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Bourbaki = Bishops or Banditos?

Published July 5, 2023 by lievenlb

In this series I’m trying to make sense of the inclusion of Nicolas Bourbaki in the storyline of Trench, the fifth studio album by American musical duo Twenty One Pilots (or TØP).

That story is about the walled city of Dema, ruled by nine bishops dressed in red cloaks. They enforce their religion, called Vialism, on the inhabitants of Dema. The end-goal in Vialism is that you take your own life, having maximal impact (think: suicide bombers).



Outside the walls of Dema is the land of Trench, where a group of fighters (the Banditos) set up camp. They are dressed in grey trenchcoats adorned with yellow ribbons, and their goal is to help people escape from Dema, via its east side.

What on earth has the Bourbaki group to do with any of this?

We know from a tweet by Tyler Joseph that one Bourbaki-photograph (or at least a PhotoShopped version of it) played an important role in the creative process, as he used it as the background image on his Mac while producing the album.

It can also be seen, blurred in the background, in the opening seconds of his interview with Zane Lowe on Apple Music:

Here are the three versions: the original photo, overlayed with the tweet-image, and a screenshot from the interview:




In the original photo, taken at the 1938 Dieulefit Bourbaki congress, we see seven people, from left to right

In the overlayed image an additional eight person, a bearded man, is PhotoShopped in the doorway, and in the screenshot we see that apart from this mystery man the empty chair in the lower left corner is replaced by a ninth person.

Common belief among the ‘clique’ (TØP’s fanbase name) is that the nine people in the desktop image are the nine bishops of Dema, with the bearded man being Nico (the head-bishop), Andre Weil bishop Andre, and Simone Weil bishop Sacarver (the only known female bishop).

But who are these two additional persons?

In a remarkable tour de force, Reddit user ‘banditosleepers’ was able to find the man sitting in the lower left corner (though he identified him wrongly)

I found one of the people shopped into Tyler’s desktop (2018)
by u/banditosleepers in twentyonepilots

There’s this other famous pre-WW2 photo of a Bourbaki congress, this time the 1937 congress in Chancay:

Here we see, from left to right:

That is, the ninth person, sitting in the left lower corner of the screenshot is Szolem Mandelbrojt (and not Claude Chevalley, as claimed in the Reddit-post).

There’s another photo, taken at about the same moment, showing that also Jean Dieudonne (sitting on the bank in front next to Andre Weil) and Charles Ehresmann (sitting on the bank on the right, next to Jean Delsarte and Claude Chevalley) were present.

Several people (myself included) have wasted too many hours trying to identify the bearded man in the doorway, starting from the assumption that he too might have some connection with Bourbaki (either the group or the general), without success.

There’s one problem with the ‘bearded man = Nico’ hypothesis. Nico is supposed to be the tallest of the bishops, and bearded man’s head is level with Andre Weil’s head, who stand on the first step, so bearded man must at least be 15cm smaller than Andre, who was already rather short.

Here’s a theory.

The original Dieulefit 1938 photo is the first one on the Wikipedia page for Nicolas Bourbaki, and if you click on it you get a link to one of my own blogposts Bourbaki and the miracle of silence.

In that post (from 2010) I found the exact location where that photo was taken: the Ecole de Beauvallon, founded in 1929 by Marguerite Soubeyran and Catherine Krafft, which was the first ‘modern’ boarding school in France for both boys and girls having behavioural problems. From 1936 on the school’s director was Simone Monnier.

The lower picture is taken at the Ecole de Beauvallon in 1943, the woman in the middle is Marguerite Soubeyran.

From 1936 on, about 20 refugees from the Spanish civil war found a home at the school, and in the ‘pension’, next to the school. When WW2 started, about 1500 people were hidden from the German occupation in Dieulefit (having a total population of 3500) : Jewish children, intellectuals, artists, trade union leaders, many in the Ecole and the Pension. None were betrayed to the Germans, and this is called Le miracle de silence à Dieulefit.



Given this historical context, there is only one possible way to include this Bourbaki-photo in the Trench-storyline: the Ecole de Beauvallon is the equivalent of the Bandito-camp, and the Bourbakis are Banditos (or at the very least, refugees having found a safe place in the camp).

In hindsight this was already given away by Tyler Joseph in that he gave the photo the color yellow, specifically Bandito-yellow 0xFCE300, which the bishops are unable to see (they see it as grey).

How does this help in identifying the bearded man in the doorway?

Standing in the doorway, he’s the one feeling at home there, gathering around him his guests or fellow fighters. My conjecture is that he is the leader of the bandito-camp, as seen at 2.12 in the movieclip of Levitate.

Granted, it is not a perfect match. I think ‘bearded man’ is how Tyler Joseph envisioned the camp-leader, and included his picture in the ‘Trench Bible’, the 60 page booklet given to the movie-director, who did the casting some months later.



Next time we will try to find City of Dema, or at least what it should be if you take the inclusion of Bourbaki in the Trench storyline seriously.

In this series:

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Bourbaki and TØP : East is up

Published June 22, 2023 by lievenlb

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.

In this series:

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Grothendieck’s gribouillis (5)

Published May 4, 2023 by lievenlb

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?

In December last year, there was the official opening of the Istituto Grothendieck in the little town of Mondovi in Northern Italy.The videos of the talks given at that meeting are now online.

The Institute houses two centres, the Centre for topos theory and its applications with mission statement:

The Centre for Topoi Theory and its Applications carries out highly innovative research in the field of Grothendieck’s topos theory, oriented towards the development of the unifying role of the concept of topos across different areas of mathematics.

Particularly relevant to these aims is the theory of topos-theoretic ‘bridges’ of Olivia Caramello, coordinator of the Centre and principal investigator of the multi-year project “Topos theory and its applications”.

and the Centre for Grothendiecian studies with mission:

The Centre for Grothendiecian Studies is dedicated to honoring the memory of Alexander Grothendieck through extensive work to valorize his work and disseminate his ideas to the general public.

In particular, the Centre aims to carry out historical/philosophical and editorial work to promote the publication of the unpublished works of A. Grothendieck, as well as to promote the production of translations of already published works in various languages.

No comment on the first. You can look up the Institute’s Governance page, contemplate recent IHES-events, and conjure up your own story.

More interesting is the Centre of Grothendiec(k)ian studies. Here’s the YouTube-clip of the statement made by Johanna Grothendieck (daughter of) at the opening.

She hopes for two things: to find money and interested persons to decrypt and digitalise Grothendieck’s Lasserre gribouillis, and to initiate the re-edition of the complete mathematical works of Grothendieck.

So far, Grothendieck’s family was withholding access to the Lasserre writings. Now they seem to grant access to the Istituto Grothendieck and authorise it to digitalise the 30.000 pages.

Further good news is that a few weeks ago Mateo Carmona was appointed as coordinator of the Centre of grothendieckian studies.



You may know Mateo from his Grothendieck Github Archive. A warning note on that page states: “This site no longer updates (since Feb. 2023) and has been archived. Please visit [Instituto Grothendieck] or write to Mateo Carmona at mateo.carmona@csg.igrothendieck.org”. So probably the site will be transferred to the Istituto.

Mateo Carmona says:

As Coordinator of the CSG, I will work tirelessly to ensure that the Centre provides comprehensive resources for scholars, students, and enthusiasts interested in Grothendieck’s original works and modern scholarship. I look forward to using my expertise to coordinate and supervise the work of the international group of researchers and volunteers who will promote Grothendieck’s scientific and cultural heritage through the CSG.

It looks as if Grothendieck’s gribouillis are in good hands, at last.

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