Author: lievenlb

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.

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.

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.