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the bumpy road to the first Bourbaki congress

The first Bourbaki congress took eventually place in Besse-en-Chandesse. But, its organization suffered from the ‘usual’ inter-departemental fighting, and also from a power-struggle within the group itself. On many issues de Possel and André Weil were on opposite sides, and it didn’t really help that there was a woman involved…

Because Mandelbrojt, de Possel and Coulomb all held a position at the University Blaise Pascal of Clermont-Ferrand I assumed that the Bourbaki-group had no problem procuring the universities’ biology-outpost in Besse-en-Chandesse for their first congress in 1935. However, the relevant Bourbaki files tell a different story. As might have been expected, the project suffered from the ‘usual’ inter-departemental fighting, but also from a power-struggle within the group itself.

An excellent account of the first 10 ‘proto-Bourbaki’ meetings in the Capoulade-Café, 63 boulevard Saint- Michel, is told magnificently by Liliane Beaulieu in her 1993 paper A Parisian Café and Ten Proto-Bourbaki Meetings(1934-1935). Here we will concentrate on the preparations of the Besse congress.

At their very first meeting on december 10th 1934, they already state the importance of the upcoming summer-congress where a precise plan and a distribution of the writing-load for the first volumes will be discussed : “Aux prochaines grandes vacances aura lieu une réunion pléniere d’ou sortira un plan définitif tres précis et une répartition du travail de rédaction des différents fascicules”. The second meeting, on january 14th 1935, decides that the definite list of Bourbaki-members will consist of those (among the nine ‘possibles’ Weil, Delsarte, Mandelbrojt, Cartan, Dubreil, Dieudonné, de Possel, Chevalley and Leroy) present at the congress : “Il est entendu que la liste définitive, extraite de la précédente, sera composée des noms des membres présents a la réunion pléniere d’Aout ou Septembre prochain, réunion dans laquelle sera dressé le plan définitif et précis du traité”.

On march 25th 1935, the first precise plans are made about the location, the lodgings and the extremely important issue of the meals which will be taken in a nearby Hotel of which “la cuisine est, parait-il, fort bonne”.

René de Possel obtained a mandate to do whatever it took for the group to have their congress in Besse between 12 and 25 July, and, to enquire until what date they could still change their mind.
His biography contains the following lines :
“On many issues de Possel and André Weil were on opposite sides in the arguments. At the first Bourbaki congress in July 1935 de Possel was still an active member of the group and much involved with contributing but, largely due to differences with Weil, he dropped out of the project. De Possel married Yvonne Liberati on 12 August 1935; they had three children, Yann, Maya, and Daphné.”

By and large, the Bourbaki-differences between de Possel and Weil were of a professional nature. They had different mathematical interests, different mathematical talents, different ambitions, and, a different level of commitment wrt. the work ahead (Weil being the lazier one of the two). Still, it is difficult to understand the group-dynamics of the first generation Bourbakis without mentioning a personal tragedy, often ‘forgotten’ (as in the above biography) or given no more than half a sentence, in passing…

Aged 24, René de Possel marries Evelyne Gillet in 1929 and their son, Alain, is born on august 16th 1931. However, the marriage breaks up, one account dates the separation in 1933, another around the time of the Besse conference in 1935.

What is certain is that Evelyne Gillet and André Weil start a relationship no later than the autumn of 1935. At that time, Weil is concocting the Bourbaki Comptes-Rendus note and as the Academy demands a short biography of the author, he has to come up with a first name (at the Besse conference, they only decided on the name ‘N. Bourbaki’). Evelyne chooses Nicolas and is referred to ever after as ‘Bourbaki’s godmother’. Early 1936, the couple spends a vacation together in Spain.

Early 1937, the official divorce papers come through, allowing Weil and Evelyne to marry on october 30th 1937. The very same year, René de Possel remarries with Yvonne Liberati. For more information, you can traverse Evelyne’s genealogy-tree here, but bear in mind that not all information is included (for example, Evelyne died on may 24th, 1986).

Contrary to the suggestion made in the biography, there is no evidence that de Possel left the Bourbaki-group as a result of this affaire or because of his arguments with Weil. In fact, at least until the second Chançay-congress in 1937, de Possel was one of the hardest workers in the group, present at all meetings, doing his share of the write-up and even chastising his fellow-Bourbakis for not being as committed to the project as they ought to be, see for example the 7 theses of Chançay document. It was only in the fall of 1941 that de Possel asked to be transferred to the university of Algiers and left the Bourbaki-group.


At the meeting of march 25th 1935, de Possel attempts a coup d’état. He comes up with an entirely new plan for the summer-congress. Paul Valéry, the French poet, essayist, and philosopher (in the notules he is described as ‘le célebre fantaisiste’) proposed the Bourbaki-group to use his ‘centre universitaire mediterranéen’ (the proto-University of Nice) as their place of venue. They could choose any period between july and october and they wouldn’t have to pay a thing! de Possel was in contact with Valéry at that time, he was writing a 44 page booklet on game theory Sur la théorie mathématique des jeux de hasard et de réflexion, with a preface by Paul Valéry, which appeared later in 1937 via Valéry’s center for mediterranean studies.

There is one small catch though … Valéry insists that de Possel should be president of the Bourbaki-group during the meeting! Naturally, this wasn’t received enthusiastically by the others, but they didn’t rule the plan out, requesting additional information and observing that july and august may be way too hot in Nice.

The next meeting (May 6th 1935), de Possel tries to increase the pressure by asserting that the original Besse-plan is in danger because “Les naturalistes de Clermond-Ferrand semblent vouloir se servir de ce qui leur appartient” (the biologists of Clermond-Ferrand want to use their facilities themselves). But the others are not impressed and they give de Possel “pleins pouvoirs pour réagir avec violence.”

A fortnight later, Weil demands to know the latest on the Besse-negotiations and de Possel replies “en principe les biologistes de Clermond-Ferrand pourront y séjourner des le 15 juin, il y a tout lieu de présumer que ces derniers ne seront que trois ou quatre; ils seront donc fort peu génante étant donné le nombre des locaux dont nous pourrons disposer”, that is, there won’t be more than 3 or 4 biologists around, and, there’s plenty of room for everyone!

Putsch averted, the Bourbakis can start packing their suitcases, hire a secretary for the meeting, and split the costs among all committee-members. Because even this circulaire is preserved, we now know such trivia as the cost of full-pension in the Besse-Hotel with the excellent kitchen : 25 Ffr/day…

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When was the Bourbaki wedding?

It’s great fun trying to decode some of the puns contained in Betti Bourbaki’s wedding invitation. Below a photograph, taken on May 13th 1939, of three of the practical jokers (from left to right : Ralph Boas, Frank Smithies and Andre Weil), the others were Claude Chabauty, Weil’s wife Eveline and Louis Bouckaert (from Louvain).



Part of this picture is on the front cover of the book Lion Hunting & other Mathematical Pursuits. This book clarifies the ‘Secrétaire de l’Oevre du Sou du Lion’-phrase as well as some of the names on the card.

Inspired by the Bourbaki-hoax, a group of postdoctoral fellows visiting Princeton University in 1937-1938 (Boas, Smithies and John Tuckey) published their inventions, allegedly devised by Hector Pétard (aka ‘H(oist) W(ith) O(wn) Petard’ after the Shakespeare line “For ’tis the sport to have the engineer, hoist with his own petard…” Hamlet act III scene IV) who was writing under the pseudonym of E.S. Pondiczery. Pétard’s existence was asserted in the paper “A Contribution to the Mathematical Theory of Big-Game Hunting” Amer. Math. Monthly 45 (1938) 446-447.

Smithies recalls the spring 1939 period in Cambridge as follows : “The climax of the academic year, as far as we were concerned, came in the Easter term. André Weil, Claude Chabauty, and Louis Bouckaert (from Louvain) were all in Cambridge, and the proposal was mooted that a marriage should be arranged between Bourbaki’s daughter Betti and Hector Pétard; the marriage announcement was duly printed in the canonical French style – on it Pétard was described as the ward of Ersatz Stanislas Pondiczery – and it was circulated to the friends of both parties. A couple of weeks later the Weils, Louis Bouckaert, Max Krook (a South African astrophysicist), Ralph and myself made a river excursion to Grantchester by punt and canoe to have tea at the Red Lion; there is a photograph of Ralph and myself, with our triumphantly captured lion between us and André Weil looking benevolently on.”

From this and the date of the photograph (May 13th 1939) one can conclude that the marriage-card was drawn up around mid april 1939. As weddings tend to follow their announcement by a couple of months, this contradicts the following passage from Notice sur la Vie et l ‘oeuvre de Nicolas Bourbaki by an unidentified author :



“Nominated as Privat-Dozent at the University of Dorpat in 1913, he (that is, N. Bourbaki) married two years later; a single girl, Betti, married in 1938 to the Lion hunter H. Pétard, was born out of this marriage.”

But then, when was the Bourbaki-Pétard wedding scheduled? Surely, a wedding announcement should provide that information. Here’s the relevant part :



“The trivial isomorphism (aka the sacrament of matrimony) will be given to them by P. Adic, of the Diophantine Order, at the Principal Cohomology of the Universal Variety, the 3 Cartember, year VI, at the usual hour.”

Here’s my guess : the first Bourbaki-meeting took place December 10th 1934. Actually, it was a ‘proto-Bourbaki-meeting’, but nevertheless founding members such as [Jean Delsarte counted 1934 as the first Bourbaki year as is clear from the ‘Remarque’ at the top of his notes of the first meeting : 34+25=59, trying to figure out when the 25-year festivity was going to be held …



Thus, if 1934 is year 1 of the Bourbaki-calender, year VI should be 1939. The notules also give a hint of ‘the usual hour’. In the 1934-1940 period, the Bourbakis met twice a month before the monday-afternoon seminar, at 12 o’clock sharp, the ‘sacred hour’, for a meeting over lunch.

Remains the ‘Cartembre’-puzzle. We know ‘Septembre (7), Novembre (9), Decembre (10)’ so if ‘Cart’ is short for ‘Quatre’ (4), Cartembre might be June. I guess the wedding was scheduled to be held on June 3rd, 1939 at 12h.

It fits with the date the announcement was drawn up and June 3rd, 1939 sure enough was a saturday, the ‘canonical’ day for a wedding. Remains the problem of the wedding place. Suggestions anyone?

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Bourbakism & the queen bee syndrome

Probably the smartest move I’ve made after entering math-school was to fall in love with a feminist.

Yeah well, perhaps I’ll expand a bit on this sentence another time. For now, suffice it to say that I did pick up a few words in the process, among them : the queen bee syndrome :

women who have attained senior positions do not use their power to assist struggling young women or to change the system, thereby tacitly validating it.

A recent study by the Max Planck Institute for Human Development asserts that the QBS

likely stems from women at the top who feel threatened by other women and therefore, prefer to surround themselves with men. As a result, these Queen Bees often jeapordize the promotions of other females at their companies.

Radical feminists of the late 70-ties preferred a different ‘explanation’, clearly.

Women who fought their way to the top, they said, were convinced that overcoming all obstacles along the way made them into the strong persons they became. A variant on the ‘what doesn’t kill you, makes you stronger’-mantra, quoi. These queen bees genuinely believed it to be beneficial to the next generation of young women not to offer them any shortcuts on their journey through the glass ceiling.

But, let’s return to mathematics.

By and large, the 45+generation decides about the topics that should be (or shouldn’t be) on the current math-curriculum. They also write most of the text-books and course-notes used, and inevitably, the choices they make have an impact on the new generation of math-students.

Perhaps too little thought is given to the fact that the choices we (yes, I belong to that age group) make, the topics we deem important for new students to master, are heavily influenced by our own experiences.

In the late 60ties, early 70ties, Bourbaki-style mathematics influenced the ‘modern mathematics’ revolution in schools, certainly in Belgium through the influence of George Papy.

In kintergarten, kids learned the basics of set theory. Utensils to draw Venn diagrams were as indispensable as are pocket-calculators today. In secondary school, we had a formal axiomatic approach to geometry, we learned abstract topological spaces and other advanced topics.

Our 45+generation greatly benefitted from all of this when we started doing research. We felt comfortable with the (in retrospect, over)abstraction of the EGAs and SGAs and had little difficulties in using them or generalizing them to noncommutative levels…

Bourbakism made us into stronger mathematicians. Hence, we are convinced that new students should master it if they ever want to do ‘proper’ research.

Perhaps we pay too little attention to the fact that these new students are a lot worse prepared than we were in the old days. Every revolution inevitably provokes a counter-revolution. Secondary school mathematics sank over the last two decades to a debilitating level under the pretense of ‘usability’. Tim Gowers has an interesting Ivory tower post on this.

We may deplore this evolution, we may try to reverse it. But, until we succeed, it may not be fair to freshmen to continue stubbornly as if nothing changed since our good old days.

Perhaps, Bourbakism has become our very own queen bee syndrome…

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