neverendingbooks

Le Guide Bourbaki: Aumont-Aubrac

lievenlb — Mon, 09 Jun 2025 17:48:32 +0000

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

Le Guide Bourbaki : Cabris

lievenlb — Wed, 04 Jun 2025 09:38:30 +0000

“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)

The dangerous bend symbol

lievenlb — Sat, 31 May 2025 09:31:05 +0000

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…

In this series:

Closure (2)

lievenlb — Wed, 26 Jun 2024 19:26:00 +0000

I told you six months ago that I’ll be out of my office by the end of summer and will no longer have access to the webserver running this blog.

There’s a slight possibility that the new inhabitant is willing to inherit said iMac and as long as (s)he doesn’t shut it down, this site may be online for a few extra months.

With help from Pieter Belmans I managed to create a static version of this blog on GitHub. Its URL is

https://lievenlebruyn.github.io/neverendingbooks

All internal links should work (if not, please tell me) and if you ever bookmarked a post here with URL something like
http://www.neverendingbooks.org/that_post
you’ll be able to view it till eternity comes using this URL: https://lievenlebruyn.github.io/neverendingbooks/that_post.

The more you link to the static GitHub version from now on, the more likely it is all static NeB posts will show up in a Google search.

I may even continue to blog and will update the GitHub repository whenever I can.

If you ever come in a similar situation (WordPress blogger, whose server will become unavailable, and want to set up a static version of your blog, with the possibility to keep on blogging) I’ll walk you through the main steps (and, if I could do this, anyone can).

1. Install Local.WP

On a computer you will continue to have access to, say your laptop (not serving to the web) install Local.WP which allows you to build local WordPress sites.

2. Clone your blog locally

Set up a default WP-blog, name it as your blog, say myblog, install all plugins you have on your regular blog and set it up to use your preferred theme.

Then. clone your blog with the export/import tool from WP. That is, export your blog and then import it in this local blog and delete the standard first post and page local.WP created.

Oh, and make sure you local site serves https (may be important later if you want to use the GitHub API). The local.wp helpfiles provide you with all info.

3. Get all internal links right

Install the Better search and replace plugin.

Use it to set all your internal links right. Assume your blog has address http://myblog.org and your local version serves it at https://myblog.local do a global search and replace of these two terms.

Check if indeed all local links (including images) work.

4. Make a GitHub repository

Set up a GitHub account, let’s call is myname and set up your first repository and name it after your blog myblog.

5. Do the Simply Static magic

Install on your local blog the Simply Static wordpress plugin.

In the general settings of Simply Static choose for replacing URLs ‘Absolute URLs’ and for scheme/host choose https://myname.github.io/myblog and force URL replacements.

Choose as your deployment method ‘ZIP archive’ and hit generate. When it finishes download the ZIP file.

6. Upload to GitHub pages

Upload the obtained folder to your GitHub repository and make it into a Github-page (lots of pages tell you how you can do both). You’re done, your static site is now available at https://myname.github.io/myblog.

If you would opt for the paid version of Simply Static the last step is done automatically (hence the importance of the https scheme on your local clone) and it promises to make even comments to your static site available as well as semi-automatic updates if you write a new post on your local blog.

Vialism versus Weilism

lievenlb — Sun, 02 Jun 2024 13:16:25 +0000

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:

What about Simone Weil?

lievenlb — Mon, 13 May 2024 09:22:22 +0000

In recent weeks, a theory that Simone Weil is the key to Dema-lore is getting a lot of traction.

Image credit

In two words, this theory is based on the assumption that Vialism=Weilism and on textual similarities between the writings of Simone Weil and the lyrics of 21 pilots and the Clancy letters.

The Keons YouTube channel explains this in great detail.

Until now, I thought that Andre Weil was crucial to the story, and that Simone’s role was merely to have a boy/girl archetypical situation.

There’s this iconic photograph of them from 1922, taken weeks before Andre entered the ENS:

The same setting, boy on the left, girl to the right was used in the Nico and the niners-video, when they are young and in Dema

and when they are a quite a bit older, and in Trench, at the end of the Outside-video.

These scenes may support my theory that Dema was the ENS (both Andre and Simone studied there) as is explained in the post Where’s Bourbaki’s Dema?, and when they were both a bit older, and at the Bourbaki meetings in Chancay and Dieulefit, that they were banditos operating in Trench, as explained in the post Bourbaki = Bishops or Banditos.

There are two excellent books to read if you want to know more about the complex relationship between Andre and Simone Weil.

The first one is The Weil Conjectures: On Math and the Pursuit of the Unknown by Karen Olsson.

From it we get the impression that, at times, Simone felt intellectually inferior to Andre, who was three years older. She often asked him to explain what he was working on. Famous is his letter to her written in 1940 when he was jailed. Here’s a nice Quanta-article on it, A Rosetta stone for mathematics. This was also the reason why she wanted to attend some Bourbaki-meetings in order to get a better understanding of what mathematics was all about and how mathematicians think.

She was then very critical about mathematics because all that thinking about illusory objects had no immediate effect in real life. Well Simone, that’s the difference between mathematics and philosophy.

The second one is Chez les Weil, Andre et Simone written by Andre’s eldest daughter Sylvie.

From it we get another impression, namely that Andre may have been burdened by the fact that, after Simone’s death, his parents life centered exclusively around the preservation of her legacy, ignorant of the fact that their remaining child was one of the best mathematicians of his generation.

Poor Andre, on their family apartment in the Rue Auguste-Comte (which Andre used until late in his life when he was in Paris) is now this commemorative plaque

Well Andre, that’s the difference between a mathematician and a philosopher.

Let’s return to the role Simone Weil may play in Dema-lore. For starters, how did she appear in it?

She makes her appearance through a picture on Tyler’s desktop at the start of the Trench-era. This picture is a combination of two photographs from Bourbaki meetings, and Simone Weil features in both of them.

The photograph on the left is from the september 1937 meeting in Chancay, that on the right is from the september 1938 meeting in Dieulefit.

These are exactly the years crucial in Simone’s conversion to catholicism.

In the spring of 1937 she experienced a religious ecstasy in the Basilica of Santa Maria degli Angeli in Assisi.

Over Easter is 1938, Simone and her mother attended Holy Week services at the Solesmes Abbey where she had a mystic experience in which “Christ himself came down and took possession of me”.

One might ask whether there’s any connection between these religious experiences and her desire to attend these upcoming Bourbaki meetings. So, what was discussed during these conferences?

Mathematically, the 1938 meeting was not very exciting. Hardly any work was done, as they were preoccupied with all news of the Nazis invading Czechoslovakia. During the conference, Simone and Alain even escaped to Switzerland because they were convinced war was imminent. After a couple of days the Munich Treaty was signed, and Alain returned to Dieulefit, whereas Simone stayed in Switzerland, before returning to Paris.

On the other hand, the Chancay meeting was revolutionary as the foundations of topology were rewritten there with the introduction of the filter concept, dreamed up on the spot by Henri Cartan (the guy in the deckchair), while the others were taking a walk.

Simone was pretty impressed by the power of TOPology. In 1942 she wrote in her ‘Cahiers’:

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.

Interestingly, she mentions the two math-subjects closest to the pilots’ universe: set theory studies all objects you can make starting from the empty set $\emptyset$, and topology studies the properties of objects and figures that remain unchanged even when you
morph them.

We’ll have to say more about this in a next post when we look into the Vialism=Weilism assumption.

Another appearance of Simone Weil in the lore might be through the cropped image you can find on the dmaorg-website.

The consensus opinion is that this is a picture of the young Clancy, next to one of the Bishops (Keons? Andre? Nico?).

In fact, the ‘little boy’ is actually a girl and her identity is unresolved as far as I know. But, given the date of the photograph (1956) the girl might be (mistakingly) taken for Andre’s daughter Sylvie.

Now, almost everyone, in particular her grandparents and Andre himself, found that Sylvie was a spitting image (almost a ‘copy’) of Simone Weil.

There are further indications that Simone Weil might be a Clancy.

Morph

In Morph there are these lines

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

During the meetings she attended, the other Bourbakis mocked Simone that she was a copy of het brother. From Karen Olsson’s book mentioned above:

To the others it’s startling to see his same glasses, his same face attached to this body clothed in an. unstylish dress and an off-kilter brown beret, carrying on in that odd monotone as she argues, via the chateau’s telephone, with the editors who publish her political articles.

Early in her career, Simone Weil was far from an original thinker. For her end-essay on Descartes she got the lowest score possible in order to pass from the ENS. Even Andre urged her to have a work-plan to develop her own ideas, rather than copying ideas from philosophers from the past.

Jumpsuit

Whereas Andre tried everything to avoid the draft, Simone was more of a warrior. In 1935 she volunteered to fight on the Republican side in the Spanish civil war, until a kitchen accident forced her to return to France.

Later in 1943 she left New-York to return to England and enlist in the French troupes of General de Gaulle, hoping to be parachuted behind enemy lines. Given her physical state, the military command decided against it. Upset by this refusal, she felt she had no other option than to deny herself food in empathy with the starving French.

She didn’t succeed in crossing Paladin Strait, sorry the Channel.

Overcompensate

Can this be Simone Weil?

In this series:

Clancy and Nancago

lievenlb — Fri, 03 May 2024 08:56:53 +0000

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:

Bourbaki and Dema, two remarks

lievenlb — Mon, 26 Feb 2024 15:08:04 +0000

While this blog is still online, I might as well correct, and add to, previous posts.

Later this week new Twenty One Pilots material is expected, so this might be a good time to add some remarks to a series of posts I ran last summer, trying to find a connection between Dema-lore and the actual history of the Bourbaki group. Here are links to these posts:

In the post “9 Bourbaki founding members, really?” I questioned Wikipedia’s assertion that there were exactly nine founding members of Nicolas Bourbaki:

I still stand by the arguments given in that post, but my opinion on this is completely irrelevant. What matters is who the Bourbaki-gang themself deemed worthy to attach their names to their first publication ‘Theorie des Ensembles’ (1939).

But wait, wasn’t the whole point of choosing the name Nicolas Bourbaki for their collective that the actual authors of the books should remain anonymous?

Right, but then I found this strange document in the Bourbaki Archives : awms_001, a preliminary version of the first two chapters of ‘Theorie des Ensembles’ written by Andre Weil and annotated by Rene de Possel. Here’s the title page:

Next to N. Bourbaki we see nine capital letters: M.D.D.D.E.C.C.C.W corresponding to nine AW-approved founding members of Bourbaki: Mandelbrojt, Delsarte, De Possel, Dieudonne, Ehresmann, Chevalley, Coulomb, Cartan and Weil!

What may freak out the Clique is the similarity between the diagram to the left of the title, and the canonical depiction of the nine Bishops of Dema (at the center of the map of Dema) or the cover of the Blurryface album:

In the Photoshop mysteries post I explained why Mandelbrojt and Weil might have been drawn in opposition to each other, but I am unaware of a similar conflict between either of the three C’s (Cartan, Coulomb and Chevalley) and the three D’s (Delsarte, De Possel and Dieudonne).

So, I’ll have to leave the identification of the nine Bourbaki founding members with the nine Dema Bishops as a riddle for another post.

The second remark concerns the post Where’s Bourbaki’s Dema?.

In that post I briefly suggested that DEMA might stand for DEutscher MAthematiker (German Mathematicians), and hinted at the group of people around David Hilbert, Emil Artin and Emmy Noether, but discarded this as “one can hardly argue that there was a self-destructive attitude (like Vialism) present among that group, quite the opposite”.

At the time, I didn’t know about Deutsche Mathematik, a mathematics journal founded in 1936 by Ludwig Bieberbach and Theodor Vahlen.

Deutsche Mathematik is also the name of a movement closely associated with the journal whose aim was to promote “German mathematics” and eliminate “Jewish influence” in mathematics. More about Deutsche Mathematik can be found on this page, where these eight mathematicians are mentioned in connection with it:

Perhaps one can add to this list:

Whether DEutsche MAthematik stands for DEMA, and which of these German mathematicians were its nine bishops might be the topic of another post. First I’ll have to read through Sanford Segal’s Mathematicians under the Nazis.

Added February 29th:

The long awaited new song has now surfaced:

I’ve only watched it once, but couldn’t miss the line “I fly by the dangerous bend symbol“.

Didn’t we all fly by them in our first readings of Bourbaki…

(Fortunately the clique already spotted that reference).

No intention to freak out clikkies any further, but in the aforementioned Weil draft of ‘Theorie des Ensembles’ they still used this precursor to the dangerous bend symbol

Skeletons anyone?

Closure

lievenlb — Sun, 31 Dec 2023 08:26:10 +0000

Exactly 20 years ago I wrote my first blogpost, ‘a blogging 2004’. I wasn’t using WordPress yet (but something called pMachine), and this blog was not called ‘neverendingbooks’, but ‘matrix.ua.ac.be’ (the URL of the mac still running this blog).

At the time I wanted to find out whether blogging was something for me. “I’m just starting out. Give me a couple of weeks/months to develop my own style and topics and I’ll change the layout accordingly.”

Well, after 20 years I know what I can, and more important, what I cannot do within this framework. Time to move on.

There are other reasons why this might be the right time to pull the plug.

– I’m on retirement since October 1st and soon I’ll have to vacate my office, containing the webserver on which NeB runs.

– My days are filled with more activities now, and I don’t think you want to read here for example about my struggles with chestnut-farming.

– I like to explore other channels to talk about mathematics. This may happen on Mathstodon, MathOverflow or YouTube. Or it might be through teaching or writing a book, perhaps even a children’s book.

NeB will remain reachable until mid 2024. I’ll check out options to preserve its content after that (suggestions are welcome).

I wish you a better 2024.

WBM

Grothendieck’s gribouillis (6)

lievenlb — Mon, 02 Oct 2023 16:49:52 +0000

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?

Well, finally we have closure!

Last Friday, Grothendieck’s children donated the 30.000 Laserre pages to the Bibliotheque Nationale de France.

Via Des manuscrits inédits du génie des maths Grothendieck entrent à la BnF (and Google-translate):

“The singularity of these manuscripts is that they “cover many areas at the same time” to form “a whole, a + cathedral work +, with undeniable literary qualities”, analyzes Jocelyn Monchamp, curator in the manuscripts department of the BnF.

More than in “Récoltes et semailles”, very autobiographical, the author is “in a metaphysical retreat”, explains the curator, who has been going through the texts with passion for a month. A long-term task as the writing, in fountain pen, is dense and difficult to decipher. “I got used to it… And the advantage for us was that the author had methodically paginated and dated the texts.” One of the parts, entitled “Structures of the psyche”, a book of enigmatic diagrams translating psychology into algebraic language. In another, “The Problem of Evil”, he unfolds over 15,000 pages metaphysical meditations and thoughts on Satan. We sense a man “caught up by the ghosts of his past”, with an adolescence marked by the Shoah, underlines Johanna Grothendieck whose grandfather, a Russian Jew who fled Germany during the war, died at Auschwitz.

The deciphering work will take a long time to understand everything this genius wanted to say.

On Friday, the collection joined the manuscripts department of the Richelieu site, the historic cradle of the BnF, alongside the writings of Pierre and Marie Curie and Louis Pasteur. It will only be viewable by researchers.“This is a unique testimony in the history of science in the 20th century, of major importance for research,” believes Jocelyn Monchamp.

During the ceremony, one of the volumes was placed in a glass case next to a manuscript by the ancient Greek mathematician Euclid.”

Probably, the recent publication of Récoltes et Semailles clinched the deal.

Also, it is unclear at this moment whether the Istituto Grothendieck, which harbours The centre for Grothendieck studies coordinated by Mateo Carmona (see this post) played a role in the decision making, nor what role the Centre will play in the further studies of Grothendieck’s gribouillis.

For other coverage on this, see Hermit ‘scribblings’ of eccentric French math genius unveiled.