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Leila Schneps on Grothendieck

If you have neither the time nor energy to watch more than one interview or talk about Grothendieck’s life and mathematics, may I suggest to spare that privilege for Leila Schneps’ talk on ‘Le génie de Grothendieck’ in the ‘Thé & Sciences’ series at the Salon Nun in Paris.

I was going to add some ‘relevant’ time slots after the embedded YouTube-clip below, but I really think it is better to watch Leila’s interview in its entirety. Enjoy!

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Grothendieck stuff

January 13th, Gallimard published Grothendieck’s text Recoltes et Semailles in a fancy box containing two books.

Here’s a G-translation of Gallimard’s blurb:

“Considered the mathematical genius of the second half of the 20th century, Alexandre Grothendieck is the author of Récoltes et semailles, a kind of “monster” of more than a thousand pages, according to his own words. The mythical typescript, which opens with a sharp criticism of the ethics of mathematicians, will take the reader into the intimate territories of a spiritual experience after having initiated him into radical ecology.

In this literary braid, several stories intertwine, “a journey to discover a past; a meditation on existence; a picture of the mores of a milieu and an era (or the picture of the insidious and implacable shift from one era to another…); an investigation (almost police at times, and at others bordering on the swashbuckling novel in the depths of the mathematical megapolis…); a vast mathematical digression (which will sow more than one…); […] a diary ; a psychology of discovery and creation; an indictment (ruthless, as it should be…), even a settling of accounts in “the beautiful mathematical world” (and without giving gifts…)”.”

All literary events, great or small, are cause for the French to fill a radio show.

January 21st, ‘Le grand entretien’ on France Inter invited Cedric Villani and Jean-Pierre Bourguignon to talk about Grothendieck’s influence on mathematics (h/t Isar Stubbe).

The embedded YouTube above starts at 12:06, when Bourguignon describes Grothendieck’s main achievements.

Clearly, he starts off with the notion of schemes which, he says, proved to be decisive in the further development of algebraic geometry. Five years ago, I guess he would have continued mentioning FLT and other striking results, impossible to prove without scheme theory.

Now, he goes on saying that Grothendieck laid the basis of topos theory (“to define it, I would need not one minute and a half but a year and a half”), which is only now showing its first applications.

Grothendieck, Bourguignon goes on, was the first to envision the true potential of this theory, which we should take very seriously according to people like Lafforgue and Connes, and which will have applications in fields far from algebraic geometry.

Topos20 is spreading rapidly among French mathematicians. We’ll have to await further results before Topos20 will become a pandemic.

Another interesting fragment starts at 16:19 and concerns Grothendieck’s gribouillis, the 50.000 pages of scribblings found in Lasserre after his death.

Bourguignon had the opportunity to see them some time ago, and when asked to describe them he tells they are in ‘caisses’ stacked in a ‘libraire’.

Here’s a picture of these crates taken by Leila Schneps in Lasserre around the time of Grothendieck’s funeral.

If you want to know what’s in these notes, and how they ended up at that place in Paris, you might want to read this and that post.

If Bourguignon had to consult these notes at the Librairie Alain Brieux, it seems that there is no progress in the negotiations with Grothendieck’s children to make them public, or at least accessible.

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G-spots : Saint-Girons

Roy Lisker (remember him from the Mormoiron post?) has written up his Grothendieck-quest(s), available for just 23$, and with this strange blurb-text:

“The author organized a committee to search for him that led to his discovery, in good health and busily at work, in September, 1996. This committee has since become the Grothendieck Biography Project. All of this is recorded in a 300 page account in 3 parts.”

Probably he refers to the trip made by Leila Schneps and Pierre Lochak, nicely described in Sam Leith’s The Einstein of maths:

“One of the last members of the mathematical establishment to come into contact with him was Leila Schneps. Through a series of coincidences, she and her future husband, Pierre Lochak, learned from a market trader in the town he left in 1991 that ‘the crazy mathematician’ had turned up in another town in the Pyrenees. Schneps and Lochak in due course staked out the marketplace of the town, carrying an out-of-date photograph of Grothendieck, and waited for the greatest mathematician of the 20th century to show up in search of beansprouts.

‘We spent all morning there in the market. And then there he was.’ Were they not worried he’d run away? ‘We were scared. We didn’t know what would happen. But he was really, really nice. He said he didn’t want to be found, but he was friendly. We told him that one of his conjectures had been proved. He had no idea. He’d stopped being interested in maths at that stage. He thought his unpublished work would all have been long forgotten.’”

To city-cats this may seem an improbable coincidence, but if you live in the French mountains for some time, you learn to group your shoppings, and do them on market-days. The nearest market-town, where you can find a decent ‘boulangerie’ or supermarket, may be just 20 kms down the road, but it’ll take you close to an hour to get there.

If you sit near the town-fountain on market-days, for some weeks, you will have seen most of the people living in the vast neighborhood.

So, we’d better try to find Leila’s market-town.

One of the nicer talks on the life of Grothendieck was given by Winfried Scharlau (who also has two books on offer on Grothendieck’s life, seems to become an emerging bisiness …) at the IHES Grothendieck colloque.

Colloque Grothendieck Winfried Scharlau par Ihes_science

This video is stuffed with unknown (at least to me) pictures of Grothendieck, his places at Mormoiron and Villecun and of his four children still living in France. Highly recommended!

But, the lecture has a very, very strange ending.

At 1hr 06.51 into the video he shows the slide reproduced on the left below and says: “Okay and here’s a picture on which I will not further comment. That’s the last thing I want to show you. I thank you very much for your patience.”

Leila Schneps has a page with pictures on her website, including 3 pictures of her house, and then the one on the right above, merely described as ‘Another house’.

And then there’s this paragraph from Roy Lisker’s (him again) Travelogue-France (March 8-April 5, 2005) part 2

“I left the IHP around 11 to return to the CNRS research center at 175 rue du Chevaleret. Pierre Lochak and I discussed the possibility of my going to the town of St. Giron outside of Toulouse to make another impromptu visit to La Maison d’Alexandre Grothendieck.”

So, here we have three founding members of the Grothendieck circle linking publicly to the same picture of that one place they want to keep secret at all cost?

Dream on!

If you followed this series at all and have looked at the pictures of Grothendieck’s houses in Mormoiron or Villecun it is hard to imagine him living in a bourgeois-house, dating from the end of the 19th century, in a medium-sized market-town.

Still, it is quite likely that the picture is indeed taken in Saint-Girons, on some saturday in 1996 when Leila and Pierre bumped into Grothendieck on the market in Saint-Girons.

After all, Saint-Girons is the market-town closest to the final Grothendieck-spot…

Added after Grothendieck’s death on november 13th 2014: Here I got things wrong. For example, from the article La vie secrète d’un génie des maths à Lasserre it is clear that ‘another house’ is indeed Grothendieck’s last house, and it is not situated in Saint-Girons, but in the nearby village Lasserre.

Previous in this series:
un petit village de l’Ariège

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In Belgium the hashtag-craze of the moment is #cestjoelle. Joelle Milquet is perceived to be the dark force behind everything, from the crisis in Greece, over DSK, to your mother-in-law coming over this weekend? #cestjoelle.

Sam Leith used the same meme in his book the coincidence engine.

A hurricane assembling a passenger jet out of old bean-cans? #cestGrothendieck

All shops in Alabama out of Chicken & Broccoli Rica-A-Roni? #cestGrothendieck

Frogs raining down on Atlanta? #cestGrothendieck

As this is a work of fiction, Alexandre Grothendieck‘s name is only mentioned in the ‘author’s note’:

“It is customary to announce on this page that all resemblances to characters living or dead are entirely coincidental. It seems only courteous to acknowledge, though, that in preparing the character of Nicolas Banacharski I was inspired by the true-life story of the eminent mathematician Alexandre Grothendieck.”

The name ‘Nicolas Banacharski’ is, of course, chosen on purpose (the old Bourbaki NB-joke even makes an appearance). The character ‘Isla Holderness’ is, of course, Leila Schneps, the ‘Banacharski ring’ is, of course, the Grothendieck circle. But, I’d love to know the name of the IRL-‘Fred Nieman’, who’s described as ‘an operative for the military’.

Sam Leith surely knows all the Grothendieck-trivia which shouldn’t come as a surprise because he wrote in 2004 a piece for the Spectator on the ‘what is a metre?’ incident (see also this n-category cafe post).

The story of ‘the coincidence engine’ is that Grothendieck did a double (or was it triple) bluff when he dropped out of academia in protest of military money accepted by the IHES. He went into hiding only to work for a weapons company and to develop a ‘coincidence bomb’. As more and more unlikely events happen during a car-ride by a young Cambridge postdoc though the US (to propose to his American girlfriend), the true Grothendieck-aficianado (and there are still plenty of them in certain circles) will no doubt begin to believe that the old genius succeeded (once again) and that Ana’s (Grothendieck’s mother) $\infty$-ring is this devilish (pun intended) device…


“There was no coincidence engine. Not in this world. It existed only in Banacharski’s imagination and in the imaginations he touched. But there was a world in which it worked, and this world was no further than a metre from our own. Its effect spilled across, like light through a lampshade.

And with that light there spilled, unappeased and peregrine, fragments of any number of versions of an old mathematician who had become his own ghost. Banacharski was neither quite alive nor quite dead, if you want the truth of it. He was a displaced person again, and nowhere was his home.”

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