Author: lievenlb

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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Le Guide Bourbaki : Cabris

Published June 4, 2025 by lievenlb

“La Tribu” (“The Tribe”) was the internal Journal of the Bourbaki group between 1940 and 1977.

It’s main purpose was to record the editorial decisions made during the Bourbaki congresses, but it always started out with a humorous account of some of the events that happened during the meeting or in the world at large.

Every Tribe issue starts with a list of all people and things attending that meeting. Here’s one example, from the 1954 summer congress in Murols:

Some time ago, I’ve used the then available issues of “La Tribu” to locate the Hotels, Abbeys, Spas etc. where the Bourbaki congresses took place between 1940 and 1960. Here are some links:

In one of these post I pleaded:

“Dear Collaborators of Nicolas Bourbaki, please make all Bourbaki material (Diktat, La Tribu, versions) publicly available, certainly those documents older than 50 years.”

When I checked the Bourbaki Archives a few weeks ago, I was delighted to see that by now they have released all issues of “La Tribu” until 1973!

A few more places for me to locate, and a lot of fun intros to read.

From 1960 on, Cabris, in the Alpes-Maritime, near Grasse, and not too far from Cannes and Antibes, was by far the most popular congress spot for the second and third generation Bourbakistas.

Between 1960 and 1973 they visited the place no less than thirteen times, see the “La Tribu” issues nrs. 60,61,64,65,66,68,70,71,73,74,77,81 and 85.

Starting from 1965 they even held their annual two week summer conference there for five consecutive years.

Probably they kept returning there, even after 1973.

In the book Bourbaki, a secret society of mathematicians by Maurice Mashaal there are several photographs of the July 1975 Bourbaki Congress in Cabris.

Finding their popular venue is quite easy, as “La Tribu” usually mentions “La Messuguiere, Cabris”.

(Photo credit)

The “Villa La Messuguiere” has an interesting history.

In 1938, Mrs. Mayrisch, formerly Aline de Saint-Hubert, purchased a plot of land in Cabris and built a house there, which she called La Messuguière. The name is derived from ‘le messugue’, the Provençal name for the cottony cistus, or Cistus albidus, a characteristic shrub of the ‘garrigue’ which thrives there.

She took refuge at La Messuguiere in 1940 and remained there until her death on January 20, 1947.
During the war, she welcomed her friends Andre Gide, Jean Schlumberger, Roger Martin
du Gard, Gaston Gallimard, Marie Delcourt, Alexis Curvers, Henri Michaux, and Andre Malraux.

Aline Mayrisch-de Saint-Hubert was attracted to the region because her friend Maria Van Rysselberghe, a Belgian writer and wife of the painter Theo Van Rysselberghe, lived at the ‘Villa Les Audides’, not far from La Messuguière.

Until 1979, Villa La Messuguiere hosted the French and international intellectual elite as paying guests. Gide was one of the first to settle there and received many visitors, among them: Henry de Montherlant, André Malraux and his wife Clara, Jean-Paul Sartre, and Albert Camus.

Clara Malraux wrote “Our Twenty Years” at the Villa, and Henri Thomas “The Promontory”, which earned him the Prix Fémina.

Apart from writers, also the philosopher Lucien Goldmann, the sociologist Georges Friedmann, the politician Jules Moch, and the micro-biologist and Nobel Prize winner Andre Lwoff stayed at La Messuguiere.

In the mid 1960s, at the height of their influence over French and international mathematics, the Bourbaki group probably only felt entitled to hold their meetings at this intellectual hotspot. Perhaps, the upcoming closure of the Villa as a conference centre in 1979 contributed to the rapid decline of the group in the late 1970s.

(Photo credit)

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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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