Alexander Grothendieck

Alexander Grothendieck, who later adopted the French spelling Alexandre, was a mathematician born in Germany who later became a French citizen. He is widely regarded as the central architect of modern algebraic geometry. His work broadened the field’s reach and wove together commutative algebra, homological algebra, sheaf theory, and category theory into its core. His “relative” viewpoint brought about transformative breakthroughs across large portions of pure mathematics, and many consider him the most outstanding mathematician of the twentieth century.

He began his mathematical career in 1949. In 1958, he became a research professor at the Institut des hautes études scientifiques (IHÉS), where he stayed until 1970. He left then because of personal and political convictions, after a disagreement about military funding. In 1966, he received the Fields Medal for his contributions to algebraic geometry, homological algebra, and K-theory. He later took a professorship at the University of Montpellier. Though he continued to produce significant mathematics, he gradually stepped away from the mathematical community, turning his attention to political and religious pursuits—first Buddhism, and later a Catholic Christian outlook. In 1991, he moved to the isolated village of Lasserre in the Pyrenees, where he lived in seclusion, continuing to work on mathematics and his philosophical and religious ideas until his death in 2014.

**Life**

**Family and childhood**

Grothendieck was born in Berlin to anarchist parents. His father, Alexander “Sascha” Schapiro (also known as Alexander Tanaroff), came from a Hasidic Jewish background and had been imprisoned in Russia before moving to Germany in 1922. His mother, Johanna “Hanka” Grothendieck, was from a Protestant German family in Hamburg and worked as a journalist. Both parents had broken away from their early backgrounds as teenagers. At the time of his birth, his mother was married to the journalist Johannes Raddatz, and he was initially registered as “Alexander Raddatz.” That marriage ended in 1929, and Schapiro acknowledged paternity, though he never married Hanka. Grothendieck had a maternal half-sister named Maidi.

He lived with his parents in Berlin until the end of 1933, when his father moved to Paris to escape the Nazis. His mother followed soon after. Grothendieck was left in the care of Wilhelm Heydorn, a Lutheran pastor and teacher in Hamburg. According to Winfried Scharlau, his parents took part in the Spanish Civil War as non-combatant auxiliaries, though others say Schapiro fought in the anarchist militia.

**World War II**

In May 1939, Grothendieck was put on a train from Hamburg to France. Shortly afterward, his father was interned at Le Vernet. Grothendieck and his mother were then held in various camps from 1940 to 1942 as “undesirable dangerous foreigners.” The first was the Rieucros Camp, where his mother may have contracted the tuberculosis that eventually killed her in 1957. While there, Grothendieck managed to attend the local school in Mende. He once escaped from the camp, intending to assassinate Hitler. Later, his mother was transferred to the Gurs internment camp for the rest of World War II. Grothendieck was allowed to live separately from her.

In the village of Le Chambon-sur-Lignon, he was sheltered and hidden in local boarding houses, though he sometimes had to flee to the woods during Nazi raids, surviving for days without food or water. His father was arrested under Vichy anti-Jewish laws, sent to the Drancy internment camp, then handed over by the Vichy government to the Germans, who sent him to Auschwitz in 1942, where he was murdered.

In Le Chambon, Grothendieck attended the Collège Cévenol, a secondary school founded in 1938 by local Protestant pacifists. Many refugee children hidden in the village went there, and it was at this school that he first became fascinated with mathematics. In 1990, the entire village was recognized as “Righteous Among the Nations” for risking their lives to rescue Jews.

**Studies and contact with research mathematics**

After the war, Grothendieck studied mathematics in France, starting at the University of Montpellier, where he initially struggled, failing courses like astronomy. Working on his own, he rediscovered the Lebesgue measure. After three years of increasingly independent study there, he went to Paris in 1948 to continue.

He first attended Henri Cartan’s Seminar at the École Normale Supérieure, but lacked the background to follow it. On the advice of Cartan and André Weil, he moved to the University of Nancy, where two leading experts in his area of interest—topological vector spaces—were working: Jean Dieudonné and Laurent Schwartz, the latter a recent Fields Medalist. They showed him their latest paper, *La dualité dans les espaces (F) et (LF)*, which ended with a list of 14 open questions about locally convex spaces. Grothendieck developed new mathematical methods and solved all of them within a few months.

In Nancy, from 1950 to 1953, he wrote his dissertation under Dieudonné and Schwartz on functional analysis. By then, he was a leading expert in the theory of topological vector spaces.