Tag: bourbaki

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

Comments closed

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…

Comments closed

Clancy and Nancago

Published May 3, 2024 by lievenlb

Later this month, 21 pilots‘ next album, “Clancy”, will be released, promising to give definite answers to all remaining open questions in Dema-lore.

By then we will have been told why Andre Weil and the Bourbaki group show up in the Trench/Dema tale.

This leaves me a couple of weeks to pursue this series of posts (see links below) in which I try to find the best match possible between the factual history of the Bourbaki group and elements from the Dema-storyline.

Two well-known Bourbaki-photographs seem important to the pilots. The first one is from the september 1938 Dieulefit/Beauvallon Bourbaki congress:

At the time, Bourbaki still had to publish their first text, they were rebelling against the powers that be in French mathematics, and were just kicked out of the Julia seminar.

In clikkies parlance: at that moment the Bourbakistas are Banditos, operating in Trench.

The second photograph, below on the left, is part of a famous picture of Andre Weil, supposedly taken in the summer of 1956.

At that time, Bourbaki was at its peak of influence over French mathematics, suffocating enthusiastic math-students with their dry doctrinal courses, and forcing other math-subjects (group theory, logic, applied math, etc.) to a virtual standstill.

In clique-speech: at that moment the Bourbakistas are Bishops, ruling Dema.

Let me recall the story of one word, associated to the Bourbaki=Bishops era which lasted roughly twenty years, from the early 50ties till Bourbaki’s ‘death’ in 1968 : Nancago.

From the 50ties, Nicolas Bourbaki signed the prefaces of ‘his’ books from the University of Nancago.

Between 1951 and 1975, Weil and Diedonne directed a series of texts, published by Hermann, under the heading “Publications de l’Institut mathematique de l’Universite de Nancago”.

Bourbaki’s death announcement mentioned that he “piously passed away on November 11, 1968 at his home in Nancago”.

Nancago was the name of a villa, owned by Dieudonne, near Nice. Etc. etc.

But then, what is Nancago?

Well, NANCAGO is a tale of two cities: NANcy and ChiCAGO.

The French city of Nancy because from the very first Bourbaki meetings, the secretarial headquarters of Bourbaki, led by Jean Delsarte, was housed in the mathematical Institute in Nancy.

Chicago because that’s where Andre Weil was based after WW2 until 1958 when he moved to Princeton.

Much more on the history of Nancago can be found in the newspaper article by Bourbaki scholar par excellance Liliane Beaulieu: Quand Nancy s’appelait Nancago (When Nancy was called Nancago).

Right, but then, if Nancago is the codeword of the Bourbaki=Bishops era, what would be the corresponding codeword for the Bourbaki=Banditos era?

As mentioned above, from 1935 till 1968 Bourbaki’s headquarters was based in Nancy, so even in 1938 Nancy should be one of the two cities mentioned. But what is the other one?

In 1938, Bourbaki’s founding members were scattered over several places, Jean Delsarte and Jean Dieudonne in Nancy, Szolem Mandelbrojt and Rene de Possel in Clermont-Ferrand, and Andre Weil and Henri Cartan in Strasbourg. Claude Chevalley was on a research stay in Princeton.

Remember the Bourbaki photograph at the Beauvallon meeting above? Well, it was taken in september 1938 when the Munich Agreement was reached.

Why is this relevent? Well, because Strasbourg was too close to the German border, right after the Munich agreement the Strasbourg Institute was ordered to withdraw to the University of Clermont-Ferrand.

Clermont-Ferrand lies a bit south of Vichy and remained in WW2 in the ‘free zone’ of France, whereas Strasbourg was immediately annexed by Germany.

For more on the importance of Clermont-Ferrand for Bourbaki during 1940-1942 see the article by Christophe Eckes and Gatien Ricotier Les congrès de Clermont-Ferrand de 1940, 1941 et 1942.

That is, all Bourbaki members where then either affiliated to Nancy or to Clermont-Ferrand.

A catchy codeword for the Bourbaki=Banditos era, similar to Nancago as the tale of two cities, might then be:

CLermont-Ferrand + nANCY = CLANCY.

[For clikkies: rest assured, I’m well aware of the consensus opinion on the origins of Clancy’s name. But in this series of posts I’m not going for the consensus or even intended meanings, but rather for a joyful interplay between historical facts about the Bourbaki group and elements from Dema-lore.]

In this series:

6 Comments