Category: tBC

Hasse = “le P. Adique, de l’Ordre des Diophantiens”

Published October 12, 2016 by lievenlb

The Bourbaki wedding invitation is probably the most effective branding- and marketing-campaign in the history of mathematics.

It contains this, seemingly opaque, paragraph:

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.

It was pretty easy to decode the date of the wedding “3 Cartember, year VI” to be June 3rd, 1939, and (a bit more difficult) the wedding place “the Principal Cohomology of the Universal Variety” as the l’église royale Notre-Dame du Val-de-Grâce in Paris.

The identity of the celebrating priest “P. Adic, of the Diophantine Order” remained unclear. The most likely suspect was Helmut Hasse, but I couldn’t place him in Paris on June 3rd, 1939.

Hasse is the central figure in the picture above, taken in Oberwolfach in 1952, before one of his cars. Here’s another picture of car-freak Hasse (trains were to Andre Weil what cars were to Helmut Hasse). Both pictures are from the MFO photo collection.

Thanks to Peter Roquette’s publishing of Helmut Hasse’s letters we can now prove that Hasse was not in Paris on that particular day (however, he was there a couple of days earlier) but Weil had every reason to believe he might be there at the time he wrote the wedding invitation.

When was the wedding invitation written?

Frank 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.”

We know that this picture is taken on May 13th 1939 so the wedding-invitation was drawn up around mid april 1939.

“What did Weil know about Hasse’s visit to Paris?”

Hasse had been invited by Julia to give a series of lectures at the Institut Henri Poincare in 1938, but Hasse postponed his trip to Paris until May 1939.

In his letter to Hasse of January 20th 1939, Andre Weil writes:

“It is quite unfortunate that you couldn’t accept your invitation to Paris before this year, because last year all our number-theorists would have been present. By a sad coincidence all of us will be on travel this coming May (except for Chevalley perhaps who might have returned from the US by then). Pisot will be in Gottingen, Chabauty in Manchester visiting Mordell and I will be in Cambridge as I obtained a travel grant for England and Scandinavia.”

Clearly, Weil was aware of the upcoming visit of Hasse to Paris at the end of May, and there was no reason for him to assume that he wouldn’t be able to stay a weekend longer.

What do we know of Hasse’s visit to Paris?

Because Julia was exhausted and was on a three months sick leave, Elie Cartan took over the job of organising Hasse’s lecture series. In a letter of April 25th 1939 he proposes some possible dates, to which Hasse replies on April 30th 1939:

In it he fixes for the first time the dates of his talks which will be on “New results in the arithmetic of algebraic function fields” and consist of three lectures:

– On Friday 19th 1939: “Generalities: the group of divisor classes and the multiplier ring”

– On Saturday 20th 1939: “Rational and integral points on algebraic curves over the integers”

– On Tuesday 23rd 1939: “Rational points on algebraic curves with coefficient mod p”

He also mentions that he would stay for 15 days in Paris, arriving on May 17th, in time for the Jubilee Conference for Elie Cartan, scheduled on May 18th.

Weil must have known that Hasse would be present at the Cartan-fest and give a series of lectures in the following weeks. He had every reason to believe that Hasse would still be in Paris on Saturday June 3rd.

Where was Hasse on June 3rd 1939?

Back at home, as on that very day he wrote a letter to Henri Cartan, thanking him for an enjoyable day’s stay in Strasbourg, on the way back from Paris, on June 1st 1939:

If you want to catch up with previous posts on the Bourbaki wedding, you might want to download the booklet The Bourbaki Code.

16 ways to capture a lion (in 1938)

Published February 13, 2013 by lievenlb

A classic among mathematical jokes is the paper in the August/September 1938 issue of the American Mathematical Monthly “A contribution to the mathematical theory of big game hunting” by one Hector Petard of Princeton who would marry, one year later, Nicolas Bourbaki’s daughter Betti.

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There are two main sources of information on the story behind this paper. There are Frank Smithies’ “Reminiscences of Ralph Boas” in the book Lion Hunting & Other Mathematical Pursuits and the transcript of an interview with John Tukey and Albert Tucker at Princeton University on 11 April 1984, part of the oral-history project on the Princeton mathematics community in the 1930s.

Smithies recalls being part of a lively group of people in Princeton during the academic year 1937/38 including Arthur Brown, Ralph Traber, Lyman Spitzer, Hugh Dowker, John Olmsted, Henry Walman, George Barnard, John Tukey, Mort Kanner (a physicist), Dick Jameson (a linguist) and Ralph Boas. Smithies writes:

“At some time that winter we were told about the mathematical methods for lion-hunting that have been devised in Gottingen, and several of us came up with new ones; who invented which method is now lost to memory. Ralph (Boas) and I decided to write up all the methods known to us, with a view to publication, conforming as closely as we could to the usual style of a mathematical paper. We choose H. Petard as a pseudonym (“the engineer, hoist with his own petard”; Hamlet, Act III, Scene IV), and sent the paper to the Americal Mathematical Monthly, over the signature of E. S. Pondiczery.”

Pondiczery was Princeton’s answer to Nicolas Bourbaki, and in the interview John Tukey recalls from (sometimes failing) memory:

“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. Then there’s the wedding invitation done by the Bourbakis. It was for the marriage of Betti Bourbaki and Pondiczery. It was a formal wedding invitation with a long Latin sentence, most of which was mathematical jokes, three quarters of which you could probably decipher. Pondiczery even wrote a paper under a pseudonym, namely “The Mathematical Theory of Big Game Hunting” by H. Petard, which appeared in the Monthly. There were also a few other papers by Pondiczery.”

Andrew Tucker then tells the story of the paper’s acceptance:

“Moulton, the editor of the Monthly at that time, wrote to me saying that he had this paper and the envelope was postmarked Princeton and he assumed that it was done by some people in math at Princeton. He said he would very much like to publish the paper, but there was a firm policy against publishing anything anonymous. He asked if I, or somebody else that he knew and could depend on, would tell him that the authorship would be revealed if for any reason it became legally necessary. I did not know precisely who they were, but I knew that John [Tukey] was one of them. He seemed to be in the thick of such things. John agreed that I could accept Moulton’s terms. I sent a letter with this assurance to Moulton and he went ahead and published it.”

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

Published July 9, 2011 by lievenlb

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…