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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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the Bourbaki code revisited

The fictitious life of Nicolas Bourbaki remains a source of fascination to some.

A few weeks ago, Michael Barany wrote an article for the JStor Daily The mathematical pranksters behind Nicolas Bourbaki.

Here’s one of the iconic early Bourbaki pictures, taken at the Dieulefit-meeting in 1938. More than a decade ago I discovered the exact location of that meeting in the post Bourbaki and the miracle of silence.



Bourbaki at Beauvallon 1938 – Photo Credit

That post was one of a series on the pre-war years of Bourbaki, and the riddles contained in the invitation card of the Betti Bourbaki-Hector Petard wedding that several mathematicians in Cambridge, Princeton and Paris received in the spring of 1939.



A year ago, The Ferret made the nice YouTube clip “Bourbaki – a Tale of Mathematics, Lions and Espionage”, which gives a quick introduction to Bourbaki and the people mentioned in the wedding invitation.

This vacation period may be a good opportunity to revisit some of my older posts on this subject, and add newer material I discovered since then.

For this reason, I’ve added a new category, tBC for ‘the Bourbaki Code’, and added the old posts to it.

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Where’s Bourbaki’s tomb?

In according to Groth IV.22 we tried to solve one of the riddles contained in Roubaud’s announcement of Bourbaki’s death.

Today, we’ll try our hands on the next one: where was Bourbaki buried?

The death announcement gives this fairly opaque clue:

“The burial will take place in the cemetery for Random Functions (metro stations Markov and Gödel) on Saturday, November 23, 1968 at 3 o’clock in the afternoon.”

What happened on November 23rd 1968?

Bourbaki died on November 11th, 1968 (exactly 50 years after the end of WW1). Perhaps an allusion to the mandatory retirement age for members of Bourbaki, as suggested by the Canulars Bourbaki.

Be that as it may, I believe this date was chosen because it is conveniently close to the intended time of the burial.

But then, what’s so special about November 23rd, 1968?

Well, is there a more suitable moment to burry Bourbaki than during a Seminaire Bourbaki? And, yes, in the fall of 1968 the seminar was organised from saturday 23rd till monday 25th of november:


So, where would all of Bourbaki’s close family be at 3 o’clock on that particular saturday? Right, at l’Institut Henri Poincare.

But, it’s hard to view the IHP as a cemetery. Besides, it’s nowhere close to two metro stations as a quick look on the map shows. The closest one is the RER-station at the Luxembourg gardens, but the RER-line didn’t exist in 1968.

(True Parisians may object that the Gare du Luxembourg was at the time the terminus of the Ligne de Sceaux which has a fascinating history, but let’s try to remain on track…)

If the first clue is the Institut Henri Poincare, then if we are looking for a cemetery, we might ask:

Where’s Poincare’s tomb?

Jules Henri Poincare is burried in the family tomb at the Montparnasse cemetery

He’s not the only mathematician buried there. Évariste Galois, Jean Victor Poncelet, Joseph Liouville, Charles Hermite, and Gaston Darboux also found their last resting place in Montparnasse.

In fact, there are at least 104 mathematicians buried at Montparnasse.

This is hardly surprising as the Montparnasse cemetery is close to the IHP, the Collège de France, the Sorbonne, the “rue d’Ulm” aka the ENS, l’Observatoire and until 1976 l’École polytechnique.

Here’s a map with pointers to some of these tombs:

So, the Montparnasse cemetery appears to be a plausible place to host Bourbaki’s tomb.

But, what about the other “clues”?

“Cemetery of random functions (metro stations Markov and Gödel)”

There are several references lo logic, set theory and applied mathematics in Bourbaki’s death announcement. Why?

Roubaud (and many with him) feel that the Bourbaki enterprise failed miserably in these areas.

He writes on page 49 of his book Mathematics, a novel:

“But Bourbaki, that ‘collective mathematician”, as Raymond Queneau put it, also had a good knowledge of the current state of mathematics at the time when his Treatise was being composed; with, of course, a few “gaps”:

for example, probability, which was considered to be just an “applied” brand of measure theory”; and logic, especially logic, which was made almost a pariah because of (so it was rumored) the premature death of Herbrand, who, in the generation of founders, Normaliens to a man, had studied under Hilbert, and thus had been associated with his meteoric rise; in sum, logic had died in a climbing accident along with Herbrand.”

This might explain the cemetery of “random functions” and the metro stations named after the logicians and set theorists Kurt Gödel and A.A. Markov or the father of stochastic processes Andrey Markov.

Is there more into these references?

Probably not, but just to continue with our silly game, the two metro stations closest to the Montparnasse cemetery are Raspail and Edgar Quinet.

Now, François-Vincent Raspail was a French chemist, naturalist, physician, physiologist, attorney, and socialist politician.

More relevant to our quest is that the Centre d’analyse et de mathématique sociales (CAMS) was based at 54, boulevard Raspail. The mission statement on their website tells that this institute is clearly devoted to all applications of mathematics. That is, “Raspail” may be another pointer to applied mathematics and random functions.

As for the other metro station, Edgar Quinet was a French historian and intellectual. Is there a connection to logic or set theory? Well, sort of. The Encyclopedia Britannica has this to say about Edgar Quinet:

“His rhetorical power was altogether superior to his logical power, and the natural consequence is that his work is full of contradictions.”

I rest my case.

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