Tag: bourbaki

Clancy and Nancago

Published May 3, 2024 by lieven

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.]

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Bourbaki and Dema, two remarks

Published February 26, 2024 by lieven

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?

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9 Bourbaki founding members, really?

Published August 21, 2023 by lieven

The Clique (Twenty Øne Piløts fanatic fanbase) is convinced that the nine Bishops of Dema were modelled after the Bourbaki-group.

It is therefore of no surprise to see a Photoshopped version circulating of this classic picture of some youthful Bourbaki-members (note Jean-Pierre Serre poster-boying for Elon Musk’s site),

replacing some of them with much older photos of other members. Crucial seems to be that there are just nine of them.

I don’t know whether the Clique hijacked Bourbaki’s Wikipedia page, or whether they were inspired by its content to select those people, but if you look at that Wikipedia page you’ll see in the right hand column:

Founders

Henri Cartan
Claude Chevalley
Jean Coulomb
Jean Delsarte
Jean Dieudonné
Charles Ehresmann
René de Possel
André Weil

Really? Come on.

We know for a fact that Charles Ehresmann was brought in to replace Jean Leray, and Jean Coulomb to replace Paul Dubreil. Surely, replacements can’t be founders, can they?

Well, unfortunately it is not quite that simple. There’s this silly semantic discussion: from what moment on can you call someone a Bourbaki-member…

The collective name ‘Nicolas Bourbaki’ was adopted only at the Bourbaki-congress in Besse in July 1935 (see also this post).

But, before the Besse-meeting there were ten ‘proto-Bourbaki’ meetings, the first one on December 10th, 1934 in Cafe Capoulade. These meetings have been described masterly by Liliane Beaulieu in A Parisian Cafe and Ten Proto-Bourbaki Meetings (1934-35) (btw. if you know a direct link to the pdf, please drop it in the comments).

During these early meetings, the group called itself ‘The Committee for the Treatise on Analysis’, and not yet Bourbaki, whence the confusion.

Do we take the Capoulade-1934 meeting as the origin of the Bourbaki group (in which case the founding-members would be Cartan, Chevalley, De Possel, Delsarte, Dieudonne, and Weil), or was the Bourbaki-group founded at the Besse-congress in 1935 (when Cartan, Chevalley, Coulomb, De Possel, Dieudonne, Mandelbrojt, and Weil were present)?

Here’s a summary of which people were present at all meetings from December 1934 until the second Chancay-congress in September 1939, taken from Gatien Ricotier ‘Projets collectifs et personnels autour de Bourbaki dans les années 1930 à 1950′:

07-1935 is the Besse-congress, 09-1936 is the ‘Escorial’-congress (or Chancay 1) and 09-1937 is the second Chancay-congress. The ten dates prior to July 1935 are the proto-Bourbaki meetings.

Even though Delsarte was not present at the Besse-1935 congress, and De Possel moved to Algiers and left Bourbaki in 1941, I assume most people would agree that the six people present at the first Capoulade-meeting (Cartan, Chevalley, De Possel, Delsarte, Dieudonne, and Weil) should certainly be counted among the Bourbaki founding members.

What about the others?

We can safely eliminate Dubreil: he was present at just one proto-Bourbaki meeting and left the group in April 1935.

Also Leray’s case is straightforward: he was even excluded from the Besse-meeting as he didn’t contribute much to the group, and later he vehemently opposed Bourbaki, as we’ve seen.

Coulomb’s role seems to restrict to securing a venue for the Besse-meeting as he was ‘physicien-adjoint’ at the ‘Observatoire Physique du Globe du Puy-de-Dome’.

Because of this he could rarely attend the Julia-seminar or Bourbaki-meetings, and his interest in mathematical physics was a bit far from the themes pursued in the seminar or by Bourbaki. It seems he only contributed one small text, in the form of a letter. Due to his limited attendance, even after officially been asked to replace Dubreil, he can hardly be counted as a founding member.

This leaves Szolem Mandelbrojt and Charles Ehresmann.

We’ve already described Mandelbrojt as the odd-man-out among the early Bourbakis. According to the Bourbaki archive he only contributed one text. On the other hand, he also played a role in organising the Besse-meeting and in providing financial support for Bourbaki. Because he was present already early on (from the second proto-Bourbaki meeting) until the Chancay-1937 meeting, some people will count him among the founding members.

Personally I wouldn’t call Charles Ehresmann a Bourbaki founding member because he joined too late in the process (March 1936). Still, purists (those who argue that Bourbaki was founded at Besse) will say that at that meeting he was put forward to replace Jean Leray, and later contributed actively to Bourbaki’s meetings and work, and for that reason should be included among the founding members.

What do you think?

How many Bourbaki founding members are there? Six (the Capoulade-gang), seven (+Mandelbrojt), eight (+Mandelbrojt and Ehresmann), or do you still think there were nine of them?

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