Category: stories

the bumpy road to the first Bourbaki congress

Published October 22, 2009 by lievenlb

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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The artist and the mathematician

Published October 19, 2009 by lievenlb

Over the week-end I read The artist and the mathematician (subtitle : The story of Nicolas Bourbaki, the genius mathematician who never existed) by Amir D. Aczel.

Whereas the central character of the book should be Bourbaki, it focusses more on two of Bourbaki’s most colorful members, André Weil and Alexander Grothendieck, and the many stories and myths surrounding them.

The opening chapter (‘The Disappearance’) describes the Grothendieck’s early years (based on the excellent paper by Allyn Jackson Comme Appelé du Néant ) and his disappearance in the Pyrenees in the final years of last century. The next chapter (‘An Arrest in Finland’) recount the pre-WW2 years of Weil and the myth of his arrest in Finland and his near escape from execution (based on Weil’s memoires The Apprenticeship of a Mathematician). Chapter seven (‘The Café’) describes the first 10 proto-Bourbaki meetings following closely the study ‘A Parisian Café and Ten Proto-Bourbaki Meetings (1934-1935)‘ by Liliane Beaulieu. Etc. etc.

All the good ‘Bourbaki’-stories get a place in this book, not always historically correct. For example, on page 90 it is suggested that all of the following jokes were pulled at the Besse-conference, July 1935 : the baptizing of Nicolas, the writing of the Comptes-Rendus paper, the invention of the Bourbaki-daughter Betti and the printing of the wedding invitation card. In reality, all of these date from much later, the first two from the autumn of 1935, the final two no sooner than april 1939…

One thing I like about this book is the connection it makes with other disciplines, showing the influence of Bourbaki’s insistence on ‘structuralism’ in fields as different as philosophy, linguistics, anthropology and literary criticism. One example being Weil’s group-theoretic solution to the marriage-rules problem in tribes of Australian aborigines studied by Claude Lévi-Strauss, another the literary group Oulipo copying Bourbaki’s work-method.

Another interesting part is Aczel’s analysis of Bourbaki’s end. In the late 50ties, Grothendieck tried to convince his fellow Bourbakis to redo their work on the foundations of mathematics, changing these from set theory to category theory. He failed as others felt that the foundations had already been laid and there was no going back. Grothendieck left, and Bourbaki would gradually decline following its refusal to accept new methods. In Grothendieck’s own words (in “Promenade” 63, n. 78, as translated by Aczel) :

“Additionally, since the 1950s, the idea of structure has become passé, superseded by the influx of new ‘categorical’ methods in certain of the most dynamical areas of mathematics, such as topology or algebraic geometry. (Thus, the notion of ‘topos’ refuses to enter into the ‘Bourbaki sack’ os structures, decidedly already too full!) In making this decision, in full cognizance, not to engage in this revision, Bourbaki has itself renounced its initial ambition, which has been to furnish both the foundations and the basic language for all of modern mathematics.”

Finally, it is interesting to watch Aczel’s own transformation throughout the book, from slavishly copying the existing Weil-myths and pranks at the beginning of the book, to the following harsh criticism on Weil, towards the end (p. 209) :

“From other information in his autobiography, one gets the distinct impression that Weil was infatuated with the childish pranks of ‘inventing’ a person who never existed, creating for him false papers and a false identity, complete with a daughter, Betti, who even gets married, parents and relatives, and membership in a nonexistent Academy of Sciences of the nonexistent nation of Polvedia (sic).
Weil was so taken with these activities that he even listed, as his only honor by the time of his death ‘Member, Poldevian Academy of Sciences’. It seems that Weil could simply not go beyond these games: he could not grasp the deep significance and power of the organization he helped found. He was too close, and thus unable to see the great achievements Bourbaki was producing and to acknowledge and promote these achievements. Bourbaki changed the way we do mathematics, but Weil really saw only the pranks and the creation of a nonexistent person.”

Judging from my own reluctance to continue with the series on the Bourbaki code, an overdose reading about Weil’s life appears to have this effect on people…

Where is the Royal Poldavian Academy?

Published October 11, 2009 by lievenlb

Among the items found on Andre Weil at the time of his arrest was “a packet of calling cards belonging
to Nicolas Bourbaki, member of the Royal Academy of Poldavia”.

But then, where is the Royal Poldavian Academy situated? Well, surely in the Kingdom of Poldavia, which is a very strange country indeed, its currency unit being the bourbaki and there exist only two types of coins: gold ones (worth n bourbakis) and silver ones (worth m bourbakis). Using gold and silver coins, it is possible to obtain sums such as 10000 bourbakis, 1875 bourbakis, 3072 bourbakis, and so on. Prove that any payment above mn-2 bourbakis can be made without the need to receive change.

However, the Kingdom of Poldavia isn’t another Bourbaki concoction. The name goes back at least to a joke pulled by the right-wingers of the Action Francaise in may 1929. Here’s the TIME article of May 20th 1929 :

“When 28 French Republican deputies sat down to their breakfast coffee and croissants early last week, each found a large crinkly letter from Geneva in his morning’s mail. Innocent and refreshed after a sound night’s sleep, not one Republican deputy saw anything untoward in the fact that the large crinkly letters were embossed on the stationery of “Foreign Minister Lamidaeff, of the Kingdom of Poldavia.” They saw nothing strange in the fact that Poldavians were in financial difficulties, and they found Minister Lamidaeff most thoughtful in not asking for money, but merely for an expression of “moral support” from the Deputies in his campaign to aid Poldavian sufferers. “We believe that our interests were betrayed at the Peace Conference,” wrote Poldavian Lamidaeff. “and we appeal to you as a member of the French Parliament to do your utmost to help us in this our hour of need. The whole nation of Poldavia and its noble monarch who disregarded personal safety in 1916, and joined France in her War for justice and righteousness, pray you to remember our sacrifices.”

What could be fairer than that? Legislators all over the world are always ready to write enthusiastic platitudes in favor of anything that sounds like a good cause. The wronged Poldavians seemed a very good cause. Each of the 28 deputies sat down at his desk and pledged his moral support to “Foreign Minister Lamidaeff of Poldavia.”

None of the 28 deputies noticed that the old Poldavian name of Lamidaeff might read “I’Ami d’A. F.”—”the friend of A. F.,” “the friend of L’Action Française” famed royalist newspaper of which the editor is Leon Daudet, bon vivant, practical jokester, son of famed Author Alphonse Daudet (Tartarin de Tarascon), exile from the republic he has so consistently lampooned (TIME, June 13, 1927, et seq.). Three days after the 28 gullible deputies replied to the “Poldavian Minister,” a special edition of L’Action Française appeared.

“People of France,” wrote exiled Editor Daudet, who once escaped from La Sante prison through a hoaxed release order telephoned from the office of the Minister of the Interior, “—People of France, how much longer will you permit such ignorant deputies to represent you before the world? Here are 28 of your elected representatives, and they actually believe there is a Kingdom of Poldavia, and that Lamidaeff is its Foreign Minister. Lamidaeff, c’est moi!””

The consul of Poldavia also appears in the 1936 Tintin-story The Blue Lotus by Hergé. In view of the above AF-connection, it should’t come as a surprise that Hergé is often accused of extreme-right sympathies and racism.

To some, Poldavia is a small country in the Balkans, to others it lies in the Caucasus, but has disappeared from the map of Europe. All accounts do agree on one point, namely that Poldavia is a mountainous region.

Today we are pleased to disclose the exact location of the Royal Poldavian Academy, and, thanks to the wonders of Google Earth you can explore the Kingdom of Poldavia at your leisure if you give it the coordinates 45.521082N,2.935495E. Or, you can use the Google-map below :

View Larger Map

The evidence is based on a letter sent by Andre Weil to Elie Cartan when the Bourbakis wanted to submit a note for the Comptes Rendus des Séances Hebdomadaires de l’Académie des Sciences under the pseudonyme Nicolas Bourbaki. As the academy requires a biographical note on the author, Weil provided the following information about Bourbaki’s life :

“Cher Monsieur,
Je vous envoie ci-joint, pour les C.R., une note que M.Bourbaki m’a chargé de vous transmettre. Vous n’ignorez pas que M.Bourbaki est cet ancien professeur à l’Université Royale de Besse-en-Poldévie, dont j’ai fait la connaissance il y a quelque temps dans un café de Clichy où il passe la plus grande partie de la journée et même de la nuit ; ayant perdu, non seulement sa situation, mais presque toute sa fortune dans les troubles qui firent disparaître de la carte d’Europe la malheureuse nation poldève, il gagne maintenant sa vie en donnant, dans ce café, des leçons de belote, jeu où il est de première force.
Il fait profession de ne plus s’occuper de mathématiques, mais il a bien voulu cependant s’entretenir avec moi de quelques questions importantes et même [ajout manuscrit : me laisser] jeter un coup d’œil sur une partie de ses papiers ; et j’ai réussi à le persuader de publier, pour commencer, la note ci-jointe, qui contient un résultat fort utile pour la théorie moderne de l’intégration, je pense que vous ne verrez pas de difficulté à l’accueillir pour les Comptes-Rendus ; si même les renseignements que je vous donne au sujet de M.Bourbaki ne paraissaient pas suffisamment clairs, j’imagine qu’il n’appartient à l’Académie, et en particulier à celui qui présente la note, que de s’assurer de la valeur scientifique de celle-ci, et non de faire une enquête au sujet de l’auteur. Or j’ai examiné soigneusement le résultat de M.Bourbaki, et son exactitude est hors de doute.
Veuillez recevoir, je vous prie, les remerciements de M.Bourbaki et les miens, et croyez toujours à mes sentiments bien affectueusement et respectueusement dévoués.
A.Weil”

That is, ‘Besse-en-Poldevie’, or simply ‘Besse’ as in this line from the wedding announcement “Mademoiselle Betti Bourbaki, a former student of the Well-Ordereds of Besse” must be the capital of Poldavia where the Academy is housed.

You may have never heard of Poldavia, but if you are a skiing or cycling enthusiast, the name of its capital sure does ring a bell, or rather so does the name of its sub-part Super Besse. The winter sports resort of Super Besse is located in the commune of Besse-et-Saint-Anastaise in the Parc naturel régional des volcans d’Auvergne in the department of Puy de Dôme, in Auvergne. Situated approximately 50 km from Clermont-Ferrand, it is located at an altitude of 1350 m on the slopes of Puy de Sancy, Puy de la Perdrix and Puy Ferrand. Surely a mountainous region …

Besse-et-Saint-Anastaise, or rather Besse-en-Chandesse as it was formerly called, was the venue of the very first Bourbaki Congres 1935. Surely, they used the ‘Royal Poldavian Academy’ as their meeting place. But, where is it?

At the Besse meeting were present : Claude Chevalley, Jean Dieudonné, René de Possel, Henri Cartan, Szolem Mandelbrojt, Jean Delsarte, André Weil, the physicist Jean Coulomb, Charles Ehresmann and a ‘cobaye’ called Mirles.

Of these men three held a position at the University Blaise Pascal of Clermont-Ferrand : Mandelbrojt, de Possel and Coulomb and they arranged that the Bourbaki-group could use the universities’ biology-outpost in Besse-en-Chandesse. Photographic evidence for this is provided by the man standing apart in the right hand-picture above : the biologist Luc Olivier.

Concluding : the Royal Poldavian Academy is located at the ‘Station Biologique de l’Université Blaise Pascal’, Rue du Lavoir, Besse-et-Saint-Anastaise.

On July 12th 2003 a ceremony was held at the Biology-station commemorating the birth of Nicolas Bourbaki (the group), supposedly born July 12th 1935. A plate at an exterior wall of the Biology-station was unveiled.

More information about the mysterious country of Poldavia can be found in the article La verité sur la Poldévie by Michele Audin.