The elusive archives of Alexander Grothendieck

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Some 70,000 pages of a giant of mathematics who died in 2014 are sleeping in a cellar in Paris. These manuscripts, written while living as a hermit in Ariège, remain to be deciphered. No institution has yet taken over this complicated inheritance.

By Philippe Douroux Posted today at 18h01

Time to Reading 14 min.

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The mathematician Alexander Grothendieck, during a conference at the Institute of Higher Scientific Studies of Bures-sur-Yvette (Essonne), in January 1960.
The mathematician Alexander Grothendieck, during a conference at the Institute of Higher Scientific Studies of Bures-sur-Yvette (Essonne), in January 1960. IHES / AFP

Is it a scientific treasure or old papers not even good for recycling, as they are loaded with blue ink? How many hours did it take to cover 70,000 pages between 19 August 1992 and 24 August 2014, today deposited in a cellar in Paris? The author of these lines drawn in a very fine, very flat, sometimes readable, often difficult to decrypt, the mathematician Alexandre Grothendieck (1928-2014) has taken extreme care to order what looks like an indecipherable message, numbering each page, dating each bundle and sometimes raising its working hours. It is to write that he had retired from the world in August 1991, in Lasserre, an isolated village of Ariège, limiting to the minimum the contact with the men and women he had loved so much.

Tireless worker

He whose mathematics allow the exchange of phenomenal amounts of encrypted data via tiny devices, he whose tools forged in the 1950s and 1960s helped to prove the existence of the Higgs boson, which explains why such particle has a mass , whose mathematical work contributed to the demonstration of Fermat's theorem by Andrew Wiles wanted to disappear, reducing its presence to thousands of pages.

Article reserved for our subscribers Read also Archives of Alexander Grothendieck: what price, between epsilon and infinity?

A tireless worker, mainly at night between 10 pm and 6 am, he had already left 28 000 pages in Montpellier, the university where he had obtained a bachelor's degree in mathematics in 1948, and where he had returned to teach after turning his back on the scientific community, by posing at the beginning of the 1970s the question of the legitimacy and the finality of science. His peers had removed him from the College de France, when the largest American universities agreed to ask this question. He feared that technology would eventually destroy the planet, inaugurating a radical ecology when the word did not exist yet. How could he be wrong today, even if he assured his students that the end of the world was to come in 1982?

It was his method, starting from scratch to get to the heart of things without bothering with examples, exercises or pedagogy

In the Parisian cellar, Georges Maltsiniotis, mathematician by vocation, grothendieckien by character – he refuses to speak to journalists – could serve us as a guide. Before the 15,000 pages written during the first two years that the mathematician dedicated to a solitary reflection were transferred there, he spent two days in Lasserre, in February 2015, to examine them "Very summarily". The first 4,800 pages represent mathematics "In good and due form", he notes in his account. Then comes physics, a strange escapade for the one who practiced the purest mathematics. After, he would have tried to resume the reconstruction of the Universe from scratch. It was his method, starting from scratch to get to the heart of things without bothering with examples, exercises or pedagogy.

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