Alexander Grothendieck

Lore & Background

Grothendieck was born in Berlin to anarchist parents. His father, Alexander 'Sascha' Schapiro, had Hasidic Jewish roots and had been imprisoned in Russia; his mother, Johanna 'Hanka' Grothendieck, came from a Protestant German family. During World War II, he and his mother were interned in various camps as 'undesirable dangerous foreigners,' and his father was murdered at Auschwitz. Grothendieck was sheltered in Le Chambon-sur-Lignon, where he attended Collège Cévenol and first became fascinated with mathematics.

After the war, he studied at the University of Montpellier, initially performing poorly, but rediscovered the Lebesgue measure on his own. He moved to Paris in 1948, then to the University of Nancy, where under Jean Dieudonné and Laurent Schwartz he solved all 14 open questions in their latest paper within months. He completed his dissertation on functional analysis from 1950 to 1953. In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS), where he gathered a strong school and produced foundational work through seminars. He received the Fields Medal in 1966.

Reader's Guide

Grothendieck's significance lies in his transformation of algebraic geometry through a relative perspective and the integration of commutative algebra, homological algebra, sheaf theory, and category theory. His work at IHÉS from 1958 to 1970 produced a vast body of foundational results, largely disseminated through seminar notes rather than conventional journal papers. He attracted and trained a generation of mathematicians, including Pierre Deligne, Michel Raynaud, and Jean-Louis Verdier. His earlier work on topological vector spaces, including the Grothendieck inequality, later found applications in physics and computer science, notably in quantum physics. After leaving IHÉS in 1970 due to a dispute over military funding, he withdrew from the mathematical community, pursued political and religious interests (first Buddhism, later a Catholic Christian vision), and lived in seclusion in Lasserre from 1991 until his death in 2014. Despite his withdrawal, he continued mathematical work. He is considered by many to be the greatest mathematician of the twentieth century.

Did You Know?

• Grothendieck once escaped from an internment camp intending to assassinate Hitler.
• He refused to sign a loyalty oath to visit Harvard University in 1957, a refusal that threatened him with prison.
• He rediscovered the Lebesgue measure on his own while an underperforming student at the University of Montpellier.
• His father was murdered at Auschwitz after being handed over by the French Vichy government to the Germans.

Notable Quotes (Wikiquote)

"The introduction of the digit 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps..." — Alexander Grothendieck "We should ask our fellow physicists to invent a principle of anti-interference, which would bring light out of two obscurities (Leray and Grothendieck)." — Alexander Grothendieck "André Weil in 1958, quoted by Pierre Cartier, « André Weil (1906-1998) : adieu à un ami », Séminaire de Philosophie et Mathématiques, 1998, p. 18." — Alexander Grothendieck "Amir D. Aczel (29 April 2009). The Artist and the Mathematician. Basic Books. pp. 54. ISBN 978-0-7867-3288-3." — Alexander Grothendieck