Alexander Grothendieck

Alexander Grothendieck bigraphy, stories - Mathematician

Alexander Grothendieck : biography

28 March 1928 –

Alexander Grothendieck ( born 28 March 1928) is a German-born mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory into its foundations. This new perspective led to revolutionary advances across many areas of pure mathematics.

Within algebraic geometry itself, his theory of schemes has become the universally accepted language for all further technical work. His generalization of the classical Riemann-Roch theorem launched the study of algebraic and topological K-theory. His construction of new cohomology theories has left deep consequences for algebraic number theory, algebraic topology, and representation theory. His creation of topos theory has had an impact on set theory and logic.

One of his most celebrated achievements is the discovery of the first arithmetic Weil cohomology theory: the ℓ-adic étale cohomology. This key result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne. To this day, ℓ-adic cohomology remains a fundamental tool for number theorists, with important applications to the Langlands program.

Grothendieck’s way of thinking has influenced generations of mathematicians long after his departure from mathematics. His emphasis on the role of universal properties brought category theory into the mainstream as an important organizing principle. His notion of abelian category is now the basic object of study in homological algebra. His conjectural theory of motives has been a driving force behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration.

Driven by deep personal and political convictions, Grothendieck left the Institut des Hautes Études Scientifiques, where he had been appointed professor and accomplished his greatest work, after a dispute over military funding in 1970. His mathematical activity essentially ceased after this, and he devoted his energies to political causes. He formally retired in 1988 and within a few years moved to the Pyrenees, where he currently lives in isolation from human society.


Family and childhood

Alexander Grothendieck was born in Berlin to anarchist parents: a father from an originally Hassidic family, Alexander "Sascha" Schapiro aka Tanaroff, who had been imprisoned in Russia and moved to Germany in 1922, and a mother from a Protestant family in Hamburg, Johanna "Hanka" Grothendieck, who worked as a journalist; both of his parents had broken away from their early backgrounds in their teens. At the time of his birth Grothendieck’s mother was married to the journalist Johannes Raddatz, and his birthname was initially recorded as Alexander Raddatz. The marriage was dissolved in 1929 and Schapiro/Tanaroff acknowledged his paternity, but never married Hanka Grothendieck.

Grothendieck lived with his parents until 1933 in Berlin. At the end of that year, Schapiro moved to Paris to evade the Nazis, and Hanka followed him the next year. They left Grothendieck in the care of Wilhelm Heydorn, a Lutheran Pastor and teacher

in Hamburg where he went to school. During this time, his parents took part in the Spanish Civil War in supporting rather than fighting roles.Scharlau (2008), p. 931 Grothendieck could speak French, English and German. 

During WWII

In 1939 Grothendieck went to France and lived in various camps for displaced persons with his mother, first at the Camp de Rieucros, and subsequently lived for the remainder of the war in the village of Le Chambon-sur-Lignon, where he was sheltered and hidden in local boarding-houses or pensions. His father was arrested and sent via Drancy to the Auschwitz concentration camp where he died in 1942. While Grothendieck lived in Chambon, he attended the Collège Cévenol (now known as the Le Collège-Lycée Cévenol International), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists. Many of the refugee children being hidden in Chambon attended Cévenol and it was at this school that Grothendieck apparently first became fascinated with mathematics.