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Grothendieck’s gribouillis (6)

After the death of Grothendieck in November 2014, about 30.000 pages of his writings were found in Lasserre.

Since then I’ve been trying to follow what happened to them:

So, what’s new?

Well, finally we have closure!

Last Friday, Grothendieck’s children donated the 30.000 Laserre pages to the Bibliotheque Nationale de France.

Via Des manuscrits inédits du génie des maths Grothendieck entrent à la BnF (and Google-translate):

“The singularity of these manuscripts is that they “cover many areas at the same time” to form “a whole, a + cathedral work +, with undeniable literary qualities”, analyzes Jocelyn Monchamp, curator in the manuscripts department of the BnF.

More than in “Récoltes et semailles”, very autobiographical, the author is “in a metaphysical retreat”, explains the curator, who has been going through the texts with passion for a month. A long-term task as the writing, in fountain pen, is dense and difficult to decipher. “I got used to it… And the advantage for us was that the author had methodically paginated and dated the texts.” One of the parts, entitled “Structures of the psyche”, a book of enigmatic diagrams translating psychology into algebraic language. In another, “The Problem of Evil”, he unfolds over 15,000 pages metaphysical meditations and thoughts on Satan. We sense a man “caught up by the ghosts of his past”, with an adolescence marked by the Shoah, underlines Johanna Grothendieck whose grandfather, a Russian Jew who fled Germany during the war, died at Auschwitz.

The deciphering work will take a long time to understand everything this genius wanted to say.

On Friday, the collection joined the manuscripts department of the Richelieu site, the historic cradle of the BnF, alongside the writings of Pierre and Marie Curie and Louis Pasteur. It will only be viewable by researchers.“This is a unique testimony in the history of science in the 20th century, of major importance for research,” believes Jocelyn Monchamp.

During the ceremony, one of the volumes was placed in a glass case next to a manuscript by the ancient Greek mathematician Euclid.”

Probably, the recent publication of Récoltes et Semailles clinched the deal.

Also, it is unclear at this moment whether the Istituto Grothendieck, which harbours The centre for Grothendieck studies coordinated by Mateo Carmona (see this post) played a role in the decision making, nor what role the Centre will play in the further studies of Grothendieck’s gribouillis.

For other coverage on this, see Hermit ‘scribblings’ of eccentric French math genius unveiled.

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Weil photos used in Dema-lore

On April 20th of 2018, twenty one pilots updated their store page to include a video with a hidden message at the end of it.

and with a bit of sleuthing it led to a page on the site containing:

This was immediately identified as part of the photo on the right, which is on the French Wikipedia page for Andre Weil.

The photo is clipped in such a way one cannot be certain whether the child is a boy or girl, so a logical explanation is that this is supposed to be the nine year old Clancy, shielding his eyes from the violence (vialism) he just discovered in Dema.

The full picture suggests that Clancy’s struggles might mirror some in Andre Weil’s life.

Andre Weil was born May 6th, 1906, so ‘in his ninth year’ World War 1 breaks out in 1914.

Last time we’ve seen that Bourbaki’s Dema = Ecole Normal Superieure in Paris during WW1, Vialism = militant patriotism sending ENS-graduates as trained reserve second lieutenants in the infantry to the trenches, and there getting killed ‘pour la patrie’ and the glory of the ENS and its director Ernest Lavisse, “L’instituteur national”.

Here’s a G-translation of his letter to the young French, published September 23rd 1914:

Dear children of France, You will be old one day, and, like the old, you will like to remember times past. There will come evenings when your little children, seeing you dreaming, will say to you: Tell us, grandfather. And you will tell. It will be a few episodes of the war, a long march, an alert, a bayonet assault, a cavalry charge, the feat of a battery of 75, the strewn enemy dead on the plain, or else, in the streets of a city, the serried ranks of corpses left standing for lack of room to fall; and then the death of comrades, the terrible losses of your company and your regiment, your wounds received in Belgium, in Champagne, on the banks of the Rhine, beyond the Rhine; but the joy of victories, the poles knocked down on too narrow frontiers, triumphal entries.

On those evenings, after the amazed children have gone to sleep, you will open a drawer where you will have collected precious objects, a bullet extracted from a wound, a piece of shell, a cloth where your blood will have turned pale, a cross of honour, I hope, or a military medal, at the very least a medal from the 1914 war, on the ribbon of which the silver clasps will bear the names of immortal battles. And whatever your life, happy or unhappy, you will be able to say: I lived great days such as the history of men had not yet seen. And you will be right to be proud of your youth, because you are sublime young people!

I have read your letters; I have spoken with the wounded. Through you, I know what heroism is. I had heard a lot about it, being a historian by profession, but now I see it, I touch it, and how beautiful your heroism is, embellished with grace and smiling in the French way! Young soldiers if you were given one chevron per battle, your march would not be enough to accommodate them, because at the end of the war you would count more chevrons than years;

Young soldiers you are glorious old warriors.

Oh! Thanks thanks! Thank you for the beautiful end of life that you give to the elderly who, for forty-four years have suffered so much from the abasement of the fatherland.

The 44 years refers to the Franco-Prussian war of 1870 in which Bourbaki (the general) played a dramatic role.

The next cycle of militant patriotism occurred in the years leading up to the second world war. Here, Andre Weil’s experiences mirror those of Clancy. He tried several times to escape, first from military action (although he too was a reserve officer in the French army), then from France itself. He was captured in Finland, brought back to France to face trial and imprisonment, was released on the condition that he did active military duty, escaped with the French army to England, there demobilised he refused to join de Gaulle’s troops, left England on a boat to Marseille, from where he escaped to the US.

All this, and much more, you can read in his autobiography The Apprenticeship of a Mathematician, especially Chapter VI, The War and I: A Comic Opera in Six Acts.

(for TØP-ers, note the Bishop-red cover…)

Comic or not, the book tries to ‘explain’ his actions in those years, but failed to convince the French from offering him a professorship at a French university after the war.

Perhaps it may be worth looking into a comparison between Weil’s autobiography and the collected Clancy letters.

I guess that’s the best I can do to explain the use of that Weil photo by TØP. Surely they didn’t search any deeper as to where and when this picture was taken, or who the girl was next to Weil.

In case anyone might be interested, I’ll be happy to explain my own theory about this in another post.

I’m sure the full photograph ended up in the ‘Trench-bible’, given to the director of their clip-movies. The scenery is used at the end of the Jumpsuit video when ‘Clancy’ takes out a jumpsuit from the burning car and walks away along a road very similar to that in the photo.

The boy/girl shielding his/her eyes for the violence, should have been used at about minute one into the Outside video

Now, there’s another Weil (or rather Bourbaki) photograph we know did inspire Twenty One Pilots, the classic picture at the Dieulefit/Beauvallon 1938 Bourbaki-congress

which was photoshopped in order to get Szolem Mandelbrojt in from the Chancay (quite similar to Clancy now that i type this) 1937 Bourbaki congress

Now, these were the only two Bourbaki-meetings Simone Weil (Andre’s sister) attended, and she features prominently in both pictures.

Probably this brother/sister thing struct a chord with Twenty One Pilots. But then, you quickly end up with this iconic picture of both of them, taken in the summer of 1922, just before Andre entered the Ecole Normale (he entered the ENS at age 16…)

I’d love to be send a copy of the ‘Trench bible’ because I’m fairly certain also this photograph is in it. At the end of the Nico and the niners-video you see this boy and girl (who may be around age 9 and discover the truth about Dema) finding a jumpsuit with the Bishops approaching

and they reappear a bit older at the end of the Outside-video, with a burning Dema in the background.

Previous in the Bourbaki&TØP series:

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Bourbaki and TØP : East is up

Somehow I missed all the excitement, five years ago. From Bourbaki’s Wikipedia page.

In 2018, the American musical duo Twenty One Pilots released a concept album named Trench. The album’s conceptual framework was the mythical city of “Dema” ruled by nine “bishops”; one of the bishops was named “Nico”, short for Nicolas Bourbaki. Another of the bishops was named Andre, which may refer to André Weil. Following the album’s release, there was a spike in internet searches for “Nicolas Bourbaki”.

Google Trends for Nicolas Bourbaki
by u/HiLlBiLlYjOeL_ in twentyonepilots

With summer and retirement coming up, I’m all in for another Bourbaki riddle.

So, what’s going on?

Tyler Joseph and Josh Dun have weaved complicated storylines around the different albums of their band Twenty One Pilots (or TØP for short), each referring to a distinct era (the Blurryface-era, the Trench-era, the Scaled and Icy-ra, etc.), each having a different color scheme, characters and so on.

You can easily get lost forever in their sub-Reddit, or the numerous YouTube-clips and blogposts made by the ‘clique’ (as their fanbase calls itself). Perhaps the quickest intro in the TØP-world is this site.

The Bourbaki-group is important to the Trench-era, yet there are very few direct references in the songs. There’s the song “Morph” (lol!) containing:

He’ll always try to stop me, that Nicolas Bourbaki
He’s got no friends close, but those who know him most know
He goes by Nico
He told me I’m a copy
When I’d hear him mock me, that’s almost stopped me

So Nico=Nicolas Bourbaki, and there’s the song “Nico and the niners”

starting off with:

East is up
I’m fearless when I hear this on the low
East is up
I’m careless when I wear my rebel clothes
East is up
When Bishops come together they will know that
Dema don’t control us, Dema don’t control
East is up

and that’s about it.

We’ll cover Dema and the Bishops in later posts, but for now remember the mantra “East is up”, which supposedly indicates the direction of escape from the Bishops and the city of Dema.

A few months before the release of Trench, a mysterious website appeared, containing letters from someone called ‘Clancy’ and some pictures and gifs. One of these pictures was soon found out to be part of an iconic photo of Andre Weil.

This caught the attention of the ‘clique’ because another picture indicated that the name of one of the Bishops was Andre.

Poor Andre was credited for just two things he managed to do : he founded a secret group of mathematicians, called Nicolas Bourbaki (important because another Bishop’s name was ‘Nico’) and he invented the symbol $\emptyset$ for the empty set (important because TØP used it since the Blurryface-era). I guess most mathematicians will remember Andre Weil for other things.

The clique-consensus seems to be that the girl next to Andre (some even thought it was a boy) is his daughter Sylvie Weil.

If you ever read her novel Chez les Weil you’ll remember that Sylvie did have from a very young age the same exuberant hairstyle as her aunt Simone Weil. So no, she’s definitely not Sylvie.

I’ll save my theory as to where and when this photo was taken, who the girl next to Andre is, and how this picture was used later on in TØP-iconography, for another post.

For now, I just want to point out one tiny detail: the girl is shielding her eyes from the blistering summer-sun, and shadows are falling from right to left.

Got it? Yes: East is up!

The Bourbaki-hype intensified when Tyler Joseph tweeded on August 19th, indicating that a new Album called ‘Trench’ was coming up:

Again, there’s a lot more to say about this tweet, but for now look at the desktop-image. It’s part of one of the most known Bourbaki images of all time (also featuring on their Wikipedia page): the Dieulefit 1938-congress (which we discovered to be taken at Beauvallon).

(Left to right: Simone Weil, C. Pisot, Andre Weil, Jean Dieudonne (seated), Claude Chabauty, Charles Ehresmann and Jean Delsarte)

Ah, you spotted it too? We’ll come back to this, and the clique made even more surprising discoveries wrt this picture.

You see, we’ll have a lot of ground to cover, so let’s stick to the “East is up” motto,for now.

Via Google maps you can check that the exit-door in the picture is located to the East side of the main building of the Ecole de Beauvallon.

All Bourbakie-congress followers are outside, so does this mean they’ve escaped Dema? Are they now Banditos (whence the Yellow-background-color)?

If you’ve never heard about Banditos or te relevance of the color Yellow, we’ll cover that too.

There’s another ‘East is up’-side to the Beauvallon-story. For this we have to recall some of the history of the spiritual father of the B-gang, General Charles-Denis Bourbaki.

In the Franco-Prussian war of 1870-71, he was given the command of ‘armee de l’Est (yes, the ‘East’-army!), a ramshackle of ill-trained men.

After some initial successes they suffered defeat in the battle of Lizaine and were forced to escape to Switzerland (Yes: East!) where they were disarmed, and treated for their injuries (this was one of the first cases of the International Red Cross, and is remembered in the Bourbaki Panorama in Luzern).

For clique-people: Red cross & Red architecture of the Boubaki-panorama = color of the Bishops.

Anyway, the important fact is that General Bourbaki had to escape to the East.

During the Bourbaki-congress in Beauvallon in 1938 a similar situation occurred. From Andre Weil’s The Apprenticeship of a Mathematician (page 123-124):

In 1938, Bourbaki held a congress in Dieulefit, where Chabauty, who had joined the ranks of the Master’s collaborators, had familie ties. Elie Cartan graciously joined us and took part in some of our discussions.

This was precisely the time of the Munich conference. There were sinister forebodings in the air. We devoured the newspapers and huddled over the radio: this was one Bourbaki congress where hardly any real work was accomplished.

By the time I had resolved that, if war broke out, I would refuse to serve. In the middle of the congress, after confiding in Delsarte, I thought up some pretext or other and left for Switzerland.

But the immediate threat of war soon seemed to have dissipated, so I returned after two days.

So, there’s a remarkable analogy between General Bourbaki’s escape to the East in 1871, and Andre and Simone Weil’s flight to the East at the time of the Munich agreement.

Clearly, the ‘East is up’ mantra is not the only reason why Tyler Joseph used these two Bourbaki-related photos in his narrative, but it illustrates that none of these choices is arbitrary.

I think Tyler knows a lot about Bourbaki. His knowledge about them goes certainly deeper than that of the average clique-member (who state that Bourbaki was a group of mathematicians trying to prove God’s existence, or that there where exactly nine Bourbaki founders, corresponding to the nine Bishops of Dema).

But then, TØP never corrects erroneous clique-statements, every fan-theory is correct to them. In fact, they see the interactions with their fanbase as a collective work in storytelling: they pose a riddle, the clique proposes various possible solutions, and afterwards they may use one of these proposals in their further work.

Here’s an interview making clear that Tyler knows a lot more about Bourbaki than most people (1.50 till 4.40)

Interviewer: “How far are you into a Wikipedia wormhole when you come across this? (the Bourbaki group)”
Tyler: “No, no THEY named their group after Nicolas Bourbaki”
Interviewer: “but there is no Nicolas Bourbaki, right?”
Tyler: They named their group after Blurryface.”
Interviewer: “Even though it was the 1930″s?”
Tyler: “Yeah.”
Interviewer: “So how does it relate?”
Tyler: “its EVERYTHING and at the same time, has nothing to do with it”
Interviewer: “See I’m no good at math, this is difficult for me.”
Tyler: “Math?! *laughs* Math has nothing to do with it… and yet it has everything to do with it.”

Okay, in the next couple of posts I’ll use the little I know about the Bourbaki group trying to make sense of the Trench-era narrative.


A newish toy in town

In a recent post I recalled Claude Levy-Strauss’ observation “In Paris, intellectuals need a new toy every 15 years”, and gave a couple of links showing that the most recent IHES-toy has been spreading to other Parisian intellectual circles in recent years.

At the time (late sixties), Levy-Strauss was criticising the ongoing Foucault-hype. It appears that, since then, the frequency of a hype cycle is getting substantially shorter.

Ten days ago, the IHES announced that Dustin Clausen (of condensed math fame) is now joining the IHES as a permanent professor.

To me, this seems like a sensible decision, moving away from (too?) general topos theory towards explicit examples having potential applications to arithmetic geometry.

On the relation between condensed sets and toposes, here’s Dustin Clausen talking about “Toposes generated by compact projectives, and the example of condensed sets”, at the “Toposes online” conference, organised by Alain Connes, Olivia Caramello and Laurent Lafforgue in 2021.

Two days ago, Clausen gave another interesting (inaugural?) talk at the IHES on “A Conjectural Reciprocity Law for Realizations of Motives”.

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Against toposes

The French anthropologist and ethnologist Claude Levi-Strauss once observed

“In Paris, intellectuals need a new toy every 15 years.”

Some pointers to applications of their toy of choice for the past ten years:

How do Parisian mathematicians with a lifelong interest in topos theory react to this hype?

With humour!

Here’s an ‘exposé parodique’ (parodical lecture) by Stéphane Dugowson on “Contre les topos” (against toposes).

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