Alexander Grothendieck: Enthusiasm and Creativity

Alexander Grothendieck was born in Berlin on 28 March 1928. His father, Sascha Shapiro, an anarchist originally from Russia, took an active part in the revolutionary movements first in Russia, and then in Germany, during the 1920s, where he met Hanka Grothendieck, Alexander’s mother. After the Nazis came to power in Germany it was too dangerous for a Jewish revolutionary to stay there, and the couple moved to France, leaving Alexander in the care of a family near Hamburg. In 1936, during the Spanish Civil War, Sascha joined the anarchists in the resistance against Franco. In 1939 Alexander joined his parents in France, but Sascha was arrested and – partly as a consequence of the race laws enacted by the Vichy government in 1940 – sent to Auschwitz, where he died in 1942. Hanka and Alexander Grothendieck were also deported, but they escaped the holocaust. Alexander, separated from his mother, was able to attend high school at the Collège Cévenol in Chambon-sur-Lignon, lodging at the Secours Suisse, a hostel for refugee children, but he had to flee into the woods every time there was a Gestapo raid. He then enrolled at the University of Montpellier and in autumn 1948 he arrived in Paris with a letter of introduction to Élie Cartan. This led to his being accepted at the École Normale Supérieure as an auditeur libre for the 1948–1949 academic year, where he assisted in the debut of algebraic topology in the seminar taught by Henri Cartan (Élie’s son). His earliest interests, however, were in functional analysis, and following Cartan’s advice, he moved to Nancy. Under the guidance of J. Dieudonné and L. Schwartz, he earned his doctorate in 1953. During his years in high school and university, Grothendieck never much enjoyed the courses and programs he attended, nor can it be said that he was a model student. His curiosity, coupled with a sense of dissatisfaction, drove him, not quite 20-years old, to develop on his own a theory of measurement and integration.