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Tag: Serre

Le Guide Bourbaki : Murol(s)

Published July 23, 2022 by lievenlb

The preparations for the unique Bourbaki-congress in Murols, start already in La Tribu 32 (fall 1953). On page 3:

“Summer 54: To suit Phileas Chevalley, Sammy Fogg and eventual Mexicans and Colombians, this Congress will be held from August 17 to 30. Samuel will look for a hotel in Auvergne, but everyone is asked to also prospect the hotels in his region.”

One should recall that the ICM 1954 was held in Amsterdam from September 2nd-9th. It was convenient for Chevalley and Eilenberg (who were in the US) and for possible more foreigners to have Bourbaki’s summer congress just before the ICM.

(Of course, Phileas Fogg is the main character in Jules Verne’s Around the World in 80 days.)

A lot of people attended the Murols-meeting (La Tribu 34, ‘Congres super-oecumenique du frigidaire et des revetements troues’).

Apart from the regular crowd (Cartan, Chevalley, Delsarte, Dieudonne, Dixmier, Godement, Koszul, Sammy (=Eilenberg), Samuel, Schwartz, Serre and Weil), there was a guinea-pig (Serge Lang), an ‘efficiency expert’ (Saunders MacLane), two ‘foreign visitors’ (Hochschild and John Tate) and two ‘honorable foreign visitors’ (Iyanaga and Kosaku Yosida).

Probably because of this, extremely detailed travel instructions were given in La Tribu 33 (page 2):

“Next congress: will be held at the Hotel des Pins, in Murols (Puy-de-Dome) from August 17 to 30.
There is at least one night train departing from Paris, going to Clermont or Issoire, followed by a bus-ride to Murols; details will be given as soon as we know the summer schedules.
For motorized people not coming from the South by the N.9, nor from the West by the N.89: go to Clermont-Ferrand, leave it by the N.9 (route d’Issoire), turn right about 17 kms further (after the village of Veyre) to take the N.678 towards Champeix; in Champeix take (on the right) the N.496 (direction of St-Nectaire, Murols and Mont-Dore).
For those coming from the South by the N.9: turn left at Issoire to take the N.496 towards Campais, St-Nectaire, Murols. For those coming from the West by the N.89: leave it a little before Lequeille to take (on the right) the N.122, turn left 2 km further to take the N.496 towards Mont-Dore, the Chambon lake and Murols (road continuing towards Champeix and Issoire).”

If you follow this route on the map, you’ll know that the congress was not held in Murols (departement de l’Aveyron), but in Murol (departement du Puy-de-Dome).

This time we do not have to search long for the place of venue as Hotel des Pins a Murol is still in operation.

Note the terras on the first floor, and the impressive line of trees in front of the hotel.

At first I felt frustrated as I couldn’t figure out where this well-known photograph of the Murol-meeting was taken.

From left to right, Godement, Dieudonne, Weil, MacLane, and a smug looking Serre (he knew he would be awarded a Fields medal in a few days time).

Today it is impossible to have this view from the hotel-terras because of the trees in front. Still, the picture was taken from the terras, and the imposing building in the background is the late Turing Hotel in Murol.

Here’s a picture of it with the Hotel des Pins in the background.

We’ve encountered the Murol-congress before on this blog when trying to piece together the history of the Yoneda lemma (Iyanaga was Yoneda’s Ph.D. advisor, and probably on his advice MacLane met with Yoneda in the Gare du Nord to hear about his lemma).

On MacLane’s role as ‘efficiency expert’ we have this in La Tribu 34:

“Frightened by the disorder of the discussions, some members had brought a world-renowned efficiency expert from Chicago. This one, armed with a hammer, tried hard and with good humor, but without much result. He quickly realized that it was useless, and turned, successfully this time, to photography.”

As we’ve seen in Amboise and Pelvoux, Bourbaki likes to have His summer venues close to places of great sentimental value.

Murol is very close to Besse-et-Saint Anastaise, the place of the very first Bourbaki-meeting in 1935.

As always, this asks for a little pilgrimage. From La Tribu 34 (page 2):

“Despite the incessant rain, Bourbaki was attracted by the waters, and went to explore lots of Auvergnian lakes. Besse and its Lac Pavin were naturally entitled to a pilgrimage. Courageous founding-fathers and lower-members, braving the rain and fog, rushed across to the lake of Guery where their dripping pants aroused the suspicions of a bar maid, and beat the motorized elements there by several lengths. Others swam and rowed. Even the Japanese were entitled to their lake.”

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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.

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Bourbaki and Grothendieck-Serre

Published April 16, 2021 by lievenlb

This time of year I’m usually in France, or at least I was before Covid. This might explain for my recent obsession with French math YouTube interviews.

Today’s first one is about Bourbaki’s golden years, the period between WW2 and 1975. Alain Connes is trying to get some anecdotes from Jean-Pierre Serre, Pierre Cartier, and Jacques Dixmier.

If you don’t have the time to sit through the whole thing, perhaps you might have a look at the discussion on whether or not to include categories in Bourbaki (starting at 51.40 into the clip).

Here are some other time-slots (typed on a qwerty keyboard, mes excuses) with some links.

  • 8.59 : Canular stupide (mort de Bourbaki)
  • 15.45 : recrutement de Koszul
  • 17.45 : recrutement de Grothendieck
  • 26.15 : influence de Serre
  • 28.05 : importance des ultra filtres
  • 35.35 : Meyer
  • 37.20 : faisceaux
  • 51.00 : Grothendieck
  • 51.40 : des categories, Gabriel-Demazure
  • 57.50 : lemme de Serre, theoreme de Weil
  • 1.03.20 : Chevalley vs. Godement
  • 1.05.26 : retraite Dieudonne
  • 1.07.05 : retraite
  • 1.10.00 : Weil vs. Serre-Borel
  • 1.13.50 : hierarchie Bourbaki
  • 1.20.22 : categories
  • 1.21.30 : Bourbaki, une secte?
  • 1.22.15 : Grothendieck C.N.R.S. 1984

The second one is an interview conducted by Alain Connes with Jean-Pierre Serre on the Grothendieck-Serre correspondence.

Again, if you don’t have the energy to sit through it all, perhaps I can tempt you with Serre’s reaction to Connes bringing up the subject of toposes (starting at 14.36 into the clip).

  • 2.10 : 2e these de Grothendieck: des faisceaux
  • 3.50 : Grothendieck -> Bourbaki
  • 6.46 : Tohoku
  • 8.00 : categorie des diagrammes
  • 9.10 : schemas et Krull
  • 10.50 : motifs
  • 11.50 : cohomologie etale
  • 14.05 : Weil
  • 14.36 : topos
  • 16.30 : Langlands
  • 19.40 : Grothendieck, cours d’ecologie
  • 24.20 : Dwork
  • 25.45 : Riemann-Roch
  • 29.30 : influence de Serre
  • 30.50 : fin de correspondence
  • 32.05 : pourquoi?
  • 33.10 : SGA 5
  • 34.50 : methode G. vs. theorie des nombres
  • 37.00 : paranoia
  • 37.15 : Grothendieck = centrale nucleaire
  • 38.30 : Clef des songes
  • 42.35 : 30.000 pages, probleme du mal
  • 44.25 : Ribenboim
  • 45.20 : Grothendieck a Paris, publication R et S
  • 48.00 : 50 ans IHES, lettre a Bourguignon
  • 50.46 : Laurant Lafforgue
  • 51.35 : Lasserre
  • 53.10 : l’humour
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