Handed fourteen open problems, a stateless student solved them all within months
Around 1949, two leading mathematicians in Nancy showed a newcomer their latest paper, which closed with 14 unsolved questions. Within a few months Alexander Grothendieck had invented methods that settled every one. He had survived a wartime childhood in camps and hiding, and would go on to rebuild algebraic geometry from its foundations.
Grothendieck was born in Berlin on 28 March 1928 to anarchist parents: Sascha Schapiro, of Hasidic Jewish roots, and Hanka Grothendieck, a journalist from a Protestant Hamburg family. When the Nazis took power his parents fled to France, leaving him with a Lutheran pastor in Hamburg. In May 1939 he was put on a train to join them. He and his mother were then interned as undesirable foreigners, and his father was deported to Auschwitz in 1942 and murdered. The boy was eventually sheltered in Le Chambon-sur-Lignon, a village later honoured as Righteous Among the Nations, where a pacifist school first sparked his love of mathematics.
His start was unpromising. At Montpellier he failed classes, and alone he reinvented the Lebesgue measure without knowing it existed. In Paris he could not follow Henri Cartan's seminar, so he moved to Nancy to study under Jean Dieudonné and Laurent Schwartz, the source of those 14 problems. Refusing French citizenship because it meant military service, he travelled on a Nansen passport to São Paulo, then to Kansas, where he switched fields. The mathematician Leila Schneps described his leap from obscurity to stardom as unique in the history of the subject.
In 1958 he joined the new IHÉS near Paris, an institute practically built for him and Dieudonné. For about a decade he dominated mathematics through vast collaborative seminars rather than journal papers, drawing in students such as Pierre Deligne. He introduced schemes, the flexible foundation algebraic geometry has used ever since, along with étale cohomology, the tool that later cracked the Weil conjectures, and topos theory. He won the Fields Medal in 1966.
His politics were radical and pacifist. He skipped the Moscow congress where the medal was awarded, lectured on category theory in the forests near Hanoi during bombing, and left IHÉS around 1970 on discovering it took military money. After teaching at Montpellier he withdrew entirely, settling in 1991 in the Pyrenean village of Lasserre, where he lived secluded until his death in 2014.
Source: Alexander Grothendieck
