Archive for Alexandre Grothendieck

The Guardian on [and on and on] Grothendieck

Posted in Books, Kids, Mountains, University life with tags , , , , , , , , , , , , , on September 11, 2024 by xi'an

A very looong piece in The Guardian of 31 August relates the life and achievements of Grothendieck in a highly romanticized way, hinting at hidden secrets contained in the tens of thousands of pages he wrote during his 26 years of retirement in Lasserre, Pyrénées… (Even when acknowledging that Grothendieck’s life and personality are providing enough fodder for a whole series of novels!)

“Grothendieck’s genius defied his attempts at erasing his own renown. He lurks in the background of one of Cormac McCarthy’s final novels, Stella Maris, as an éminence grise who leads on its psychically disturbed mathematician protagonist.”

With very little about maths, apart the mumbo-jumbo usually associated with non-specialists trying to convey the unique ability of a researcher with images and allegories aplenty! The only factual information is that Huawei sees worth in Grothendieck’s concept of topos (within his general theory of categories) toward future AIs and that they hired French 2002 Fields medalist Laurent Lafforgue to explore this subject (besides not mentioning Huawei creating an algebraic geometry chair at the IHÉS, the very place Grothendieck resigned from due to IHÉS receiving military funds).

“Applied to AI, toposes could allow computers to move beyond the data associated with, say, an apple; the geometric coordinates of how it appears in images, for example, or tagging metadata. Then AI could begin to identify objects more like we do – through a deeper “semantic” understanding of what an apple is. But practical application to create the next generation of “thinking” AI is, according to Lafforgue, some way off.”

The author of the Guardian piece, Phil Hoad, is also very reserved about the ultimate purpose of Huawei in funding this research (and the new Centre Lagrange in the centre of Paris), for its obscure links with the Chinese Government and the Chinese military, a concern also expressed by some French mathematicians who signed a tribune in 2021 calling for a boycott of the Centre… But leaving open the door open on whether or not the unexplored thousands of pages blackened by Grothendieck could contain mathematical gems, rather than esoteric ramblings aggravated by his complete shunning of society. Which sounds quite unlikely.

Alexandre Grothendieck’s visit to the Democratic Republic of Vietnam

Posted in Books, pictures, Travel, University life with tags , , , , , , , , on July 15, 2023 by xi'an

In connection with my incoming visit to Vietnam (Ho Chi Min City) for a PhD summer school, I was sent a report written by Alexandre Grothendieck of his 1967 visit to the Democratic Republic of Vietnam, around Hanoi, teaching to (North) Vietnamese mathematicians (homological) algebraic geometry and inspiring future generations of local mathematicians.  (Visit funded by the Cultural Relations Department of France Foreign Ministry.) This is a striking text, written in a fairly factual tone, and reporting the living conditions of students and faculty at the “evacuated University”, which was a relocation of the University of Hanoi in the countryside, following a general decentralisation of the North Vietnam economy facing massive bombings of urban centers by US forces. What is most impressive to me in this report is the ability to keep operating most aspects of a regular society under extreme duress. Which also finds itself repeated in the incredible resistance of the Ukrainian State against the Russian aggression. (Following this trip, Grothendieck gave his Field medal to the D.R.V. government.)

“Like most more or less public activities, the lectures were scheduled between about 6 and 10 a.m., because the bombing usually took place later in the day, rarely before 11 a.m.”

“Of the many impressions which I brought back from my visit to the D.R.V., perhaps the most striking is the calm confidence in the future which I noticed among everyone with whom I had occasion to speak.”

another mirror of ABC in Gre[e]noble

Posted in Statistics with tags , , , , , , , , , , on March 3, 2020 by xi'an

There will now be a second mirror workshop of ABC in Grenoble. Taking place at the Université de Montpellier, more precisely at the Alexander Grothendieck Montpellier Institute, Building 9, room 430 (4th floor), Triolet Campus. It is organised by my friend Jean-Michel Marin. Great to see a mirror at one of the major breeding places of ABC, where I personally heard of ABC for the first time and met several of the main A[B]Ctors..! The dates are 19-20 March, with talks transmitted from 9am to 5am [GMT+1]. Since the video connection can accommodate 1918 more mirrors, if anyone else is interested in organising another mirror, please contact me for technical details.

prime suspects [book review]

Posted in Books, Kids, University life with tags , , , , , , , , , , , , , , on August 6, 2019 by xi'an

I was contacted by Princeton University Press to comment on the comic book/graphic novel Prime Suspects (The Anatomy of Integers and Permutations), by Andrew Granville (mathematician) & Jennifer Granville (writer), and Robert Lewis (illustrator), and they sent me the book. I am not a big fan of graphic book entries to mathematical even less than to statistical notions (Logicomix being sort of an exception for its historical perspective and nice drawing style) and this book did nothing to change my perspective on the subject. First, the plot is mostly a pretense at introducing number theory concepts and I found it hard to follow it for more than a few pages. The [noires maths] story is that “forensic maths” detectives are looking at murders that connects prime integers and permutations… The ensuing NCIS-style investigation gives the authors the opportunity to skim through the whole cenacle of number theorists, plus a few other mathematicians, who appear as more or less central characters. Even illusory ones like Nicolas Bourbaki. And Alexander Grothendieck as a recluse and clairvoyant hermit [who in real life did not live in a Pyrénées cavern!!!]. Second, I [and nor is Andrew who was in my office when the book arrived!] am not particularly enjoying the drawings or the page composition or the colours of this graphic novel, especially because I find the characters drawn quite inconsistently from one strip to the next, to the point of being unrecognisable, and, if it matters, hardly resembling their real-world equivalent (as seen in the portrait of Persi Diaconis). To be completely honest, the drawings look both ugly and very conventional to me, in that I do not find much of a characteristic style to them. To contemplate what Jacques Tardi,  François Schuiten or José Muñoz could have achieved with the same material… (Or even Edmond Baudoin, who drew the strips for the graphic novels he coauthored with Cédric Villani.) The graphic novel (with a prime 181 pages) is postfaced with explanations about the true persons behind the characters, from Carl Friedriech Gauß to Terry Tao, and of course on the mathematical theory for the analogies between the prime and cycles frequencies behind the story. Which I find much more interesting and readable, obviously. (With a surprise appearance of Kingman’s coalescent!) But also somewhat self-defeating in that so much has to be explained on the side for the links between the story, the characters and the background heavily loaded with “obscure references” to make sense to more than a few mathematician readers. Who may prove to be the core readership of this book.

There is also a bit of a Gödel-Escher-and-Bach flavour in that a piece by Robert Schneider called Réverie in Prime Time Signature is included, while an Escher’s infinite stairway appears in one page, not far from what looks like Milano Vittorio Emmanuelle gallery (On the side, I am puzzled by the footnote on p.208 that “I should clarify that selecting a random permutation and a random prime, as described, can be done easily, quickly, and correctly”. This may be connected to the fact that the description of Bach’s algorithm provided therein is incomplete.)

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE. As appropriate for a book about Chance!]

Garrigue administrative

Posted in Books, pictures, University life with tags , , , , on May 20, 2019 by xi'an

A central page in Le Monde of this week (May 08), about the conundrum of dealing with the dozens of thousands of handwritten pages left by Alexandre Grothendiek, from trying to make sense of the contents to assessing the monetary value (!) of such documents. Mentioning that the most reasonable solution would be to extend the numerisation of earlier documents supervised by Jean-Michel Marin. Given the difficulty in reading these pages, as suggested by Le Monde, training an AI to translate them into regular text would make sense, if not helping with evaluating their importance…