Alexander Grothendieck

Alexander Grothendieck (born March 28, 1928, Berlin) was one of the most important mathematicians active in the 20th century. He was also one of its most extreme scientific personalities, with achievements over a short span of years that are still scarcely credible in their broad scope and sheer bulk, and an approach that antagonised even close followers. He made major contributions to algebraic geometry, homological algebra, and functional analysis. He was awarded the Fields Medal in 1966, and co-awarded the Crafoord Prize with Pierre Deligne in 1988. He declined the latter prize, on ethical grounds.

Life

Childhood and studies

Born to a Russian Jewish father and German Protestant mother, he was a displaced person during much of his childhood due to the upheavals of World War II. Alexander lived with his father, Alexander Shapiro, and his mother, Hanka Grothendieck, both of whom were socialist revolutionaries. Until 1933 they lived together in Berlin. At the end of that year, Shapiro moved to Paris, and Hanka followed him the next year. They left Alexander with a family in Hamburg where he went to school. During this time, his parents fought in the Spanish Civil War. In 1939 Alexander came to France and lived in various camps for displaced persons with his mother. His father was sent to Auschwitz where he died in 1942. After the war, young Grothendieck studied mathematics in France, initially at Montpellier. He had decided to become a math teacher because he had been told that mathematical research had been completed early in the 20th century and there were no more open problems. However, his talent was noticed, and he was encouraged to go to Paris in 1948. He wrote his dissertation under Laurent Schwartz in functional analysis, from 1950. At this time he was a leading expert in the theory of topological vector spaces. However he set this subject aside by 1957 in order to work in algebraic geometry and homological algebra.

Related Topics:
Displaced person - World War II - Socialist - Revolutionaries - 1933 - Berlin - Paris - Hamburg - Spanish Civil War - 1939 - Auschwitz - 1942 - France - Montpellier - 20th century - 1948 - Laurent Schwartz - 1950 - Topological vector space - 1957 - Homological algebra

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Politics and retreat from scientific community

Grothendieck's radical left-wing and pacifist politics were doubtless born of his wartime experiences. He gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed, to protest against the Vietnam war. He retired from scientific 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 academics a few years later as a professor at the University of Montpellier, where he stayed until

Related Topics:
Category theory - Hanoi - Vietnam war - 1970 - IHES - Montpellier

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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.

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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.

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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.

Related Topics:
La longue marche à travers la theorie de Galois - Esquisse d'un Programme

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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 Morel and Voevodsky in the mid 1990s.

Related Topics:
Pursuing Stacks - Algebraic homotopy theory - Algebraic geometry - Stacks - Les Dérivateurs

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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.

Related Topics:
Esquisse d'un programme - 1984 - Centre National de la Recherche Scientifique - Anabelian geometry - La Clef des Songes - Dream - God

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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).

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Disappearance

In 1991, he left his home and disappeared. He is said to now live in the South

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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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