain no visitors. Various false rumors have him living in Ardèche, herding goats and entertaining radical ecological theories. Though he has been inactive in mathematics for many years, he remains one of the greatest and most influential mathematicians of modern times.

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