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9 Bourbaki founding members, really?

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:


  • 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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TØP PhotoShop mysteries

Suppose you’re writing a book, and for the duration of that project you keep a certain photo as your desktop-background. I guess we might assume that picture to be inspirational for your writing process.

If you PhotoShopped it to add specific elements, might we assume these extra bits to play a crucial role in your story?

Now, let’s turn to Twenty One Pilots and the creation process of their album Trench, released on October 5, 2018

We know from this tweet (from August 19th, 2018) that Tyler Joseph’s desktop-background picture was a photoshopped version of the classic Bourbaki-1938 photo on the left below, given it Trench-yellow, and added a bearded man in the doorway (photo on the right)

And we know from this interview (from September 5th, 2018) that, apart from the bearded man, he also replaced in the lower left corner the empty chair by a sitting person (lower photo).

The original photo features on the Wikipedia page on Nicolas Bourbaki, and as Tyler Joseph has revealed that Blurryface‘s real name is Nicolas Bourbaki (for whatever reason), and that he appears in the lyrics of Morph on Trench, this may make some sense.

But, of the seven people in the picture only three were founding members of Bourbaki: Weil, Diedonne and Delsarte. Ehresmann entered later, replacing Jean Leray, and Pison and Chabauty were only guinea pigs at that moment (they later entered Bourbaki, Chabauty briefly and Pison until 1950), and finally, Simonne Weil never was a member.

There’s another strange thing about the original picture. All of them, but Andre and Simone Weil, look straight into the camera, the Weil’s seem to be more focussed on something happening to the right.

Now, TØP has something with the number 9. There are nine circles on the cover of Blurryface (each representing one of a person’s insecurities, it seems), there are nine towers in the City of Dema, nine Bishops, etc.

So, from their perspective it makes sense to Photoshop two extra people in, and looking at the original there are two obvious places to place them: in the empty doorway, and on the empty chair.

But, who are they, and what is their significance?

1. The bearded man in the doorway

As far as I know, nobody knows who he is. From a Bourbaki point of view it can only be one person: Elie Cartan.

We know he was present at the 1938 Bourbaki Dieulefit/Beauvallon meeting, and that he was kind of a father figure to Bourbaki. Among older French mathematicians he was one of few (perhaps the only one) respected by all of Bourbaki.

But, bearded man is definitely not Elie Cartan…

If bearded man exists and has a Wikipedia page, the photo should be on that page. So, if you find him, please leave a comment.

Previous in this series I made a conjecture about him, but I’m not at all sure.

2. Why, of all people, Szolem Mandelbrojt?

We know from this Twentyonepilots subReddit post that the man sitting on the previously empty chair in none other than Bourbaki founding member Szolem Mandelbrojt, shopped in from this other iconic early Bourbaki-photo from the 1937 Chancay-meeting.

Let me tell you why this surprises me.

Szolem Mandelbrojt was atypical among the first Bourbaki-gang in many ways: he was the only one who didn’t graduate from the ENS, he was a bit older than the rest, he was the only one who was a full Professor (at Clermont-Ferrand) whereas the others were ‘maitre de conference’, he was the only one who didn’t contribute actively in the Julia seminar (the proto-Bourbaki seminar) nor much to the Bourbaki-congresses either for that matter, etc. etc.

Most of all, I don’t think he would feel particularly welcome at the 1938 congress. Here’s why.

(Jacques Hadamard (left), and Henri Lebesgue (right))

From Andre Weil’s autobiography (page 120):

Hadamard’s retirement left his position open. I thought myself not unworthy of succeeding him; my friends, especially Cartan and Delsarte, encouraged me to a candidate. It seemed to me that Lebesgue, who was the only mathematician left at the College de France, did not find my candidacy out of place. He even let me know that it was time to begin my ‘campaign visits’.

But the Bourbaki-campaign against a hierarchy of scientific prizes instituted by Jean Perrin (the so called ‘war of the medals’) interfered with his personal campaign. (Perhaps more important was that Mandelbrojt did his Ph.D. under Hadamard…)

Again from Weil’s autobiography (page 121):

Finally Lebesque put an end to my visits by telling me that he had decided on Mandelbrojt. It seemed to me that my friends were more disappointed than I at this outcome.

In the spring of 1938, Mandelbrojt succeeded Hadamard at the College de France.

There’s photographic evidence that Mandelbrojt was present at the 1935 Besse-congress and clearly at the 1937-Chancay meeting, but I don’t know that he was even present at Chancay-1936. (Edit May 2024: He was present in 1936)

The only picture I know of that meeting is the one below. Standing on bench: Chevalley’s nephews, seated Andre Weil and Chevalley’s mother; standing, left to right: Ninette Ehresmann, Rene de Possel, Claude Chavalley, Jacqueline Chavalley, Mirles, Jean Delsarte and Charles Ehresmann.

Of all possible people, Szolem Mandelbrojt would be the miscast at the 1938-meeting. So, why did they shop him in?

– convenience: they had an empty chair in the original picture, another Bourbaki-photo with a guy sitting on such a chair, so why not shop him in?

– mistaken identity: in the subReddit post the sitting guy was mistakenly identified as Claude Chevalley. Now, there is a lot to say about wishing to add Chevalley to the original. He is by far the most likeable of all Bourbakis, so if these nine were ever supposed to be the nine Bishops of Dema, he most certainly would be Keons. But, Chevalley was already in the US at that time, and was advised by the French consul to remain there in view of the situation in Europe. As a result, Chevalley could not obtain a French professorship before the early 50ties.

– a deep hidden clue: remember all that nonsense about Josh Dun’s ‘alma mater’ being that Ukrainian building where Nico and the niners was shot? Well, Szolem Mandelbrojt’s alma mater was the University of Kharkiv in Ukraine. See this post for more details.

3. Is it all about Simone Weil?

If you super-impose the two photographs, pinning Mandelbrojt in both, the left border of the original 1938-picture is an almost perfect mirror for both appearances of Simone Weil. Can she be more important in all of this than we think?

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Cartan meets Lacan

In the Grothendieck meets Lacan-post we did mention that Alain Connes wrote a book together with Patrick Gauthier-Lafaye “A l’ombre de Grothendieck et de Lacan, un topos sur l’inconscient”, on the potential use of Grothendieck’s toposes for the theory of unconsciousness, proposed by the French psychoanalyst Jacques Lacan.

A bit more on that book you can read in the topos of unconsciousness. For another take on this you can visit the blog of l’homme quantique – Sur les traces de Lévi-Strauss, Lacan et Foucault, filant comme le sable au vent marin…. There is a series of posts dedicated to the reading of ‘A l’ombre de Grothendieck et de Lacan’:

Alain Connes isn’t the first (former) Bourbaki-member to write a book together with a Lacan-disciple.

In 1984, Henri Cartan (one of the founding fathers of Bourbaki) teamed up with the French psychoanalyst (and student of Lacan) Jean-Francois Chabaud for “Le Nœud dit du fantasme – Topologie de Jacques Lacan”.

(Chabaud on the left, Cartan on the right, Cartan’s wife Nicole in the mddle)

“Dans cet ouvrage Jean François Chabaud, psychanalyste, effectue la monstration de l’interchangeabilité des consistances de la chaîne de Whitehead (communément nommée « Noeud dit du fantasme » ou du « Non rapport sexuel » dans l’aire analytique), et peut ainsi se risquer à proposer, en s’appuyant sur les remarques essentielles de Jacques Lacan, une écriture du virage, autre nom de la passe. Henri Cartan (1904-2008), l’un des Membres-fondateur de N. Bourbaki, a contribué à ce travail avec deux réflexions : la première, considère cette monstration et l’augmente d’une présentation ; la seconde, traite tout particulièrement de l’orientation des consistances. Une suite de traces d’une séquence de la chaîne précède ce cahier qui s’achève par : « L’en-plus-de-trait », une contribution à l’écriture nodale.”

Lacan was not only fascinated by the topology of surfaces such as the crosscap (see the topos of unconsciousness), but also by the theory of knots and links.

The Borromean link figures in Lacan’s world for the Real, the Imaginary and the Symbolic. The Whitehead link (that is, two unknots linked together) is thought to be the knot (sic) of phantasy.

In 1986, there was the exposition “La Chaine de J.H.C. Whitehead” in the
Palais de la découverte in Paris (from which also the Chabaud-Cartan picture above is taken), where la Salle de Mathématiques was filled with different models of the Whitehead link.

In 1988, the exposition was held in the Deutches Museum in Munich and was called “Wandlung – Darstellung der topologischen Transformationen der Whitehead-Kette”

The set-up in Munich was mathematically more interesting as one could see the link-projection on the floor, and use it to compute the link-number. It might have been even more interesting if the difference in these projections between two subsequent models was exactly one Reidemeister move

You can view more pictures of these and subsequent expositions on the page dedicated to the work of Jean-Francois Chabaud: La Chaîne de Whitehead ou Le Nœud dit du fantasme Livre et Expositions 1980/1997.

Part of the first picture featured also in the Hommage to Henri Cartan (1904-2008) by Michele Audin in the Notices of the AMS. She writes (about the 1986 exposition):

“At the time, Henri Cartan was 82 years old and retired, but he continued to be interested in mathematics and, as one sees, its popularization.”

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