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Tag: Weil

Princeton’s own Bourbaki

In the first half of 1937, Andre Weil visited Princeton and introduced some of the postdocs present (notably Ralph Boas, John Tukey, and Frank Smithies) to Poldavian lore and Bourbaki’s early work.

In 1935, Bourbaki succeeded (via father Cartan) to get his paper “Sur un théorème de Carathéodory et la mesure dans les espaces topologiques” published in the Comptes Rendus des Séances Hebdomadaires de l’Académie des Sciences.

Inspired by this, the Princeton gang decided to try to get a compilation of their mathematical ways to catch a lion in the American Mathematical Monthly, under the pseudonym H. Petard, and accompanied by a cover letter signed by another pseudonym, E. S. Pondiczery.

By the time the paper “A contribution to the mathematical theory of big game hunting” appeared, Boas and Smithies were in cambridge pursuing their postdoc work, and Boas reported back to Tukey: “Pétard’s paper is attracting attention here,” generating “subdued chuckles … in the Philosophical Library.”

On the left, Ralph Boas in ‘official’ Pondiczery outfit – Photo Credit.



The acknowledgment of the paper is in true Bourbaki-canular style.

The author desires to acknowledge his indebtedness to the Trivial Club of St. John’s College, Cambridge, England; to the M.I.T. chapter of the Society for Useless Research; to the F. o. P., of Princeton University; and to numerous individual contributors, known and unknown, conscious and unconscious.

The Trivial Club of St. John’s College probably refers to the Adams Society, the St. John’s College mathematics society. Frank Smithies graduated from St. John’s in 1933, and began research on integral equations with Hardy. After his Ph. D., and on a Carnegie Fellowship and a St John’s College studentship, Smithies then spent two years at the Institute for Advanced Study at Princeton, before returning back ‘home’.

In the previous post, I assumed that Weil’s visit to Cambridge was linked to Trinity College. This should probably have been St. John’s College, his contact there being (apart from Smithies) Max Newman, a fellow of St. John’s. There are two letters from Weil (summer 1939, and summer 1940) in the Max Newman digital library.



The Eagle Scanning Project is the online digital archive of The Eagle, the Journal of St. John’s College. Last time I wanted to find out what was going on, mathematically, in Cambridge in the spring of 1939. Now I know I just had to peruse the Easter 1939 and Michaelmas 1939 volumes of the Eagle, focussing on the reports of the Adams Society.

In the period Andre Weil was staying in Cambridge, they had a Society Dinner in the Music Room on March 9th, a talk about calculating machines (with demonstration!) on April 27th, and the Annual Business Meeting on May 11th, just two days before their punting trip to Grantchester,



The M.I.T. chapter of the Society for Useless Research is a different matter. The ‘Useless Research’ no doubt refers to Extrasensory Perception, or ESP. Pondiczery’s initials E. S. were chosen with a future pun in mind, as Tukey said in a later interview:

“Well, the hope was that at some point Ersatz Stanislaus Pondiczery at the Royal Institute of Poldavia was going to be able to sign something ESP RIP.”

What was the Princeton connection to ESP research?

Well, Joseph Banks Rhine conducted experiments at Duke University in the early 1930s on ESP using Zener cards. Amongst his test-persons was Hubert Pearce, who scored an overall 40% success rate, whereas chance would have been 20%.



Pearce and Joseph Banks Rhine (1932) – Photo Credit

In 1936, W. S. Cox tried to repeat Rhine’s experiment at Princeton University but failed. Cox concluded “There is no evidence of extrasensory perception either in the ‘average man’ or of the group investigated or in any particular individual of that group. The discrepancy between these results and those obtained by Rhine is due either to uncontrollable factors in experimental procedure or to the difference in the subjects.”

As to the ‘MIT chapter of the society for useless research’, a chapter usually refers to a fraternity at a University, but I couldn’t find a single one on the list of MIT fraternities involved in ESP, now or back in the late 1930s.

However, to my surprise I found that there is a MIT Archive of Useless Research, six boxes full of amazing books, pamphlets and other assorted ‘literature’ compiled between 1900 and 1940.

The Albert G. Ingalls pseudoscience collection (its official name) comprises collections of books and pamphlets assembled by Albert G. Ingalls while associate editor of Scientific American, and given to the MIT Libraries in 1940. Much of the material rejects contemporary theories of physical sciences, particularly theoretical and planetary physics; a smaller portion builds upon contemporary science and explores hypotheses not yet accepted.

I don’t know whether any ESP research is included in the collection, nor whether Boas and Tukey were aware of its existence in 1938, but it sure makes a good story.

The final riddle, the F. o. P., of Princeton University is an easy one. Of course, this refers to the “Friends of Pondiczery”, the circle of people in Princeton who knew of the existence of their very own Bourbaki.

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Cambridge, spring 1939

One of the few certainties we have on the Bourbaki-Petard wedding invitation is that it was printed in, and distributed out of Cambridge in the spring of 1939, presumably around mid April.

So, what was going on, mathematically, in and around Trinity and St. John’s College, at that time?

Well, there was the birth of Eureka, the journal of the Archimedeans, the mathematical society of the University of Cambridge. Eureka is one of the oldest recreational mathematics publications still in existence.

Since last year the back issues of Eureka are freely available online, unfortunately missing out the very first two numbers from 1939.

Ralph Boas, one of the wedding-conspirators, was among the first to contribute to Eureka. In the second number, in may 1939, he wrote an article on “Undergraduate mathematics in America”.

And, in may 1940 (number 4 of Eureka) even the lion hunter H. Petard wrote a short ‘Letter to the editors’.



But, no doubt the hottest thing that spring in Cambridge were Ludwig Wittgenstein’s ‘Lectures on the Foundations of Mathematics’. Wittgenstein was just promoted to Professor after G.E. Moore resigned the chair in philosophy.

For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation.

These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies.

Here’s a clip from the film Wittgenstein, directed by Derek Jarman.

Missing from the list of people attending Wittgenstein’s lectures is Andre Weil, a Bourbaki member and the principal author of the wedding invitation.

Weil was in Cambridge in the spring of 1939 on a travel grant from the French research organisation for visits to the UK and Northern Europe. At that time, Weil held a position at the University of Strasbourg, uncomfortably close to Nazi-Germany.

Weil not attending Wittgenstein’s lectures is strange for several reasons. Weil was then correcting the galley proofs of Bourbaki’s first ever booklet, their own treatment of set theory, which appeared in 1939.

But also on a personal level, Andre Weil must have been intrigued by Wittgenstein’s philosophy, as it was close to that of his own sister Simone Weil

There are many parallels between the thinkers Simone Weil and Ludwig Wittgenstein. They each lived in a tense relationship with religion, with both being estranged from their cultural Jewish ancestry, and both being tempted at various times by the teachings of Catholicism.

They both underwent a profound and transformative mystical turn early into their careers. Both operated against the backdrop of escalating global conflict in the early 20th century.

Both were concerned, amongst other things, with questions of culture, ethics, aesthetics, epistemology, science, and necessity. And, perhaps most notably, they both sought to radically embody their ideas and physically ‘live’ their philosophies.

From Between Weil and Wittgenstein



Andre and Simone Weil in Knokke-Zoute, 1922 – Photo Credit

Another reason why Weil might have been interested to hear Wittgenstein on the foundations of mathematics was a debate held in Paris of few months previously.

On February 4th 1939, the French Society of Philosophy invited Albert Lautman and Jean Cavaillès ‘to define what constitutes the ‘life of mathematics’, between historical contingency and internal necessity, describe their respective projects, which attempt to think mathematics as an experimental science and as an ideal dialectics, and respond to interventions from some eminent mathematicians and philosophers.’

Among the mathematicians present and contributing to the discussion were Weil’s brothers in arms, Henri Cartan, Charles Ehresmann, and Claude Chabauty.

As Chabauty left soon afterwards to study with Mordell in Manchester, and visited Weil in Cambridge, Andre Weil must have known about this discussion.

The record of this February 4th meeting is available here (in French), and in English translation from here.

Jean Cavaillès took part in the French resistance, was arrested and shot by the Nazis on April 4th 1944. Albert Lautman was shot by the Nazis in Toulouse on 1 August 1944.



Jean Cavailles (2nd on the right) 1903-1944 – Photo Credit

A book review of Wittgenstein’s Lectures on the Foundations of Mathematics by G. Kreisel is available from the Bulletin of the AMS. Curiously, Kreisel compares Wittgenstein’s approach to … Bourbaki’s very own manifesto L’architecture des mathématiques.

For all these reasons it is strange that Andre Weil apparently didn’t show much interest in Wittgenstein’s lectures.

Had he more urgent things on his mind, like prepping for a wedding?

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What’s Pippa got to do with the Bourbaki wedding?

Last time we’ve seen that on June 3rd 1939, the very day of the Bourbaki wedding, Malraux’ movie ‘L’espoir’ had its first (private) viewing, and we mused whether Weil’s wedding card was a coded invitation to that event.

But, there’s another plausible explanation why the Bourbaki wedding might have been scheduled for June 3rd : it was intended to be a copy-cat Royal Wedding…

The media-hype surrounding the wedding of Prince William to Pippa’s sister led to a hausse in newspaper articles on iconic royal weddings of the past.

One of these, the marriage of Edward VIII, Duke of Windsor and Wallis Warfield Spencer Simpson, was held on June 3rd 1937 : “This was the scandal of the century, as far as royal weddings go. Edward VIII had just abdicated six months before in order to marry an American twice-divorced commoner. The British Establishment at the time would not allow Edward VIII to stay on the throne and marry this woman (the British Monarch is also the head of the Church of England), so Edward chose love over duty and fled to France to await the finalization of his beloved’s divorce. They were married in a private, civil ceremony, which the Royal Family boycotted.”

But, what does this wedding have to do with Bourbaki?

For starters, remember that the wedding-card-canular was concocted in the spring of 1939 in Cambridge, England. So, if Weil and his Anglo-American associates needed a common wedding-example, the Edward-Wallis case surely would spring to mind. One might even wonder about the transposed symmetry : a Royal (Betti, whose father is from the Royal Poldavian Academy), marrying an American (Stanislas Pondiczery).

Even Andre Weil must have watched this wedding with interest (perhaps even sympathy). He too had to wait a considerable amount of time for Eveline’s divorce (see this post) to finalize, so that they could marry on october 30th 1937, just a few months after Edward & Wallis.



But, there’s more. The royal wedding took place at the Chateau de Cande, just south of Tours (the A on the google-map below). Now, remember that the 2nd Bourbaki congress was held at the Chevalley family-property in Chancay (see the Escorial post) a bit to the north-east of Tours (the marker on the map). As this conference took place only a month after the Royal Wedding (from 10th till 20th of July 1937), the event surely must have been the talk of the town.

Early on, we concluded that the Bourbaki-Petard wedding took place at 12 o’clock (‘a l’heure habituelle’). So did the Edward-Wallis wedding. More precisely, the civil ceremony began at 11.47 and the local mayor had to come to the castle for the occasion, and, afterwards the couple went into the music-room, which was converted into an Anglican chapel for the day, at precisely 12 o’clock.

The emphasis on the musical organ in the Bourbaki wedding-invitation allowed us to identify the identity of ‘Monsieur Modulo’ to be Olivier Messiaen as well as that of the wedding church. Now, the Chateau de Cande also houses an impressive organ, the Skinner opus 718 organ.

For the wedding ceremony, Edward and Wallis hired the services of one of the most renowned French organists at the time : Marcel Dupre who was since 1906 Widor’s assistent, and, from 1934 resident organist in the Saint-Sulpice church in Paris. Perhaps more telling for our story is that Dupre was, apart from Paul Dukas, the most influential teacher of Olivier Messiaen.

On June 3rd, 1937 Dupre performed the following pieces. During the civil ceremony, an extract from the 29e Bach cantate, canon in re-minor by Schumann and the prelude of the fugue in do-minor of himself. When the couple entered the music room he played the march of the Judas Macchabee oratorium of Handel and the cortege by himself. During the religious ceremony he performed his own choral, adagium in mi-minor by Cesar Franck, the traditional ‘Oh Perfect Love’, the Jesus-choral by Bach and the toccata of the 5th symphony of Widor. Compare this level of detail to the minimal musical hint given in the Bourbaki wedding-invitation

“Assistent Simplexe de la Grassmannienne (lemmas chantees par la Scholia Cartanorum)”

This is one of the easier riddles to solve. The ‘simplicial assistent of the Grassmannian’ is of course Hermann Schubert (Schubert cell-decomposition of Grassmannians). But, the composer Franz Schubert only left us one organ-composition : the Fugue in E-minor.

I have tried hard to get hold of a copy of the official invitation for the Edward-Wallis wedding, but failed miserably. There must be quite a few of them still out there, of the 300 invited people only 16 showed up… You can watch a video newsreel film of the wedding.

As Claude Chevalley’s father had an impressive diplomatic career behind him and lived in the neighborhood, he might have been invited, and, perhaps the (unused) invitation was lying around at the time of the second Bourbaki-congress in Chancay,just one month after the Edward-Wallis wedding…

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If Bourbaki=WikiLeaks then Weil=Assange

In an interview with readers of the Guardian, December 3rd 2010, Julian Assange made a somewhat surprising comparison between WikiLeaks and Bourbaki, sorry, The Bourbaki (sic) :

“I originally tried hard for the organisation to have no face, because I wanted egos to play no part in our activities. This followed the tradition of the French anonymous pure mathematians, who wrote under the collective allonym, “The Bourbaki”. However this quickly led to tremendous distracting curiosity about who and random individuals claiming to represent us. In the end, someone must be responsible to the public and only a leadership that is willing to be publicly courageous can genuinely suggest that sources take risks for the greater good. In that process, I have become the lightening rod. I get undue attacks on every aspect of my life, but then I also get undue credit as some kind of balancing force.”

Analogies are never perfect, but perhaps Assange should have taken it a bit further and studied the history of the pre-war Bourbakistas in order to avoid problems that led to the eventual split-up.

Clearly, if Bourbaki=WikiLeaks, then Assange plays the role of Andre Weil. Both of them charismatic leaders, convincing the group around them that for the job at hand to succeed, it is best to work as a collective so that individual contributions cannot be traced.

At first this works well. Both groups make progress and gain importance, also to the outside world. But then, internal problems surface, questioning the commitment of ‘the leader’ to the original project.

In the case of the Bourbakis, Claude Chevalley and Rene de Possel dropped that bombshell at the second Chancay-meeting in 1937 with a 2 page pamphlet 7 theses de Chancay.

“Criticism on the state of affairs :

  • in general, a certain aging of Bourbaki, which manifests itself in a tendency to neglect internal lively opposition in favor of pursuing visible external succes ((failed) completion of versions, artificial agreement among members of the group).
  • in particular, often the working method appears to be that of suffocating any objections in official meetings (via interruptions, not listening, etc. etc.). This tendency didn’t exist at the Besse meeting, began to manifest itself at the Escorial-meeting and got even worse here at Chancay. Bourbaki-members don’t pay attention to discussions and the principle of unanimous decision-making is replaced in reality by majority rule.”

Sounds familiar? Perhaps stretching the analogy a bit one might say that Claude Chevalley’s and Rene de Possel’s role within Bourbaki is similar to that of respectively Birgitta Jónsdóttir and Daniel Domscheit-Berg within WikiLeaks.

This criticism will be neglected and at the following Bourbaki-meeting in Dieulefit (neither Chevalley nor de Possel were present) hardly any work gets done, largely due to the fact that Andre Weil is more concerned about his personal safety and escapes during the meeting for a couple of days to Switserland, fearing an imminent invasion.

After the Dieulefit-meeting, even though Bourbaki’s fame is spreading, work on the manuscripts is halted because all members are reserve-officers in the French army and have to prepare for war.

Except for Andre Weil, who’s touring the world with a clear “Bourbaki, c’est moi!” message, handing out Bourbaki name-cards or invitations to Betti Bourbaki’s wedding… That Andre and Eveline Weil are traveling as Mr. and Mrs. Bourbaki is perhaps best illustrated by the thank-you note, left on their journey through Finland.

If it were not for the fact that the other members had more pressing matters to deal with, Weil’s attitude would have resulted in more people dropping out of the group, or continuing the work under another name, a bit like what happens to WikiLeaks and OpenLeaks today.

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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
DIEUDONNE

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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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?

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