Considered as the greatest mathematician of the 20th century, Alexander Grothendieck died, Thursday November 13, at Saint-Girons hospital, not far from Lasserre, the village where he secretly retired in the early 90s, cutting off all contact with the world. He was 86 years old. Stateless, naturalized French in 1971, known for the radicality of his pacifist and environmental activities, this singular and mythical mathematician leaves a considerable scientific legacy.
He was born on March 28, 1928, in Berlin, in an atypical family. Sascha Schapiro, his father, is a Jewish Russian, photographer and anarchist activist. Also very engaged, Hanka Grothendieck, his mother, is a journalist. In 1933, Sascha leaves Berlin for Paris, where he is soon joined by Hanka. Between 1934 and 1939, the couple leaves for Spain where it joins the Popular Front, while little Alexander is left in Germany to a family friend.
HIS FATHER DIES IN AUSCHWITZ
At the end of the Spanish Civil War, in the spring of 1939, Alexander meets his parents again in southern France. In October 1940, his father is taken prisoner in Vernet camp, which he leaves in 1942, for Auschwitz, where he will be assassinated. Alexander and his mother are taken elsewhere. “During my first year of high school, in 1940, I was imprisoned with my mother in Rieucros concentration camp, near Mende”, he says in Recoltes et Semailles, a monumental autobiographical text that was never published, but can be found on the Internet.
“It was war, and we were strangers – ‘undesirables’ as they said. But the camp administration closed one eye for boys, as undesirable as they were. We entered and left as we wanted. I was the eldest, and the only one to attend high school, four or five kilometers from there, regardless of whether there was snow or wind, with cheap shoes that were always soaked.
THE MYTH OF SCHWARTZ’S AND DIEUDONNÉ’S 14 PROBLEMS
In 1944, with his high school diploma, Alexander Grothendieck had not yet been identified as the genius he was. He enrolled in math at Montpellier University, and was recommended to Laurent Schwartz and Jean Dieudonné for his thesis.
History forged his myth: the two great mathematicians gave the young student a list of fourteen problems that they viewed as a wide work program for the coming years, and asked him to pick one. A few months later, Alexander Grothendieck came back to see his supervisors: he solved them all.
In this first period of mathematical production, Grothendieck worked on functional analysis, a field of analysis that studies function spaces. His work revolutionized the field, but remains less known than the one he will conduct in the second part of his career.
AN INSTITUTE FUNDED FOR HIM
In 1953, the young mathematician was quickly pressed to seek a job in academia. Stateless, he could not work in the public sector and, unwilling to serve in the military, he doesn’t want to seek french naturalization. He goes to teach in Sao Paulo (Brazil), in Lawrence (Kansas), and Chicago (U.S.)
Two years later, when he returned to France, a wealthy industrialist interested by mathematics, Léon Motchane, fascinated by the intuition and work power of the young man – Grothendieck was only 27 – decides to fund an exceptional research institute, based on the Princeton Institute for Advanced Study: l’Institut des Hautes études Scientifiques (IHES; Institue of high scientific studies), at Bures-sur-Yvette. The place was imagined as a home for the mathematician, who will begin a second career there.
A NEW GEOMETRY
Until 1970, surrounded by a multitude of international talent, he will lead his seminar on algebraic geometry, which will be published in the form of tens of thousands of pages. His new vision of geometry, inspired by his obsession of rethinking the notion of space, has shaken the very way to do mathematics. “The ideas of Alexander Grothendieck have, so to say, penetrated the subconscious of mathematicians”, says Pierre Deligne (Princeton Institute of Advanced Study), his most brilliant student, laureate of the Fields Medal in 1978 and the Abel Prize in 2013.
The notions he has introduced or developed remain today at the heart of geometrical algebra and are heavily studied. “He was unique in his way of thinking, says Mr. Deligne, very moved by the death of his ancient mentor. He had to understand things from the most general possible point of view, and once things were understood like this, the landscape became so clear proofs looked almost trivial.”
HE LEAVES THE SCIENTIFIC COMMUNITY
In 1966, he receives the Fields medal, but refuses it for political reasons before going to Moscow to receive it. The radicality with which he will defend his convictions will never cease. He began drifting away from the scientific community at the end of the 1960s. In 1970, with two other mathematicians – Claude Chevalley and Pierre Samuel – he founded a group called Survive and Live, pacifist, ecologist, and very touched by the hippie movement. At the same time, he discovers that IHES is partially – albeit very marginally – funded by the Ministry of Defense. He leaves the institute.
The Collège de France offers him a temporary job, which he largely uses as a political platform. He leaves the Collège soon enough. In 1973, he becomes a professor at the University of Montpellier before going to the CNRS in 1984 until his retirement in 1988. The same year, he’s awarded the Crafoord prize, which comes with a big monetary award. He refuses the distinction. In 1990, he leaves his home for a secretive lair. Bitter, not on good terms with his friends, his family, the scientific community and science, he settles in a small Pyreneean village whose name he keeps secret. He will remain there, cut off from the world, until his death.