Alexander Grothendieck

Alexander Grothendieck was once married to a woman called Mireille Dufour and had three children with her.

He also had a son with his landlady during his time in Nancy and one child with a woman named Justine Skalba, with whom he lived in a commune in the early 1970s.

He became increasingly reclusive during the later years of his life. In 1991, Grothendieck moved to a new address which he shared with only a few of his contacts.

Alexander Grothendieck was born on 28 March 1928 in Berlin, Germany to anarchist parents. His mother’s name was Johanna "Hanka" Grothendieck and she was married to the journalist Johannes Raddatz at the time of Alexander’s birth. However, Alexander’s biological father was Alexander "Sascha" Schapiro (also known as Alexander Tanaroff). His mother’s marriage to Johannes Raddatz ended in 1929.

He lived with his parents till 1933 when his father moved to Paris to evade Nazism. His mother too followed suit, leaving behind her little son in the care of Wilhelm Heydorn, a Lutheran pastor and teacher.

Alexander went to France during the World War II in 1939 and lived with his mother in various camps for displaced people. They spent the later years of the war in the village of Le Chambon-sur-Lignon, sheltered and hidden in local boarding houses. His father was killed in the Auschwitz concentration camp in 1942.

He attended the Collège Cévenol (now known as the Le Collège-Lycée Cévenol International), a secondary school founded in 1938 by local Protestant pacifists and anti-war activists. It was at this school that he discovered his love for mathematics.

After the war he studied mathematics at the University of Montpellier. Working on his own he rediscovered the Lebesgue measure, and conducted several independent studies over the next three years.

Alexander Grothendieck spent several years travelling and teaching in Brazil and America before returning to France in 1956. He accepted an appointment as a professor in the newly-established Institut des hautes études scientifiques (IHÉS) in Bures-sur-Yvette in 1959.

In his years with the IHES, he completely revolutionized the theory of algebraic geometry. He received much acclaim for his work and had brilliant students like Michel Demazure, Michel Raynaud, Jean-Louis Verdier, Jean Giraud, and Pierre Deligne.

He worked for more than a decade at the IHES during the course of which he established several unifying themes in algebraic geometry, number theory, topology, category theory and complex analysis. He also provided an algebraic definition of fundamental groups of schemes.

Assisted by Jean Dieudonné, he published ‘The Éléments de géométrie algébrique’ ("Elements of Algebraic Geometry"), a treatise on algebraic geometry, published in eight parts from 1960 to 1967. In the volumes he established systematic foundations of algebraic geometry, building upon the concept of schemes.

As someone who had suffered greatly because of the war, he was a pacifist at heart. He had radical political views and was strongly opposed to both United States intervention in Vietnam and Soviet military expansionism. In 1970 he realized that the IHES was partly funded by the military and resigned from his job and retired from scientific life.

The most influential works of Alexander Grothendieck were in the field of algebraic geometry. His article, ‘Sur quelques points d'algèbre homologique’, also known as "Tôhoku paper" is considered to be one of his most important works. In this paper, he introduced abelian categories and applied their theory to show that sheaf cohomology can be defined as certain derived functors in this context.