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Category: tBC

What happened on the Bourbaki wedding day?

Early on in this series we deciphered part of the Bourbaki wedding invitation

The wedding was planned on “le 3 Cartembre, an VI” or, for non-Bourbakistas, June 3rd 1939. But, why did they choose that particular day?

Because the wedding-invitation-joke was concocted sometime between mid april and mid may 1939, the most probable explanation clearly is that they took a calendar and scheduled their fake wedding on a saturday not too far in the future.

Or, could it be that the invitation indeed contained a coded message pointing to an important event (at least as far as Bourbaki or the Weils were concerned) taking place in Paris on June 3rd 1939?

Unlikely? Well, what about this story:

André Malraux was a French writer and later statesman. He was noted especially for his novel La Condition Humaine (1933).

During the 1930s, Malraux was active in the anti-fascist Popular Front in France. At the beginning of the Spanish Civil War he joined the Republican forces in Spain, serving in and helping to organize the small Spanish Republican Air Force. The Republic government circulated photos of Malraux’s standing next to some Potez 540 bombers suggesting that France was on their side, at a time when France and the United Kingdom had declared official neutrality.

In 1938 he published L’Espoir, a novel influenced by his Spanish war experiences. In the same year, Malraux and Boris Peskine produced a movie based on the book, filmed in Spain (in Tarragon, Collbató and Montserrat) : sierra de Teruel (later called, L’Espoir)

This wikipedia-page claims that the movie was released June 13th, 1945. But this isn’t quite correct.

The first (private) viewing of the film took place … on saturday june 3rd, 1939.

In august 1939 there was another private viewing for the Spanish Government-in-Exile, and Malraux wanted the public release to take place in september. However, after the invasion by Hitler of Poland and considerable pressure of the French amassador to Madrid, Philippe Petain, the distribution of the movie was forbidden by the government of Edouard Daladier IV.
For this reason the public release had to be postponed until after the war.

But let us return to the first viewing on Bourbaki’s wedding day. We know that a lot of authors were present. There’s evidence that Simone de Beauvoir attended and quite likely so did Simone Weil, Andre’s sister.

In 1936, despite her professed pacifism, Simone Weil fought in the Spanish Civil War on the Republican side. She identified herself as an anarchist and joined the Sébastien Faure Century, the French-speaking section of the anarchist militia.

According to her biography (p. 473) she was still in contact with Malraux and, at the time, tried in vain to convince him of the fact that the Stalin-regime was as oppressive as the fascist-regimes. So, it is quite likely she was invited to the viewing, or at least knew about it.

From Andre Weil’s auto-biography we know that letters (and even telegrams) were exchanged between him and his sister, when he was in England in the spring of 1939. So, it is quite likely that she told him about the Malraux-Sierra de Tenuel happening (see also the Escorial post).

According to the invitation the Bourbaki-wedding took place “en la Cohomologie Principale”. The private viewing of Malraux’ film took place in “Cinéma Le Paris” on the Champs Elysées.

Could it be that “Cohomologie Principale”=”Cinema Le Paris”?

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Bourbaki and the miracle of silence

The last pre-war Bourbaki congress, held in september 1938 in Dieulefit, is surrounded by mystery. Compared to previous meetings, fewer documents are preserved in the Bourbaki archives and some sentences in the surviving notules have been made illegible. We will have to determine the exact location of the Dieulefit-meeting before we can understand why this had to be done. It’s Bourbaki’s own tiny contribution to ‘le miracle de silence’…

First, the few facts we know about this Bourbaki congress, mostly from Andre Weil‘s autobiography ‘The Apprenticeship of a Mathematician’.

The meeting was held in Dieulefit in the Drome-Provencale region, sometime in september 1938 prior to the Munich Agreement (more on this next time). We know that Elie Cartan did accept Bourbaki’s invitation to join them and there is this one famous photograph of the meeting. From left to right : Simone Weil (accompanying Andre), Charles Pison, Andre Weil (hidden), Jean Dieudonne (sitting), Claude Chabauty, Charles Ehresmann, and Jean Delsarte.

Failing further written documentation, ‘all’ we have to do in order to pinpoint the exact location of the meeting is to find a match between this photograph and some building in Dieulefit…

The crucial clue is provided by the couple of sentences, on the final page of the Bourbaki-archive document deldi_001 Engagements de Dieulefit, someone (Jean Delsarte?) has tried to make illegible (probably early on).

Blowing the picture up, it isn’t too hard to guess that the header should read ‘Décision du 22 septembre 1938’ and that the first sentence is ‘Le Bourbaki de 2e classe WEIL fera pour le 15 octobre’. The document is signed

Camp de Beauvallon, le 22.IX.38.
L’adjudant de jour

Now we are getting somewhere. Beauvallon is the name of an hamlet of Dieulefit, situated approximately 2.5km to the east of the center.

Beauvallon is rather famous for its School, founded in 1929 by Marguerite Soubeyran and Catherine Krafft, which was the first ‘modern’ boarding school in France for both boys and girls having behavioral problems. From 1936 on the school’s director was Simone Monnier.

These three women were politically active and frequented several circles. Already in 1938 (at about the time of the Bourbaki congress) they knew the reality of the Nazi persecutions and planned to prepare their school to welcome, care for and protect refugees and Jewish children.

From 1936 on about 20 Spanish republican refugees found a home here and in the ‘pension’ next to the school. When the war started, about 1500 people were hidden from the German occupation in Dieulefit (having a total population of 3500) : Jewish children, intellectuals, artists, trade union leaders, etc. etc. many in the Ecole and the Pension.

Because of the towns solidarity with the refugees, none were betrayed to the Germans, Le miracle de silence à Dieulefit.
It earned the three Ecole-women the title of “Juste” after the war. More on this period can be read here.

But what does this have to do with Bourbaki? Well, we claim that the venue of the 1938 Bourbaki congress was the Ecole de Beauvallon and they probably used Le Pension for their lodgings.

We have photographic evidence comparing the Bourbaki picture with a picture taken in 1943 at the Ecole (the woman in the middle is Marguerite Soubeyran). Compare the distance between door and window, the division of the windows and the ivy on the wall.

Below two photographs of the entire school building : on the left, the school with ‘Le Pension’ next to it around 1938 (the ivy clad wall with the Bourbaki-door is to the right) and on the right, the present Ecole de Beauvallon (this site also contains a lot of historical material). The ivy has gone, but the main features of the building are still intact, only the shape of the small roof above the Bourbaki-door has changed.

During their stay, it is likely the Bourbakis became aware of the plans the school had would war break out. Probably, Jean Delsarte removed all explicit mention to the Ecole de Beauvallon from the archives upon their return. Bourbaki’s own small contribution to Dieulefit’s miracle of silence.

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Who was ‘le P. Adique’?

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 $latex \hat{\mathbb{Z}}_p$ 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.

[abp:3764326506] [abp:2283023696] [abp:2213599920]

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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Where’s Bourbaki’s Escorial?

Early 1936, Andre Weil and Evelyne Gillet made a pre-honeymooning trip to Spain and visited El Escorial. Weil was so taken by the place that he planned the next Bourbaki-conference to be held in a nearby college. However, the Bourbakis never made it to to Spain that summer as the Spanish Civil War broke out July 17th, a few weeks before the intended conference. Can we GEO-tag the exact location of Bourbaki’s “Escorial”?

As explained in the bumpy-road-post, Andre Weil and Evelyne Gillet became involved sometime in 1935.
Early 1936, they made a pre-honeymooning trip to Spain and visited El Escorial. Weil was so taken by the place that he planned the next Bourbaki-conference to be held in a nearby college.

However, the Bourbakis never made it to to Spain that summer as the Spanish Civil War broke out July 17th, a few weeks before the intended conference. Still, the second Bourbaki-meeting remains often referred to as the ‘Escorial conference’. Can we GEO-tag the exact location of Bourbaki’s “Escorial”?

Claude Chevalley came up with a Plan-B and suggested they would use his parents’ place in Chançay as their venue. Chevalley’s father was a French diplomat and his house sure did possess a matching ‘grandeur’ as can be seen from the famous picture below, taken at the (second) Chançay meeting in 1937 (Weil to the left, Chevalley to the right and Weil’s sister Simonne standing).

Thanks to the Bourbaki archives we know that the meeting took place from september 16th to 28th, that each of them had to pay 16 francs for full pension and had to bring along their own sheets and towels.

But where exactly is this beautiful house? Jacques Borowczyk has written a nice paper Bourbaki et la touraine in which he describes the Bourbaki congresses of 1936 and 1937 at the Chevalley-house in Chançay and further those held in 1956, 1957 and 1959 in ‘hôtel de la Brèche’ in Amboise.

Borowczyk places the Chevalley house in the little hamlet of Chançay, called “La Massoterie”. The village files assert that in 1931 three people were living at La Massoterie : father Abel Chevalley, who took residence there after his retirement in 1931, his wife Marguerite and their son Claude. But, at the time of the Bourbaki congres in 1936, Marguerite remained the only permanent inhabitant. Sadly,
Abel Chevalley, who together with Marguerite compiled the The concise Oxford French dictionary, died in 1934.

Usually when you know the name of the hamlet, of the village and add just to be certain ‘France’, Google Maps takes you there within metres. So, this was going to be a quick post, for a change… Well, much to my surprise, typing ‘La Massoterie, Chançay, France’ only produced the answer “We could not understand the location La Massoterie, Chançay, France”.

Did I spell it wrong? Or, did the name change over times? No, Googling for it the first hit gives you the map of a 10km walk around Chançay passing through la Massoterie!

Now what? Fortunately Borowczyk included in his paper an old map, from Napoleonic times, showing the exact location of La Massoterie (just above the flash-sign), facing the castle of Volmer. If you compare it with the picture below from present day Chançay (via Google earth) it is surprising how many of the landmarks have survived the changes over two centuries.

It is now easy to pinpoint the exact location and zoom into the Chavalley-house, and, you’re in for a small surprise : the place is called La Massotterie with 2 t’s…

Probably, Googles database is more reliable than the information provided by the village of Chançay, or the paper by Borowczyk as it is the same spelling as on the old Napoleonic map. Anyway, feel free to have a peek at Bourbaki’s Escorial yourself!


Seriously now, where was the Bourbaki wedding?

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?


Where was the Bourbaki wedding?

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?


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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Where is the Royal Poldavian Academy?

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.

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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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?


The wedding invitation that nearly killed Andre Weil

Andre Weil wrote about his arrest as a Russian spy in november 1939 :

“The manuscripts they found appeared
suspicious – like those of Sophus Lie, arrested on charges of spying
in Paris, in 1870. They also found several rolls of stenotypewritten
paper at the bottom of a closet. When I said these were the text of a
Balzac novel, the explanation must have seemed far-fetched. There was
also a letter in Russian, from Pontrjagin, I believe, in response to
a letter I had written at the beginning of the summer regarding a
possible visit to Leningrad; and a packet of calling cards belonging
to Nicolas Bourbaki, member of the Royal Academy of Poldavia, and even
some copies of his daughter Betti Bourbaki’s wedding invitation
, which
I had composed and had printed in Cambridge several months earlier in
collaboration with Chabauty and my wife.”

I’ve always wondered how on earth the Finnish police could interpret mathematical texts as coded messages. Reading the ‘faire-part’ (attempted translation below) it is hard to view it as anything but a coded message…

Here it is : a copy of the ‘faire-part’ of Betti Bourbaki’s wedding to Hector Petard, that nearly did cost Andre Weil’s life.

Monsieur Nicolas Bourbaki, Canonical Member of the Royal Academy of Poldavia, Grand Master of the Order of Compacts, Conserver of Uniforms, Lord Protector of Filters, and Madame nee One-to-One, have the honor of announcing the mariage of their daughter Betti with Monsieur Hector Petard, Delegate Administrator of the Society of Induced Structures, Member of the Institute of Classified Archeologists, Secretary of the Work of the Lion Hunt.

Monsieur Ersatz Stanislas Pondiczery, retired First Class Covering Complex, President of the Reeducation Home for Weak Convergents, Chevalier of the Four U’s, Grand Operator of the Hyperbolic Group, Knight of the Total Order of the Golden Mean, L.U.B., C.C., H.L.C., and Madame nee Compact-in-itself, have the honor of announcing the marriage of their ward Hector Petard with Mademoiselle Betti Bourbaki, a former student of the Well-Ordereds of Besse.

The trivial isomorphism 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.

The organ will be played by Monsieur Modulo, Assistant Simplex of the Grassmannian (Lemmas will be sung by Scholia Cartanorum). The result of the collection will be given to the House of Retirement foor Poor Abstracts, Convergence is assured.

After the congruence, Monsieur and Madame Bourbaki will receive guests in their Fundamental Domain; there will be dancing with music by the Fanfare of the VIIth Quotient Field.

Canonical Tuxedos (ideals left of the buttonhole). QED.

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