[LUM#1] In search of Alexandre Grothendieck

[LUM Magazine] - Published on January 19, 2016 in Science-Society

Who remembers Alexandre Grothendieck? The man who was considered the greatest mathematician of the^20th century recently passed away. Emerging from obscurity, this pioneer leaves behind uncharted territory: a collection of manuscripts yet to be discovered.

He changed the landscape of mathematics. Alexandre Grothendieck passed away on November 13, 2014, at the age of 86. He had long since withdrawn from society. Taking refuge in Lasserre, a small village in the Pyrenees, the enfant terrible of mathematics had been living there as a recluse since 1991. His last public act took place three years earlier, when he refused the Crafoord Prize, intended to crown his career, and the $270,000 that came with it. "Fruitfulness is recognized by offspring, not by honors,"explained the man who had received many, including the prestigious Fields Medal.

Extraordinary genius

Jean Malgoire was his student. Now a lecturer at the University of Montpellier, he remembers the "absolute intransigence" that characterized both the man and the researcher. "He had complete faith in his ability to analyze things for himself, without being bothered by other points of view. He applied this self-confidence to all areas of life..."

Very early on, Grothendieck explored this magic, which lies at the heart of the secret harmony of the world and is known as mathematics, on his own. At the University of Montpellier, he did not shine in class, but rather in the shadows: at the age of 18, without knowing it, he reconstructed the respectable theory of Lebesgue integration. Jean Dieudonné was stunned when he met this extraordinary genius in 1949: this is not how we work!

The man who would become his closest collaborator then entrusted him with 14 functional analysis problems that neither he nor Laurent Schwartz had been able to solve. What happened next has become legendary: in just a few months, the apprentice untangled these 14 Gordian knots, each of which could have been the subject of an honorable thesis. Grothendieck was 22 years old.

From the age of miracles to the age of protest

Before him lay two decades of uninterrupted miracles. At the Institut des Hautes Études Scientifiques, founded around him, this giant with dazzling visions devoured his work. And he placed a new constellation in the mathematical sky: modern algebraic geometry, a new conceptual framework that was universally adopted.

"When did he think? We didn't know. He seemed to know everything about a new subject," says mathematician Michel Demazure, his first doctoral student, still amazed half a century after they met. " With this strange being who seemed fundamentally different, everything seemed to already be there..."

But the 20 years of grace were about to come to an abrupt end. For Grothendieck, in the aftermath of May 1968, with the Vietnam War raging, mathematics mattered less and less. Should he continue his research? he asked himself. He found his answer. In 1970, having learned that IHES received subsidies from the Department of Defense, he resigned. The master we had been following down new paths cut all ties.

Exile Notebooks

With his usual conviction, he had a vision: the world was heading for disaster. He identified the threats: "the ecological imbalance created by contemporary industrial society (...), military conflicts." He took "the first step on a new journey." A journey that would lead to his exile in 1991. In the meantime, he and a group of scientists founded one of the very first radical environmental movements: "Survive and Live."

It was in the shadows, once again, that he continued his intellectual pursuits. At the University of Montpellier, his new refuge where he taught alongside a scientific star who was becoming increasingly isolated, and even in his exile in the Pyrenees, he filled page after page with his writing. The master's thoughts flowed freely. "He never stopped doing math," says Jean Malgoire, to whom Grothendieck entrusted voluminous boxes in 1991, still largely unexploited (see box).

Grothendieck had insisted that nothing be published during his lifetime. His exile notebooks, long awaited by the scientific community, could now be published. What will we discover in them? "Seeds, no doubt, which it will be up to us to germinate," suggests Jean Malgoire. In the field of mathematics, Alexandre Grothendieck may not have finished shedding light on unknown territories.

Keywords: LUM#1, LUM Magazine, Mathematics, Research, Science