Category: tBC

Le Guide Bourbaki: Aumont-Aubrac

Published June 9, 2025 by lievenlb

Sooner or later, every generation of Bourbakistas is drawn to the natural beauty of the Auvergne-region, known for its mountain ranges and dormant volcanoes.

In the summer of 1935 the founding fathers created Nicolas Bourbaki during their congress in Besse-en-Chandesse.

Standing from left to right: Cartan, de Possel, Dieudonne, Weil and a local technician. Seated from left to right: Mirles (guinea pig), Chevalley and Mandelbrojt.

In August 1954, the remaining founding fathers gathered with second generation Bourbakistas and a bunch of guests at the Hotel des Pins in Murol.

Apart from Cartan, Chevalley, Delsarte, Dieudonne and Weil, present were of the second generation: Dixmier, Godement, Koszul, Eilenberg, Samuel, Schwartz and Serre. There was a guinea-pig (Serge Lang), an ‘efficiency expert’ (Saunders MacLane), two ‘foreign visitors’ (Hochschild and John Tate) and two ‘honorable foreign visitors’ (Iyanaga and Kosaku Yosida).

From left to right, Godement, Dieudonne, Weil, MacLane, and a smug looking Serre (he knew he would be awarded a Fields medal at the coming ICM in a few days time).

For the third generation, the Auvergne-spot of choice was Aumont-Aubrac, now part of Peyre en Aubrac. In Occitan Aumont-Aubrac is called Autmont from the Latin ‘altum montem’, haute montagne (high mountain), appropriate as the average elevation of the commune is 1045m.

‘Tribu 86’ recounts their visit in the fall of 1972, and calls it ‘Le congres des cèpes‘ (the Porcini mushrooms congress).

Bourbaki rediscovered the simple joys: slow-moving trains climbing the Cévennes, mushroom picking, peasant feasts. Douady was mistaken for a horse dealer at the fairground, Cartier was restocking his tools, and Meyer revealed himself to be a mushroom expert.

Bourbaki attracted bad luck; the Ponts-et-Chaussées had chosen his stay to repair the main road, but, despite vigilant monitoring, no notable accidents were observed. The stationmaster, a journalist between two train departures, photographed Bourbaki for the local gazette, and delayed the departure of the train for Paris to allow Yvonne Verdier and Demazure to finish their pie.

From ‘Tribu 85’ we learn that they stayed in ‘Hotel de la Gare’, and arrived by night-train from Paris.

The ‘Grand Hotel de la Gare’ aka ‘Grand Hotel Prouheze’ was run by the Prouheze family but is now closed.

‘Tribu 85’, which is the account of their previous summer congress in Cabris (called ‘The water congress’) contains:

The sky took it upon itself to suggest the title of the conference; one rarely sees so much rain at La Messuguière, perhaps to mourn its impending closure.

Perhaps it was due to the bad weather at Cabris last time, or the fear of unavailability of their favourite ‘Villa La Messuguière’, or their enjoyable stay at Aumont-Aubrac in the fall of 1972, anyway Bourbaki decided to have their summer 1973 congress again in Aumont-Aubrac, and again at the Hotel de la Gare (as we can learn from La Tribu 87).

A large group gathered on the evening of June 5th 1973, this time with their bicycles, to take the night train from Paris to Aumont-Aubrac: Hyman Bass, Louis Boutet de Monvel, François Bruhat, Pierre Cartier, Michel Demazure, Adrien Douady (with his wife Regine), André Gramain, Barry Mazur (with his wife Gretchen and their son Zeke), Michel Raynaud, Jean-Louis Verdier, and Jean-Marc Fontaine (with his wife Laurence).

Determined to get to know the real country in the absence of the p-adic country, Bourbaki returned a second time to his Auvergnian roots (Besse 1935!).

Thanks to the organisational progress of the SNCF, which now runs sleeper bike trains, and to the Fontaines who brought their car, Bourbaki did not lack means of transportation. They were necessary to ensure the connection between Bourbaki’s two bases.

Le Moulin, four kilometers from Aumont, increasingly better equipped, allowed for serious discussions to alternate with the sounds of bourrée and the sipping of lemonade and beer. A large fire chased away evil spirits and the threat of colds.

Bourbaki, ever the genius, chose as his base the pigs’ den, where he had ten thousand hectares of flowering and fragrant meadows.

‘Le Moulin’, Bourbaki’s ‘second base’ in the country is now the Chambres d’Hotes au Moulin du Chambon and lies indeed 4km from Aumont-Aubrac, and has indeed a large fireplace, a nice cantou.

Back then, it probably was a pub and the endpoint of several afternoon bicycle excursions for the Bourbakis.

The high point of the congress was their bicycle ‘tour du Gevaudan’. The Gevaudan is the old name of what is now the Lozère département. The name was derived from the Gabali, a Gallic tribe.

Today, the name Gevaudan lives on in the story of the beast of Gevaudan, which killed between 82 and 124 people between June 30, 1764 to June 19, 1767. There’s a statue of the beast in front of the Hotel-de-Ville in Aumont-Abrac.

Previously in this series

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The dangerous bend symbol

Published May 31, 2025 by lievenlb

With the upcoming Breach album by 21 pilots I’ve noticed an influx of clikkies’ clicks on this blog looking for info about the Bourbaki group.

Perhaps this is a good opportunity to add some new posts in which I’m looking for potential connections between the ‘Dema/Trench lore’ surrounding 21 pilots’ albums Blurryface, Trench, Scaled and Icy, and Clancy, and historical facts about Nicolas Bourbaki.

Here’s a list of all lore-related Bourbaki posts so far:

The Clancy album was rather disappointing lore-wise, even though it started out promising with a clear reference to Bourbaki in its first song Overcompensate.

I said, I fly by the dangerous bend symbol (wait, what? Wait, what?)
Mm, don’t hesitate to maybe overcompensate
And then by the time I catch in my peripheral (wait, what? Wait, what?)
Mm, don’t hesitate to maybe overcompensate

First, let us clear up the confusion between the dangerous bend symbol, invented and used by the Bourbaki group, and the dangerous bend (road) sign which features on the back of the Clancy-album.

The dangerous bend road sign predates Bourbaki by at least a decade, see the Wikipedia commons on Historic road signs in Germany.

Already in 1907 it’s used on a road sign of the ‘Kaiserlicher Automobil Club’ (on the left) and from 1927 on as we know it today (on the right).

It’s unclear to me why they put the road sign on their album (perhaps for design reasons) rather than the bend symbol (the curly Z inside) which was used by the Bourbakistas (several of them studied in Germany in the 1920s) to indicate difficult paragraphs in their texts.

But even Bourbaki used the bend symbol only in their later works. In the first versions of their ‘Theorie des Ensembles’ they still used the ‘Danger de Mort’ or ‘Skull and Bones’ sign as precursor:

Now, what is the use of the dangerous bend symbol in 21pilots’ lore?

As far as I know, there is no further mention of this symbol but for one interview in which they relate it to the road sign. In the music videos of the Clancy-songs the dangerous bend symbol (not the sign) is clearly visible on the garbage can in front of the shop in the Backslide-video.

Here’s something strange.

If you look at the clip frame-by-frame from 0:18 till 0:21 you’ll see that twice some frames are cut out, first when he walks to his bike and then when he leaves with it. Both times in the vicinity of the trash can, or better, of the dangerous bend symbol.

It is as if the dangerous bend symbol is an indication of a time warp, action speeds up in its vicinity.

Or perhaps, it indicates a region where memory lapses occur?

Anyway, this could be a coincidence and merely an editing quirk.

However, in the remainder of the clip no further such quirks appear, until the very end (from 3:00 till 3:02) when he returns to the shop.

Then again, frames are missing twice. First when he arrives with the bike, and then after he dropped the sack in the garbage can.

To me this looks like something deliberate, and connected to the dangerous bend symbol.

What exactly is anybody’s guess, but no doubt all will become clear when Breach comes out in September.

This gives me just a couple of months to come up with more wild theories…

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Vialism versus Weilism

Published June 2, 2024 by lievenlb

Here’s how 21 pilots themselves define Vialism, the ‘religion’ of Dema, in the ‘I am Clancy’ video:

Their authority comes from two things: a miraculous power and a hijacked religion. One feeds the other. A cycle. It’s called Vialism, and all you really need to know is that it teaches that self-destruction is the only way to paradise.

Some people think that Vialism means Weilism, after the Weil siblings Andre and Simone.

Simone Weil (1909-1943) was a French philosopher and political activist. In her later years she became increasingly religious and inclined towards mysticism.

Andre Weil (1906-1998) was a French mathematician and founding member of the Bourbaki group.

They enter the lore via a picture on Tyler Joseph’s desktop in the Zane Lowe interview in 2018, which is an overlay of two photographs of Bourbaki meetings in 1937 and 1938 featuring Andre and Simone.

For Simone this is the crucial period in her conversion to Catholicism, for Andre these meetings led to a reformulation of the foundations of TOPology, and discussions on Bourbaki’s version of Set theory which would lead to Bourbaki’s first book, published in 1939.

Both topics left a lasting impression on Simone Weil, as she wrote in 1942:

One field of mathematics that deals with all the diverse sorts of orders (set theory and general topology) is a treasure-house that holds an infinity of valuable expressions that show supernatural truth.

Now, Simone was fairly generous in her use of the adjective ‘supernatural’. Here’s another quote:

“The supernatural greatness of Christianity lies in the fact that it does not seek a supernatural remedy for suffering but a supernatural use for it.”

This suggests that if Vialism really is Weilism, then the ‘miraculous power’ might be mathematics (or at least the topics of set theory and topology), and the ‘hijacked religion’ might be the (ab)use of mathematics in theology.

Roughly speaking, axiomatic Zermelo-Fraenkel set theory gives a precise list of instructions to construct all sets out of two given sets, the empty set $\emptyset$ (the set containing nothing) being one of them.

Emptiness, or the void, is important in Simone Weil’s theology, see for example her book Love in the void: where God finds us

or consider this quote by her:

God stripped himself of his godhood and became empty, and fulfilled us with false godhood. Let us strip off this false godhood and become empty. This very act is the ultimate purpose to creating us.

which sounds a lot like Vialism, becoming an ’empty vessel’ for the Bishops (or God) to fill.

Also in 21 pilots’ iconography, the empty set $\emptyset$ is important.

Btw. the symbol $\emptyset$ for the empty set was first used by Andre Weil who remembered the Norwegian ‘eu’ from his studies of nordic languages preparing for his ‘Finnish fugue’ in 1939.

The other pre-given set challenges the Gods and theology. The Axiom of Infinity in the Zermelo-Fraenkel system asserts the existence of an infinite set, usually denoted $\omega$ and interpreted as the set of all finite numbers $\{ 0,1,2,3,4,5,6,\dots \}$.

In other words, mathematical set theory contains an object which is actual infinity!

From the ancient Greeks on to early modern times, philosophers adhered to the motto “Infinitum actu non datur”, there is only a potential infinity (the idea of infinity) but actual infinity belongs to the realm of the Gods (infinite power, infinite wisdom,…).

As if this was not heretic enough, in comes Georg Cantor.

Georg Cantor (1845-1918) might very well be another Clancy.

He was a German mathematician, discoverer of the secrets of infinity, which brought him in conflict with several influential mathematicians in his time (notably Kronecker and Poincare), and inventor of Cardinal numbers (compare Bishops).

He suffered from depression and mental illness, was often admitted to the Halle nerve clinic. In between he was a founding member of the DEutscher MAthematiker Vereinigung (DeMa) of which he was the first president (Nico), he suffered from malnourishment during WW1 (compare Simone Weil in WW2) and died of a heart attack in the sanatorium where he had spent the last year of his life.

Cantor showed that the only distinguishing feature between two sets is their Cardinality (Bishopy power), roughly speaking the number of things they contain. He then showed that for every set of a certain Bishopy power, there’s one of even higher power!

For example, there exists a set with higher cardinality than $\omega$, that is, a set we cannot enumerate. An example is described in these lines from Morph

Lights they blink to me, transmitting things to me
Ones and zeroes, ergo this symphony
Anybody listening? Ones and zeroes
Count to infinity, ones and zeroes

They’re talking about all possible infinite series of $0$’s and $1$’s and one quickly proves that these cannot be enumerated using Cantor’s diagonal argument.

When applied to theology this says that Gods cannot have any actual infinity power, for there’s always an entity posessing higher powers.

That’s why Cantor resolved to God being ‘absolute infinity’, the Bishopy power of the class of all cardinal numbers (emphasis only important for mathematicians).

Much more on the interplay between Cantor’s mathematical results on infinities and his theological writings can be found in the paper Absolute Infinity: A Bridge Between Mathematics and Theology? by Christian Tapp.

The compassionate God of Christianity has presented theologians for centuries with the following paradox: how can a God having infinite power suffer because humans suffer?

In comes TOPology and one of its founding fathers Felix Hausdorff.

Felix Hausdorff (1868-1942) might very well be another Clancy.

He was a German mathematician who made substantial contributions to topology as well as set theory. For years he felt opposition because he was Jewish.

After the Kristallnacht in 1938 he tried to escape Nazi-Germany (DeMa) but couldn’t obtain a position in the US. On 26 January 1942, Felix Hausdorff, along with his wife and his sister-in-law, died by suicide, rather than comply with German orders to move to the Endenich camp.

He was also a philosopher and writer under the pseudonym Paul Mongré. In 1900 he wrote a book of poems, Ecstasy, of which the first poem is “Den Ungeflügelten” (To The Wingless Ones). Am I the only one to think immediately of The isle of the flightless birds?

Anyway, as to how the topology of Weilism solves the contradiction of the suffering God of Christianity is explained in the paper The Theology of Simone Weil and the Topology of Andre Weil by Ochiai Hitoshi, professor of ‘Mathematical Theology’ at Doshisha University, Kyoto.

He has a follow-up post Incarnation and Reincarnation on the Apeiron Centre (where he also has a post on the Theology of Georg Cantor). Here’s a summary of his thesis:

God is Open
Incarnation is Compactified God
The soul is Open
Reincarnation is Compactified Soul
God and the Soul are Homeomorphic
God is without Boundaries
The soul is with Boundaries
God and the Soul are not Diffeomorphic

This succinctly sums up Weilism for you.

I now understand why so many people in the 21 pilots sub-Reddit thought at the beginning of the Trench-era that Bourbaki was a group of mathematicians trying to prove the existence of God.

In the paper The Theology of Simone Weil and the Topology of Andre Weil the next quote is falsely attributed to Bourbaki

God is the Alexandroff compactification of the universe.

If you are interested in the history behind this quote you may read my post According to Groth. IV.22.

If you want an alternative explanation of Vialism, you may read my post Where’s Bourbaki’s Dema?.

Btw. I forgot to mention in that post the “Annual Assemblage of the Glorified”. Since 1918 this takes place November 11th, on Armistice Day.

In this series: