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Where’s Bourbaki’s Dema?

Published July 15, 2023 by lieven

In this series I’m trying to figure out why the Bourbaki-group was an inspiration for the storyline of Trench, the fifth studio album by American musical duo Twenty One Pilots (or TØP).

Trench-lore centers around the city of Dema, ruled by nine Bishops enforcing Vialism (a fake religion asking people to take their own lives to glorify Dema).

It is an unfortunate coincidence that the city of Dema in the movie-clip of Nico and the Niners was inspired, and shot in Kyiv and Charkiv, Ukraine (the clip is from 2018).

I’ve just found out that Dema is situated in my country… (NATN was made in Kyiv and Charkiv, Ukraine)
by u/Sasha0503 in twentyonepilots

Here’s the corresponding ‘beyond the movie’-clip, from which we learn (or rather are told) that the movie’s ‘city of Dema’ was shot in ‘the former Ukranian high-school’ of Josh Dun (he even calls it his ‘Alma Mater’), all in quotes because I don’t buy any of it, but take it as a desperate hint to identify Dema.

In the Trench movie-clips, Josh Dun is always cast as a Bandito, and last time we saw that also the Bourbaki-gang is likely to be close to the Banditos. Dema is supposed to be the Alma Mater of (at least some of) the Banditos. Hold that thought.

As for the connection between the City of Dema and the Bourbaki-group, we only have one piece of solid information:

That the Bourbaki-group named themselves after Nico=Nicolas Bourbaki clearly resonates with Twenty Øne Pilots who got their name from the 1947 play ‘All My Sons’ by American playwright Arthur Miller.

But the crucial info is: “The story of Dema happened before them”, so the story of Dema with the Bishops and Vialism happened before the Bourbaki-group. An extra piece of evidence that there is no way the Bourbaki-group are the nine Bishops of Dema.

So, what happened before the Bourbaki-group?

Mathematically, their direct predecessors were David Hilbert, Emil Artin, Emmy Noether and her boys, in short German mathematicians from the 1920’s and early 1930’s.

Several of the Bourbaki founding members studied in Germany (Weil in Gottingen in 1927, Chevalley in Hamburg in 1931 and Marburg in 1932, and Ehresmann in Gottingen in 1930).

They were inspired by Hilbert’s program (We must know, we will know), and set out to introduce the German style of writing and doing mathematics in France.

So, a first candidate (also given the Bauhaus-like architecture of Dema) might be ‘German Mathematicians’, or in German, DEutscher MAthematiker = DEMA.

But one can hardly argue that there was a self-destructive attitude (like Vialism) present among that group, quite the opposite.

Still, one can ask why German mathematics was that strong in the 1920’s, compared to the French. France and Germany took different approaches with their intelligentsia during WW1: while Germany protected its young students and scientists, France instead committed them to the front, owing to the French culture of egalitarianism.

Remember that the album is called Trench, and the dirtiest trench-war in all of human history was WW1. Hold that thought.

But, how does this help us in identifying Dema.

A few months before the release of Trench, a website was launched containing letters (from a character named Clancy) and some photos (including part of a photo of Andre Weil). That website’s URL still is dmaorg.info.

On the rear of the boat in the movie-clip Saturday, we see ‘030904 DMA ORG’ (the 030904 is simplistic code for CID, believed to mean ‘Clancy Is Dead’).

Compare this to the official email address of the ‘Association des collaborateurs de Nicolas Bourbaki’ which is: bourbaki@dma.ens.fr.

Here, ‘dma’ stands for ‘Département de mathématiques et applications’, one of the fifteen departments of the ENS, the Ecole Normal Superieure in Paris, Rue d’Ulm.

Remember the inspirational, photoshopped photo of the Bourbaki 1938 congress in Dieulefit/Deauvallon:




All seven people in the original picture are ‘normaliens’, that is, their ‘Alma Mater’ is the Ecole Normale Superieure’. All but Simone Weil graduated from the DEpartement de MAthematiques=DEMA, as DMA was called then.

Whence the hypothesis: Bourbaki’s Dema = ENS before and during WW1

It is a conglomerate of buildings and its central courtyard forms a kind of secular cloister around its basin. This space is called “la Cour aux Ernests” in reference to a former director, Ernest Bersot. He had placed red (!) fish (=the Ernests in ENS-slang) in the basin, which have become one of the symbols of the school.

More important to us is that the pond of the Ernests is reached by crossing the “aquarium”, where the ENS war memorial is located, commemorating the 239 (former) ENS-students killed in WW1 on a tatal of about 1400 of them drafted…

From the Wikipedia-page on Nicolas Bourbaki:

“The deaths of ENS students resulted in a lost generation in the French mathematical community; the estimated proportion of ENS mathematics students (and French students generally) who died in the war ranges from one-quarter to one-half, depending on the intervals of time (c. 1900–1918, especially 1910–1916) and populations considered.”

A chilling, and very detailed account of the circumstances that lead to the deaths of about 50% of ENS-student from the period 1910-1913 can be found in the paper Pourquoi les normaliens sont-ils morts en masse en 1914-1918 ? Une explication structurale (Why the normaliens suffered mass-death in 1914-18, a structural explanation) by Nicolas (!) Mariot. Here’s the abstract:

“The École Normale Supérieure d’Ulm is always mentioned when historians summarize the ravages of World War I in France: the institution embodies the commitment of intellectuals at the front. The article offers an interpretation of mortality rates of the School which allows to understand why it is primarily students during schooling (Classes 1910-1913) that are heavily affected. Rather than basing the interpretation on the single assumption of sacrifice, it puts forward arguments pertaining to the history of the school in the immediate pre-war, including the institution of military training after the reform service in 1905, competition with the École Polytechnique to retain the best scientific students, and finally the forced commitment of the ENS students in the infantry.”

Crucial in this is the role of Ernest Lavisse who was the director of the ENS from 1903 till 1919.



Before, normaliens had to serve 12 months in the army, just like all other students. In 1905 the law changed, and under Lavisse’s influence ENS-students were given a heavy military training. From the paper:

“From now on, normalien students, like those of other major military schools, are subject to a two-year service: a first year before their actual entry into rue d’Ulm, which they had to perform in an infantry regiment; a second on leaving, which they can finish as a reserve second lieutenant, but always in the infantry, if they pass the tests. And there is more: because between these two years, the students also follow a fairly heavy military preparation, including theoretical and physical exercises, even on Sundays, organised by two officers seconded full-time for this mission within the walls of the School.”

He also instilled in the ENS-student a radical sense of patriotism, and was a fervent propagandist for l’Union sacrée. From the paper:

“Intellectual mobilisation crystallised in the figures of Lavisse and Durkheim via their famous Letters to all French people distributed in millions of copies across the country. In the fall of 1914, the two founded and took control, respectively as director and secretary of the Committee for Studies and Documents on the War, a propaganda organ for the country’s executives.

Alongside them, eight of the nine other members of the Committee are former students of the School who have become professors at the Sorbonne (Charles Andler, Charles Seignobos, Émile Boutroux, Ernest Denis, Gustave Lanson) or at the Collège de France (Joseph Bédier, Henri Bergson, Jacques Hadamard), without even mentioning the role of editorial secretary held by Lucien Herr, legendary counterpart of Paul Dupuy at the Rue d’Ulm library.”

I would have liked that there were only nine members of the committee, but there were eleven of them…

Anyway, Lavisse and his eight professors created an extremely patriotic environment at the ENS during WW1, encouraging students to go to (the) Trench(es) and give their life for France and the glory of the Ecole. The ENS-monument is the equivalent of the Neon Gravestones in Dema-lore.

Did you spot it too? LAVIsse is almost a perfect anagram for VIALism.

Se non e vero…

Concluding, the best theory I can come up with in order to include the Bourbaki-group in Dema-lore is that their Dema is the ENS in WW1 and preceding years, and that Vialism is the regime installed by Lavisse and the other members from the committee.

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Bourbaki = Bishops or Banditos?

Published July 5, 2023 by lieven

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.

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Bourbaki and TØP : East is up

Published June 22, 2023 by lieven

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.

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