Biography of Alexander Grothendieck

Alexander Grothendieck (born 28 March 1928 in Berlin; died 13 November 2014 in Saint-Girons, France) was a German-born, later French mathematician. He is regarded as one of the defining figures of twentieth-century mathematics and transformed algebraic geometry in particular. His work created new concepts for spaces, structures and connections that later reached far beyond his own field.

Childhood between persecution and France

Grothendieck was born in Berlin. His parents, Hanka Grothendieck and Alexander Schapiro, were close to left-anarchist circles and had to flee political persecution and National Socialism. As a child, Grothendieck lived for a time separated from them; later he came to France. During the war he and his mother were interned, while his father was handed over by the Vichy authorities to the Nazis and murdered in Auschwitz. Grothendieck survived in part in Le Chambon-sur-Lignon, where he attended the Collège Cévenol.

Mathematics as reconstruction

After the war, Grothendieck studied in Montpellier and entered the French research world through Paris and Nancy. It soon became clear that he did not want only to solve individual problems. He searched for the concepts that could reorganize whole fields of problems. In functional analysis, topology and finally algebraic geometry, he developed a way of thinking that did not stop at intuitive special cases, but asked for the most general structures.

Algebraic geometry

His greatest influence lies in the renewal of algebraic geometry. Grothendieck introduced concepts such as schemes, toposes and étale cohomology in a form that newly connected algebra, geometry, topology and number theory. This sounds abstract, but it had concrete consequences: old questions about equations, spaces and numbers became treatable in a much wider framework. Later developments, including work on the Weil conjectures and Fermat's last theorem, stood in a mathematical environment that would be hard to imagine without Grothendieck's concepts.

IHES, Fields Medal and rupture

From 1959 onward, Grothendieck worked at the Institut des Hautes Études Scientifiques, where an extraordinarily productive school formed around him. In 1966 he received the Fields Medal, but did not travel to the International Congress of Mathematicians in Moscow for political reasons. In 1970 he left IHES in a dispute over military funding and turned more strongly toward ecological, antimilitarist and social criticism. This rupture was not a simple withdrawal from mathematics, but an expression of growing tension between scientific work, political responsibility and personal conviction.

Withdrawal and late writings

Even after leaving IHES, Grothendieck continued to write. Alongside mathematical manuscripts, he produced long autobiographical and philosophical texts, including Récoltes et Semailles. In the 1990s he withdrew largely from public life and lived in the Ariège department in the Pyrenees. That withdrawal has often been romanticized or pathologized; it is more fitting to see it as a late, difficult phase of a person whose thinking reached exceptionally far and whose relationship with the academic world had become difficult.

Farewell

Alexander Grothendieck died in Saint-Girons on 13 November 2014. His work remains part of the foundation of modern mathematics. It shows how strongly new language can change a field: not only by answering known questions, but by giving researchers concepts with which they can learn to ask differently.