[LUM#1] In search of Alexandre Grothendieck

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

Who remembers Alexandre Grothendieck? The man considered the greatest mathematician of the ^20th century recently passed away. From his journey through oblivion, this pioneer of worlds leaves an unknown land: a manuscript of his work that remains to be discovered.

He changed the landscape of mathematics. Alexandre Grothendieck passed away on November 13, 2014 at the age of 86. He had been on the bangs of the human community for a long time. A refugee in Lasserre, a small village in the Pyrenees, the enfant terrible of mathematics had led a hermit's life there since 1991. His last public act took place three years earlier, when he refused the Crafoord Prize that was supposed to crown his career and the $270,000 that accompanied it. " Fecundity is recognized by offspring, not honors ", explained the man who had been showered with them, including the prestigious Fields Medal.

Outstanding genius

Jean Malgoire was his pupil. Now a lecturer at Montpellier University, he remembers the " absolute intransigence " that characterized both the man and the researcher. " He had total faith in his ability to analyze things for himself, without bothering about other points of view. A self-confidence he applied to all fields...".

From an early age, Grothendieck was a solitary explorer of that magic where the secret harmony of the world resides, and which we call mathematics. At the University of Montpellier, it wasn't in the classroom that he shone, but in the shadows: at the age of 18, he unwittingly reconstructed Lebesgue's respectable theory of integration. Jean Dieudonné choked up when he met this extraordinary genius in 1949: that's not the way to work!

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

From a time of miracles to a time of protest

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

" When was he thinking? We didn't know. He seemed to know everything about a new subject," says mathematician Michel Demazure, his first doctoral student, half a century after the meeting. In this strange being, who seemed to be of a fundamentally different nature, everything seemed to be already there...".

But the 20 years of grace came to an abrupt end. For Grothendieck, in the aftermath of May '68, when the Vietnam War was raging, mathematics mattered less and less. Should he continue his research? His answer was found. In 1970, having learned that the IHES was receiving subsidies from the Ministry of Defense, he resigned. The master we had been following on new paths cut the bridges.

Carnets de l'exil

With the usual strength of his certainties, his vision is that the world is on the brink of collapse. The threats are named: " the ecological imbalance created by contemporary industrial society (...), military conflicts ". He takes " the first step on a new journey ". A journey that would lead him into exile in 1991. In the meantime, together with a group of scientists, he founded one of the very first radical ecology movements: "Survivre et vivre".

Once again, he pursued his intellectual endeavours in the shadows. At the University of Montpellier, a new refuge for a scientific star who was becoming increasingly isolated, and even in his Pyrenean exile, he blackened sheets of paper. The master's thoughts ran unhindered. " He never stopped doing maths," asserts Jean Malgoire, to whom Grothendieck entrusted voluminous boxes in 1991, still largely untapped (see inset).

Grothendieck had forbidden any further publication during his lifetime. His notebooks from exile, so long awaited by the scientific community, could now be published. What will we discover? Seeds, no doubt, that it will be up to us to germinate," suggests Jean Malgoire. In the land of mathematics, Alexandre Grothendieck may not have finished illuminating unknown lands.

Key words : LUM#1, LUM Magazine, Mathematics, Research, Science