Category: tBC

Le Guide Bourbaki : Sallieres-les-bains

Published July 17, 2022 by lievenlb

For three summers in a row, Bourbaki held its congres in ‘Sallieres-les-bains’, located near Die, in the Drôme.

La Tribu 36, from June 27th till July 9th 1955
La Tribu 39, from June 24th till July 7th 1956, ‘Congres des Tapis’
La Tribu 42, from June 23rd till July 7th 1957, ‘Congres oecumenique du diabolo’

There are several ways to determine the exact location of a Bourbaki congres.

The quickest one is to get hold of the corresponding Diktat which often not only gives the address, but also travel instructions on how to get there. But strangely, no Diktats for congresses after 1953 are cleared by the ACNB.

Next, one can look in the previous La Tribu issue, as it contains a section on the next congres. In La Tribu 35 we find on page 2 : “Next congres : from June 25th till July 6th, in a location to be determined”. La Tribu 38 on page 5 reads (rough translation)

Next congres : will be held around the usual dates (June 23rd till July 7th, with a margin of 2 or 3 days). To facilitate things for Borel and Weil, Koko (=Koszul) will quickly look for a pleasant place in the Vosges or l’Alsace region. If this fails, he’ll immediately warn Cartan who will then take care of Die.

La Tribu 41 mentions on page 6: next congress will be held in Die from June 23rd till July 7th.

Finally, it may be that La Tribu itself gives more details. Strangely, La Tribu 36 is not among the issues recently cleared by the ACNB.

We know of its existence from Kromer’s paper La Machine de Grothendieck, and from a letter from Serre to Grothendieck from July 13th 1955 in which he writes that the Bourbaki congres in Sallieres-les-bains went well and that Grothendieck’s paper on Homological algebra (now known as the Tohoku-paper) was carefully read and converted everyone (‘even Dieudonne, who seems completely functorised’).

In La Tribu 39 we immediately strike gold, the heading tells us that the congres was held in the ‘Etablissement Thermo-resineux de Sallieres les bains’.

But, if you google for this, all you get are some pretty old postcards, such as this one

with one exception, a site set up to save the chapel of the Thermes de Sallieres-les-bains, which gives some historical information (google-translated):

“In Die, in the middle of the 19th century, the thermo-resinous establishments of Salières-les-bains opened. Until 1972, i.e. for 120 years, spa guests came there every summer to treat their bronchial tubes and rheumatism with the vapours of mugho pine. The center of Die and its cathedral being 4km away, it is in this 51m² chapel that the curists gathered. Mass was even sometimes said there because a priest was regularly among the spa guests. But after the closure, the small family farm can no longer maintain all the large buildings of the inn and their chapel, whose roof has now collapsed…”

And, there is the book Des bains de vapeurs térébenthinés aux pastilles de Pin mugho by Cécile Raynal, containing a short paragraph on the installation in Sallieres: (G-translate)

“Located a short distance from Martouret, this hydro-mineral establishment was created by a breeder, owner of the Sallieres estate, Mr. Taillotte. He equipped himself with facilities for resinous baths and also used hydrotherapy. More especially frequented by the patients of the surroundings, under the supervision of Dr. Magnan, a doctor from Die, the establishment charged moderate prices and functioned only in the summer. The installations would have lasted until the 1970s.”

So, it is perfectly possible that the Bourbakis stayed here in the mid 50ties. But, how did they know of this place and what’s the link with Cartan?

If you look at the map (Sallieres is the red marker) you’ll find in the immediate neighborhood the former Abbey of Valcroissant (for the Dome du Glandasse read La Tribu 42, page2)

“The abbey was bought in the 1950s by the mathematician and philosopher Marcel Légaut and his wife, who chose to restore it while maintaining agricultural activity, particularly livestock. The restoration led in particular to the classification of the abbey in the inventory of historical monuments, a classification which took place on October 25, 1971. The restoration continued in the 21st century, led by Rémy Légaut, son of Marcel, his wife Martine, and the association of “Friends of Valcroissant” created by André Pitte and Serge Durand.”

Marcel Legaut was a very interesting person, who did a Grothendieck avant-la-lettre. From wikipedia

“Marcel Légaut was born in Paris, where he received his Ph.D. in Mathematics from the École Normale Supérieure in 1925. He taught in various faculties (among them Rennes and Lyon) until 1943. Under the impact of the Second World War and the rapid French defeat in 1940, Légaut acknowledged the lack of certain fundamental aspects in his life as well as in the lives of other university professors and civil servants. That is why he tried to alternate teaching with farm work. After three years his project was no longer accepted and he left the University to live as a shepherd in the Pré-Alpes (Haut-Diois).”

Legaut also wrote about twenty books on catholic faith. Again from wikipedia (and compare to Grothendieck’s later years):

“Légaut offers, in his books, his meditation, his testimony and his prayer, resulting from the intimate conversation he holds with himself, with his friends and with God. Meditation, testimony and prayer are, in every human being, the three categories corresponding to the different destinataries of intimate “conversation”, which is, in short, the sort of communication that every spiritual life aims to achieve according to its deep instinct.”

Marcel Legaut is also one of the 24 ‘mutants’ in Grothendieck’s Clef des songes. Is it possible the two met during the Bourbaki congres in Sallieres-les-bains?

In this article on Legaut there’s this recollection by Pierre Cartier:

“Pierre Cartier believes that Grothendieck and Légaut had already met in the fifties, on the occasion of a Bourbaki meeting which took place in the Alps in Pelvoux-le Poët. Légaut, who lived at no great distance, was acquainted with Henri Cartan, André Weil and other members of Bourbaki. Cartier remembers that he himself visited Légaut at the time, and recalls Légaut actually attending the Bourbaki meeting.”

I beg to differ on the place of the Bourbaki meeting, I’m convinced it was during a congres in Sallieres-les-bains. We now also see the link with Cartan. Probably it was Legaut who mentioned the nearby wellness-center to Cartan.

Do the buildings of the ‘Etablissement Thermo-resineux de Sallieres les bains’ still exist, and what is their exact location?

If you intend to go on a little pelgrimage, point your GPS to 44.737347, 5.398835. Perhaps you can stay for a few days in the renovated Abbaye de Valcroissant, they offer courses in herbal medicine, aromatherapy and natural cosmetics, which are organised from March to November.

Leave a Comment

Le Guide Bourbaki : Marlotte

Published July 15, 2022 by lievenlb

During the 1950ties, the Bourbakistas usually scheduled three meetings in the countryside. In the spring and autumn at places not too far from Paris (Royaumont, Celles-sur-plaines, Marlotte, Amboise…), in the summer they often went to the mountains (Pelvoux, Murols, Sallieres-les-bains,…).

Being a bit autistic, they preferred to return to the same places, rather than to explore new ones: Royaumont (6 times), Pelvoux (5 times), Celles-sur-plaine (4 times), Marlotte (3 times), Amboise (3 times),…

In the past, we’ve tried to pinpoint the exact locations of the pre-WW2 Bourbaki-conferences: in 1935 at le Station Biologique de l’Université Blaise Pascal’, Rue du Lavoir, Besse-et-Saint-Anastaise, in 1936 and 1937 at La Massotterie in Chancay, and in 1938 at l’ecole de Beauvallon (often mistakingly referred to as the ‘Dieulefit-meeting’).

Let’s try to do the same for their conferences in the 1950ties. Making use of the recent La Tribu releases for he period 1953-1960, let’s start arbitrarily with the 1955 fall meeting in Marlotte.

Three conferences were organised in Marlotte during that period:

La Tribu 37 : ‘Congres de la lune’, October 23-29 1955
La Tribu 43 : ‘Congres de la deuxieme lune’, October 6-11 1957
La Tribu 44 : ‘Congres des minutes de silence’, March 16-22 1958

Grothendieck was present at all three meetings, Weil at the last two. But let us return to the fight between these two (‘congres des minutes de silence’) regarding algebraic geometry/category theory in another post.

Today we’ll just focus on the location of these meetings. At first, this looks an easy enough task as on the opening page of La Tribu we read:

“The conference was held at the Hotel de la mare aux canards’ (‘Hotel of the duck pond’) in Marlotte, near Fontainebleau, from October 23rd till 29th, 1955”.

Just one little problem, I can’t find any reference to a ‘Hotel de la Mare aux Canards’ in Marlotte, neither at present nor in the past.

Nowadays, Bourron-Marlotte is mainly a residential village with no great need for lodgings, apart from a few ‘gites’ and a plush hotel in the local ‘chateau’.

At the end of the 19th century though, there was an influx of painters, attracted by the artistic ‘colonie’ in the village, and they needed a place to sleep, and gradually several ‘Auberges’ and Hotels opened their doors.

Over the years, most of these hotels were demolished, or converted to family houses. The best list of former hotels in Marlotte, and their subsequent fate, I could find is L’essor hôtelier de Bourron et de Marlotte.

There’s no mention of any ‘Hotel de la mare aux canards’, but there was a ‘Hotel de la mare aux fées’ (Hotel of the fairy pond), which sadly was demolished in the 1970ties.

There’s little doubt that this is indeed the location of Bourbaki’s Marlotte-meetings, as the text on page one of La Tribu 37 above continues as (translation by Maurice Mashaal in ‘Bourbaki a secret society of mathematicians’, page 109):

“Modest and subdued sunlight, lustrous bronze leaves fluttering in the wind, a pond without fairies, modules without end, indigestible stones, and pierced barrels: everything contributes to the drowsiness of these blasé believers. ‘Yet they are serious’, says the hotel-keeper, ‘I don’t know what they are doing with all those stones, but they’re working hard. Maybe they’re preparing for a journey to the moon’.”

Bourbaki didn’t see any fairies in the pond, only ducks, so for Him it was the Hotel of the duck pond.

In fact La mare aux fées is one of the best known spots in the forest of Fontainebleau, and has been an inspiration for many painters, including Pierre-August Renoir:

Here’s the al fresco restaurant of the Hotel de la mare aux fées:

Both photographs are from the beginning of the 20th century, but also in the 50ties it was a Hotel of some renown as celebreties, including the actor Jean Gabin, stayed there.

The exact location of the former Hotel de la mare aux fées is 83, Rue Murger in Bourron-Marlotte.

Leave a Comment

The (somewhat less) Secret Bourbaki Archive

Published July 14, 2022 by lievenlb

It has been many, many years since I’ve last visited the Bourbaki Archives.

The underground repository of the Bourbaki Secret Archives is a storage facility built beneath the cave of the former Capoulade Cafe. Given its sporadic use by staff and scholars, the entire space – including the Gallery of all intermediate versions of every damned Bourbaki book, the section reserved to Bourbaki’s internal notes, such as his Diktats, and all numbers of La Tribu, and the Miscellania, containing personal notes and other prullaria once belonging to its members – is illuminated by amber lighting activated only when movement is detected by strategically placed sensors, and is guarded by a private security firm, hired by the ACNB.

This description (based on that of the Vatican Secret Archives in the book The Magdalene Reliquary by Gary McAvoy) is far from the actual situation. The Bourbaki Archive has been pieced together from legates donated by some of its former members (including Delsarte, Weil, de Possel, Cartan, Samuel, and others), and consist of well over a hundredth labeled carton and plastic cases, fitting easily in a few standard white Billy Ikea bookcases.

The publicly available Bourbaki Archive is even much smaller. The Association des collaborateurs de Nicolas Bourbaki has strong opinions on which items can be put online. For years the available issues of La Tribu were restricted to those before 1953. I was once told that one of the second generation Bourbaki-members vetoed further releases.

As a result, we only had the fading (and often coloured) memories of Bourbaki-members to rely on if we wanted to reconstruct key events, for example, Bourbaki’s reluctance to include category theory in its works. Rather than to work on source material, we had to content ourselves with interviews, such as this one, the relevant part starts at 51.40 into the clip. See here for some other interesting time-slots.

On a recent visit to the Bourbaki Archives I was happy to see that all volumes of “La Tribu” (the internal newsletter of Bourbaki) are now online from 1940 until 1960.

Okay, it’s not the entire story yet but, for all you Grothendieck aficionados out there, it should be enough as G resigned from Bourbaki in 1960 with this letter (see here for a translation).

Grothendieck was present at just twelve Bourbaki congresses in the period between 1955 and 1960 (he was also present as a ‘cobaye’ at a 1951 congress in Nancy).

The period 1955-60 was crucial in the modern development of algebraic geometry. Serre’s ‘FAC’ was published, as was Grothendieck’s ‘Tohoku-paper’, there was the influential Chevalley seminar, and the internal Bourbaki-fight about categories and the functorial view.

Perhaps the definite paper on the later issue is Ralf Kromer’s La ‘Machine de Grothendieck’ se fonde-t-elle seulement sur les vocables metamathematiques? Bourbaki et les categories au cours des annees cinquante.

Kromer had access to most issues of La Tribu until 1962 (from the Delsarte archive in Nancy), but still felt the need to justify his use of these sources to the ACNB (footnote 9 of his paper):

“L’autorisation que j’ai obtenue par le Comité scientifique des Archives de la création des mathématiques, unité du CNRS qui fut chargée jusqu’en 2003 de la mise à disposition de ces archives, me donne également le droit d’utiliser les sources datant des années postérieures à l’année 1953, que j’avais consultées auparavant aux Archives Jean Delsarte, soit avant que l’ACNB (Association des Collaborateurs de Nicolas Bourbaki) ne rende publique sa décision d’ouvrir ses archives et ne décide des parties qui seraient consultables.

J’ai ainsi bénéficié d’une occasion qui ne se présenterait sans doute plus aujourd’hui, mais c’est en toute légitimité que je puis m’appuyer sur cette riche documentation. Toutefois, la collection des Archives Jean Delsarte étant à son tour limitée aux années antérieures à 1963, je n’ai pu étudier la discussion ultérieure.”

The Association des Collaborateurs de Nicolas Bourbaki made retirement from active B-membership mandatory at the age of 50. One might expect of it to open up all documents in its archives which are older than fifty years.

Meanwhile, we’ll have a go at the 1940-1960 issues of La Tribu.

Leave a Comment

Finnegans Wake’s geometry lesson

Published April 14, 2021 by lievenlb

The literary sensation that spring of 1939 no doubt was the publication of Finnegans Wake by James Joyce. On May 4th 1939 FW was published simultaneously by Faber and Faber in London and by Viking Press in New York, after seventeen years of composition.

In 1928-29, Joyce started publishing individual chapters from FW, then known as ‘Work in Progress’, including chapter II.2 ‘The Triangle’, of which a brief excerpt was already published in February 1928. The name comes from the only diagram in FW, the classical Euclidian construction of an equilateral triangle (FW, p. 293)

This Vesica piscis has multiple interpretations in FW, most of them sexual. The triangle $\Delta$ is the Sigla for Anna Livia Plurabelle throughout FW, but it also refers to the river Liffey through Dublin.

Here’s Anthony Burgess explaining some of the Sigla, the relevant part starts at 14.20 into the clip.

In fact, many of FW’s Sigla are derived from mathematical symbols, such as $\exists$ (Earwicker), $\perp$ and $\vdash$ (Issy). For more on this, please read The logic of the doodles in Finnegans Wake II.2.

Not only does the equilateral triangle $\Delta$ refer to the river Liffey, the entire Euclidian diagram can be seen as a map for Dublin and its surroundings, as emphasised by the words “Vieus Von DVbLIn” (views from Dublin) in FW right under the diagram.

Here’s Dublin with the Liffey running through it, and Phoenix Park, which also features prominently in FW, see for example Phoenix Park in Finnegans Wake.

Views of Dublin – Photo Credit

The similarity between the map and the diagram is even clearer in Joyce’s own drawing in the first draft of FW.

The Triangle – Photo Credit

There’s a lot more to say about Joyce’s uses of geometry and topography in Ulysses and Finnegans Wake, in fact Ciaran McMorran wrote an entire Glasgow Ph. D. about it, but perhaps I’ll save some of that for a future post.

But what does this have to to with the Bourbaki Code, the puzzles contained in the Bourbaki-Petard wedding announcement?

Well, I claim that Andre Weil hid the Vesica Piscis/Euclidian diagram into the ‘faire part’. The challenge is to view the wedding announcement as a partial city- map. Clearly this time, the city of Dublin should be replaced by the city of Paris. Se non e vero …

Probably, there are enough hints contained in the previous posts in this series for you to spot the triangle(s) on the map of Paris. If you do so, please leave a comment, or email me.

Meanwhile, we’ll unravel first the more obvious levels of interpretation of the wedding announcement.

Leave a Comment

Princeton’s own Bourbaki

Published April 8, 2021 by lievenlb

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.

Leave a Comment

Cambridge, spring 1939

Published April 6, 2021 by lievenlb

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?

Leave a Comment

the Bourbaki code revisited

Published April 5, 2021 by lievenlb

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.

Leave a Comment

Where’s Bourbaki’s tomb?

Published October 23, 2016 by lievenlb

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.

Leave a Comment

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.

Leave a Comment

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.

claimtoken-511b561b7a5a2

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.”

Leave a Comment