Last year we managed to solve the first few riddles of the Bourbaki code, but several mysteries still remain. For example, who was the priest performing the Bourbaki-Petard wedding ceremony? The ‘faire part’ identifies him as ‘le P. Adique, de l’Ordre des Diophantiens’.

As with many of these Bourbaki-jokes, this riddle too has several layers. There is the first straightforward mathematical interpretation of the p-adic numbers being used in the study of Diophantine problems.

For example, the local-global, or Hasse principle, asserting that an integral quadratic form has a solution if and only if there are solutions over all p-adic numbers. Helmut Hasse was a German number theorist, held in high esteem by the Bourbaki group.

After graduating from the ENS in 1929, Claude Chevalley spent some time at the University of Marburg, studying under Helmut Hasse. Hasse had come to Marburg when Kurt Hensel (who invented the p-adic numbers in 1902) retired in 1930.

Hasse picked up a question from E. Artin’s dissertation about the zeta function of an algebraic curve over a finite field and achieved the first breakthrough establishing the conjectured property for zeta functions of elliptic curves (genus one).

Extending this result to higher genus was the principal problem Andre Weil was working on at the time of the wedding-card-joke. In 1940 he would be able to settle the general case. What we now know as the Hasse-Weil theorem implies that the number N(p) of rational points of an elliptic curve over the finite field Z/pZ, where p is a prime, can differ from the mean value p+1 by at most twice the square root of p.

So, Helmut Hasse is a passable candidate for the first-level, mathematical, decoding of ‘le P. adique’.

However, there is often a deeper and more subtle reading of a Bourbaki-joke, intended to be understood only by the select inner circle of ‘normaliens’ (graduates of the Ecole Normale Superieure). Usually, this second-level interpretation requires knowledge of events or locations within the 5-th arrondissement of Paris, the large neighborhood of the ENS.

For an outsider (both non-Parisian and non-normalien) decoding this hidden message is substantially harder and requires a good deal of luck.

As it happens, I’m going through a ‘Weil-phase’ and just started reading the three main Weil-biographies : Andre Weil the Apprenticeship of a Mathematician, Chez les Weil : André et Simone by Sylvie Weil and La vie de Simone Weil by Simone Petrement.

From page 35 of ‘Chez les Weil’ : “Après la guerre, pas tout de suite mais en 1948, toute la famille avait fini par revenir à Paris, rue Auguste-Comte, en face des jardins du Luxembourg.” Sylvie talks about the Parisian apartment of her grandparents (father and mother of Andre and Simone) and I wanted to know its exact location.

More details are given on page 103 of ‘La vie de Simone Weil’. The apartment consists of the 6th and 7th floor of a building on the Montagne Sainte-Geneviève. The Weils bought it before it was even built and when they moved in, in may 1929, it was still unfinished. Compensating this, the apartment offered a splendid view of the Sacre-Coeur, the Eiffel-tower, la Sorbonne, Invalides, l’Arc de Triomphe, Pantheon, the roofs of the Louvre, le tout Paris quoi…

As to its location : “Juste au-dessous de l’appartement se trouvent l’Ecole des mines et les serres du Luxembourg, avec la belle maison ancienne où mourut Leconte de Lisle.” This and a bit of googling allows one to deduce that the Weils lived at 3, rue Auguste-Comte (the W on the map below).

Crossing the boulevard Saint-Michel, one enters the 5-th arrondissement via the … rue de l’Abbe de l’Epee… We did deduce before that the priest might be an abbot (‘from the order of the Diophantines’) and l’Epee is just ‘le P.’ pronounced in French (cheating one egue).

Abbé Charles-Michel de l’Épée lived in the 18th century and has become known as the “Father of the Deaf” (compare this to Diophantus who is called “Father of Algebra”). Épée turned his attention toward charitable services for the poor, and he had a chance encounter with two young deaf sisters who communicated using a sign language. Épée decided to dedicate himself to the education and salvation of the deaf, and, in 1760, he founded a school which became in 1791 l’Institution Nationale des Sourds-Muets à Paris. It was later renamed the Institut St. Jacques (compare Rue St. Jacques) and then renamed again to its present name: Institut National de Jeunes Sourds de Paris located at 254, rue Saint-Jacques (the A in the map below) just one block away from the Schola Cantorum at 269, rue St. Jacques, where the Bourbaki-Petard wedding took place (the S in the map).

Completing the map with the location of the Ecole Normale (the E) I was baffled by the result. If the Weil apartment stands for West, the Ecole for East and the Schola for South, surely there must be an N (for N.Bourbaki?) representing North. Suggestions anyone?

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A few days before Halloween, Norbert Dufourcq (who died december 17th 1990…), sent me a comment, containing lots of useful information, hinting I did get it wrong about the church of the Bourbali wedding in the previous post.

Norbert Dufourcq, an organist and student of Andre Machall, the organist-in-charge at the Saint-Germain-des-Prés church in 1939, the place where I speculated the Bourbaki wedding took place, concluded his comment with :

“P.S. Lieven, you do know about the Schola Cantorum, now, don’t you?!?”.

Euh… actually … no, I did not …

La Schola Cantorum is a private music school in Paris. It was founded in 1894 by Charles Bordes, Alexandre Guilmant and Vincent d’Indy as a counterbalance to the Paris Conservatoire’s emphasis on opera. Its alumni include many significant figures in 20th century music, such as Erik Satie and Cole Porter.

Schola Cantorum is situated 69, rue Saint Jacques, Paris, just around the corner of the Ecole Normal Superieure, home base to the Bourbakis. In fact, closer investigation reveals striking similarities and very close connections between the circle of artists at la Schola and the Bourbaki group.

In december 1934, the exact month the Bourbaki group was formed, a radical reorganisation took place at the Schola, when Nestor Lejeune became the new director. He invited several young musicians, many from the famous Dukas-class, to take up teaching positions at the Schola.

Here’s a picture of part of the Dukas class of 1929, several of its members will play a role in the upcoming events : from left to right next to the piano : Pierre Maillard-Verger, Elsa Barraine, Yvonne Desportes, Tony Aubin, Pierre Revel, Georges Favre, Paul Dukas, René Duclos, Georges Hugon, Maurice Duruflé. Seated on the right : Claude Arrieu, Olivier Messiaen.

The mid-1930s in Paris saw the emergence of two closely-related groups with a membership which overlapped : La Spirale and La Jeune France. La Spirale was founded in 1935 under the leadership of Georges Migot; its other committee members were Paul Le Flem, his pupil André Jolivet, Edouard Sciortino, Claire Delbos, her husband Olivier Messiaen, Daniel-Lesur and Jules Le Febvre. The common link between almost all of these musicians was their connection with the Schola Cantorum.

On the left : Les Jeunes Musiciens Français : André Jolivet on the Piano. Standing from left to right : Olivier Messiaen, Yves Baudrier, Daniel-Lesur.

Nigel Simeone wrote this about Messiaen and La Jeune France : “The extremely original and independent-minded Messiaen had already shown himself to be a rather unexpected enthusiast for joining groups: in December 1932 he wrote to his friend Claude Arrieu about a letter from another musician, Jacques Porte, outlining plans for a new society to be called Les Jeunes Musiciens Français. Messiaen agreed to become its vice-president, but nothing seems to have come of the project. Six months later, in June 1933, he had a frustrating meeting with Roger Désormière on behalf of the composers he described to Arrieu as ‘les quatre’, all of them Dukas pupils: Elsa Barraine, the recently-deceased Jean Cartan, Arrieu and Messiaen himself; during the early 1930s Messiaen and Arrieu organised concerts featuring all four composers.”

Finally, we’re getting a connection with the Bourbaki group! Norbert Dufourcq mentioned it already in his comment “Messiaen was also a good friend of Jean Cartan (himself a composer, and Henri’s brother)”. Henri Cartan was one of the first Bourbakis and an excellent piano player himself.

The Cartan family picture on the right : standing from left to right, father Elie Cartan (one of the few older French mathematicians respected by the Bourbakis), Henri and his mother Marie-Louise. Seated, the younger children, from left to right : Louis, Helene (who later became a mathematician, herself) and the composer Jean Cartan, who sadly died very young from tuberculoses in 1932…

The december 1934 revolution in French music at the Schola Cantorum, instigated by Messiaen and followers, was the culmination of a process that started a few years before when Jean Cartan was among the circle of revolutionados. Because Messiaen was a fiend of the Cartan family, they surely must have been aware of the events at the Schola (or because it was merely a block away from the ENS), and, the musicians’ revolt may very well have been an example to follow for the first Bourbakis…(?!)

Anyway, we now know the intended meaning of the line “with lemmas sung by the Scholia Cartanorum” on the wedding-invitation. Cartanorum is NOT (as I claimed last time) bad Latin for ‘Cartesiorum’, leading to Descartes and the Saint-Germain-des-Pres church, but is in fact passable Latin (plur. gen.) of CARTAN(us), whence the translation “with lemmas sung by the school of the Cartans”. There’s possibly a double pun intended here : first, a reference to (father) Cartan’s lemma and, of course, to La Schola where the musical Cartan-family felt at home.

Fine, but does this brings us any closer to the intended place of the Bourbaki-Petard wedding? Well, let’s reconsider the hidden ‘clues’ we discovered last time : the phrase “They will receive the trivial isomorphism from P. Adic, of the Order of the Diophantines” might suggest that the church belongs to a a religious order and is perhaps an abbey- or convent-church and the phrase “the organ will be played by Monsieur Modulo” requires us to identify this mysterious Mister Modulo, because Norbert Dufourcq rightfully observed :

“note however that in 1939, it wasn’t as common to have a friend-organist perform at a wedding as it is today: the appointed organists, especially at prestigious Paris positions, were much less likely to accept someone play in their stead.”

The history of La Schola Cantorum reveals something that might have amused Frank Smithies (remember he was one of the wedding-invitation-composers) : the Schola is located in the Convent(!) of the Brittish Benedictines…

In 1640 some Benedictine monks, on the run after the religious schism in Britain, found safety in Paris under the protection of Cardinal Richelieu and Anne of Austria at Val-de-Grace, where the Schola is now housed.

As is the case with most convents, the convent of the Brittish Benedictines did have its own convent church, now called l’église royale Notre-Dame du Val-de-Grâce (remember that one of the possible interpretations for “of the universal variety” was that the name of the church would be “Notre-Dame”…).

This church is presently used as the concert hall of La Schola and is famous for its … musical organ : “In 1853, Aristide Cavaillé-Coll installed a new organ in the Church of Sainte-geneviève which had been restored in its rôle as a place of worship by Prince President Louis-Napoléon. In 1885, upon the decision of President Jules Grévy, this church once again became the Pantheon and, six years later, according to an understanding between the War and Public Works Departments, the organ was transferred to the Val-de-Grâce, under the supervision of the organ builder Merklin. Beforehand, the last time it was heard in the Pantheon must have been for the funeral service of Victor Hugo. In 1927, a raising was carried out by the builder Paul-Marie Koenig, and the inaugural concert was given by André Marchal and Achille Philippe, the church’s organist. Added to the register of historic monument in 1979, Val-de-Grâce’s “ little great organ ”, as Cavaillé-Coll called it, was restored in 1993 by the organ builders François Delangue and Bernard Hurvy. The organ of Val-de-Grâce is one the rare parisian surviving witnesses of the art of Aristide Cavaillé-Coll, an instrument that escaped abusive and definitive transformations or modernizations. This explain why, in spite of its relatively modest scale, this organ enjoys quite a reputation, and this, as far as the United States.”

By why would the Val-de-Grace organiste at the time Achille Philip, “organiste titulaire du Val-de-Grâce de 1903 à 1950 et professeur d’orgue et d’harmonie à la Schola Cantorum de 1904 à 1950″, be called ‘Mister Modulo’ in the wedding-invitations line “L’orgue sera tenu par Monsieur Modulo”???

Again, the late Norbert Dufourcq comes to our rescue, proposing a good candidate for ‘Monsieur Modulo’ : “As for “modulo”, note that the organist at Notre-Dame at that time, Léonce de Saint-Martin, was also the composer of a “Suite Cyclique”, though I admit that this is just wordplay: there is nothing “modular” about this work. Maybe a more serious candidate would be Olivier Messiaen (who was organist at the Église de la Trinité): his “modes à transposition limitée” are really about Z/12Z→Z/3Z and Z/12Z→Z/4Z. “

Messiaen’s ‘Modes of limited transposition’ were compiled in his book ‘Technique de mon langage musical’. This book was published in Paris by Leduc, as late as 1944, 5 years after the wedding-invitation.

Still, several earlier works of Messiaen used these schemes, most notably La Nativité du Seigneur, composed in 1935 : “The work is one of the earliest to feature elements that were to become key to Messiaen’s later compositions, such as the extensive use of the composer’s own modes of limited transposition, as well as influence from birdsong, and the meters and rhythms of Ancient Greek and traditional Indian music.”

More details on Messiaen’s modes and their connection to modular arithmetic can be found in the study Implementing Modality in Algorithmic Composition by Vincent Joseph Manzo.

Hence, Messiaen is a suitable candidate for the title ‘Monsieur Modulo’, but would he be able to play the Val-de-Grace organ while not being the resident organist?

Remember, the Val-de-Grace church was the concert hall of La Schola, and its musical organ the instrument of choice for the relevant courses. Now … Olivier Messiaen taught at the Schola Cantorum and the École Normale de Musique from 1936 till 1939. So, at the time of the Bourbaki-Petard wedding he would certainly be allowed to play the Cavaillé-Coll organ.

Perhaps we got it right, the second time around : the Bourbaki-Pétard wedding was held on June 3rd 1939 in the church ‘l’église royale Notre-Dame du Val-de-Grâce’ at 12h?

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I’m pretty certain I got the intended date & time of the Bourbaki-Pétard wedding right : June 3rd 1939 at 12h. Finding the exact location of the wedding-ceremony is an entirely different matter. And, quite probably, we are reading way too much in these pranks of the Weil-clan.

Still, it’s fun trying to find an elegant answer, based on the (intended or imagined) clues in the text and the little we know about the early Bourbaki-days. Here, the translation of the relevant part of the wedding announcement :

“They will receive the trivial isomorphism from P. Adic, of the Order of the Diophantines, in the Principal Cohomology of the Universal Variety, on the third of Cartember, year VI, at the usual hour.
The organ will be played by Monsieur Modulo, Assintant Simplex of the Grassmannian (with lemmas sung by the Scholia Cartanorum). The collection will be donated in full to the retirement home for Poor Abstracts. Convergence will be guaranteed.”

First solution : Perhaps one might read “in the Principal Cohomology of the Universal Variety” as : “in the Principal Church of the generic type/name”. In many French cities the main church is the Cathedral and an awful lot of them are called Notre Dame, so it might mean : in the Notre Dame Cathedral. But even then, we have to choose between these two

On the left, the Notre Dame Cathedral in Paris. On the right the Cathédrale Notre-Dame-de-l’Annonciation in Nancy. As the invitation promises guests to be entertained after the ceremony by Monsieur et Madame Bourbaki at their ‘Fundamental Domains’, the choice depends on the location of the Bourbaki-household in June 1939.

‘Bourbaki’ made two applications to become an AMS-member. The first, in 1948, tells us that Bourbaki is a scientific advisor to the Hermann Publishing Co. in Paris since 1934, and, the second in 1950, that he is ‘Directeur Libre de Recherches a l’Université de Nancy’. I couldn’t find out when exactly Nicolas did change cities, and even Liliane Beaulieu’s talk Bourbaki a Nancy does not provide an answer.

Second solution : Or, one can read that sentence as a mathematical, perhaps proto-motivic, statement, and, hunt for clues elsewhere in the text. But then, what are these clues?

• Mass is celebrated by “P. Adic, of the Order of the Diophantines”. This suggests that the church itself belongs to a monastic order, and is perhaps a convent-church.
• Hymns are “sung by the Scholia Cartanorum”. Scholia Cartanorum is Latin of sorts and refers perhaps to the Paris’ Latin Quarter, le Quartier Latin.
• The collection is donated to the “retirement home for Poor Abstracts”. Perhaps the church is connected to a saint for the poor.

Let’s consider “Scholia Cartanorum” more closely. It may be Latin, admittedly very bad Latin, for ‘the Scholiums of Cartesius’, that is, ‘of Descartes‘.

One of the more famous ‘Scholia’ in scientific history is Newton’s general scholium to the Principia, which is a prime example of Descartes-bashing. Newton attacks Descartes on his vortical theory of planetary motion, his aeter to explain gravity, his God-axiom (unlike Descartes, Newton induced God from nature, rather than starting with God as an axiom) and his hypothetico-deductive method. So, there is a link between Descartes and ‘Scholium’, although the genitive form ‘Cartesiorum’ might be fairly inappropriate…

But then, Descartes died on 11 February 1650 in Stockholm (Sweden) where he was buried, so there won’t be a connection to a French or Parisian church, right? Well, not quite. The fate of Descartes’ remains is a rather strange story : “In 1666, sixteen years after his death, the bones of René Descartes were dug up in the middle of the night and transported from Sweden to France under the watchful eye of the French Ambassador. This was only the beginning of the journey for Descartes’ bones, which, over the next 350 years, were fought over, stolen, sold, revered as relics, studied by scientists, used in séances, and passed surreptitiously from hand to hand. ” For example, during the French Revolution, his remains were disinterred for burial in the Pantheon in Paris among the great French thinkers. But today, his ashes are burried in…

the abbay church of Saint-Germain-des-Prés, located in the Quartier Latin, within walking distance of the Bourbaki-café Capoulade and the Ecole Normal Superieure.

Now all the hints fall handsomely in place. St-Germain-des-Prés is the oldest church in Paris. Parts of it date to the 6th century, when a Benedictine abbey was founded on the site by Childebert, son of Clovis. Hence the sentence ‘in the Principal Cohomology of the Universal Variety’ might simply mean ‘in the first church, ever’. In medieval times, the Left Bank of Paris was prone to flooding from the Seine, so much of the land could not be built upon and the Abbey stood in the middle of fields, or prés in French, thereby explaining its appellation.

The other part of its name, Saint Germain, comes from Saint Germanus of Paris, also known as the ‘father of the poor’ (!). His remains were interred in St. Symphorien’s chapel in the vestibule of St. Vincent’s church, but in 754, when he was canonized, his relics were solemnly removed into the body of the church, in the presence of Pepin and his son, Charlemagne, then a child of seven, and the church was reconsecrated as Saint-Germain-des-Prés. That is, also the remains of the ‘father of the poor’ are buried in this church.

Here’s my best guess : the Bourbaki-Pétard wedding was held on June 3rd 1939 in the church Saint-Germain-des-Prés at 12h. Genuine aficionados of the Da Vinci code may regret it wasn’t held in the neighboring Saint-Sulpice church, but then, perhaps someone can bend the clues accordingly…

Remains this problem : who was the organist, Monsieur Modulo? Suggestions anyone?

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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.

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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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