WebzzleDon't force the problem — surround it until it dissolvesA tribute
1928 – 2014 — the mathematician who raised the sea.
Who he was
Alexander Grothendieck was born in Berlin on 28 March 1928, to anarchist parents. His father, Sascha Schapiro, was murdered at Auschwitz in 1942; his childhood was flight and internment camps, then the sheltering village of Le Chambon-sur-Lignon. After the war he studied nearly alone in Montpellier — an hour from the harbor on our home page, under the same Mediterranean light — where, unaware the problem had been solved decades earlier, he reconstructed for himself a general theory of measure and integration.
In Nancy, under Laurent Schwartz and Jean Dieudonné, he tore through functional analysis; his 1953 thesis settled a generation of open questions. Then he turned to geometry, and from 1958, as a founding professor of the IHÉS near Paris, he led the most concentrated rebuilding of a mathematical field ever undertaken: twelve years of seminars and thousands of pages — EGA, SGA — written with, and for, an entire school of mathematicians. He received the Fields Medal in 1966, and refused to travel to Moscow to accept it, in protest against Soviet repression.
In 1970 he discovered that the IHÉS took a share of military funding, and walked away at the height of his power. He co-founded the ecological group Survivre et Vivre, taught in Montpellier, wrote — Esquisse d’un Programme, and the immense meditation Récoltes et Semailles — refused the Crafoord Prize in 1988, and in 1991 withdrew to the Pyrenean village of Lasserre, where he lived in near-total solitude until his death at Saint-Girons on 13 November 2014.
What he built
A few of the cathedrals, in plain words:
He rebuilt algebraic geometry on a foundation so general that numbers and shapes became the same kind of object — the language the field still speaks today.
Never study an object alone; study the map between objects. Properties travel along maps — and whole theories organize themselves.
A “space” is no more than what its points can see together. Topoi made geometry out of contexts — and quietly rejoined logic to space.
The machinery he forged so that counting solutions became geometry — the instrument with which Deligne proved the Weil conjectures in 1974.
His “heart of hearts”: the conjectured common source from which every cohomology flows — still guiding number theory half a century on.
His first thunderclap: a classical theorem about curves, reborn as a statement about all maps at once — the relative point of view, demonstrated.
The method
He described two ways of opening a problem — the hammer and chisel, or this:
« La mer s’avance insensiblement et sans bruit, rien ne semble se casser, rien ne bouge… elle finit par entourer la substance rétive, qui peu à peu devient une presqu’île, puis une île, puis un îlot, qui finit par être submergé à son tour, comme dissous dans l’océan s’étendant à perte de vue. » — Alexandre Grothendieck, Récoltes et Semailles
He almost never attacked a problem head-on. He built the theory around it — found the right definitions, the right level of generality, named what had no name — until the problem, surrounded by understanding, opened by itself. What looks like detour is the shortest path. What looks like abstraction is care.
Why this page is here
Webzzle bears his mark.
Our method — raise the structure around a problem, treat resistance as the signal that a concept is missing, admit nothing that hasn’t survived verification — is our attempt to extend his way of working into an processor, and to measure honestly how far we get. The sea on our home page is his sea. This page is our thanks.
Further reading