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Category: france

A newish toy in town

In a recent post I recalled Claude Levy-Strauss’ observation “In Paris, intellectuals need a new toy every 15 years”, and gave a couple of links showing that the most recent IHES-toy has been spreading to other Parisian intellectual circles in recent years.

At the time (late sixties), Levy-Strauss was criticising the ongoing Foucault-hype. It appears that, since then, the frequency of a hype cycle is getting substantially shorter.

Ten days ago, the IHES announced that Dustin Clausen (of condensed math fame) is now joining the IHES as a permanent professor.

To me, this seems like a sensible decision, moving away from (too?) general topos theory towards explicit examples having potential applications to arithmetic geometry.

On the relation between condensed sets and toposes, here’s Dustin Clausen talking about “Toposes generated by compact projectives, and the example of condensed sets”, at the “Toposes online” conference, organised by Alain Connes, Olivia Caramello and Laurent Lafforgue in 2021.

Two days ago, Clausen gave another interesting (inaugural?) talk at the IHES on “A Conjectural Reciprocity Law for Realizations of Motives”.

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Against toposes

The French anthropologist and ethnologist Claude Levi-Strauss once observed

“In Paris, intellectuals need a new toy every 15 years.”

Some pointers to applications of their toy of choice for the past ten years:

How do Parisian mathematicians with a lifelong interest in topos theory react to this hype?

With humour!

Here’s an ‘exposé parodique’ (parodical lecture) by Stéphane Dugowson on “Contre les topos” (against toposes).

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Leila Schneps on Grothendieck

If you have neither the time nor energy to watch more than one interview or talk about Grothendieck’s life and mathematics, may I suggest to spare that privilege for Leila Schneps’ talk on ‘Le génie de Grothendieck’ in the ‘Thé & Sciences’ series at the Salon Nun in Paris.

I was going to add some ‘relevant’ time slots after the embedded YouTube-clip below, but I really think it is better to watch Leila’s interview in its entirety. Enjoy!

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Cartan meets Lacan

In the Grothendieck meets Lacan-post we did mention that Alain Connes wrote a book together with Patrick Gauthier-Lafaye “A l’ombre de Grothendieck et de Lacan, un topos sur l’inconscient”, on the potential use of Grothendieck’s toposes for the theory of unconsciousness, proposed by the French psychoanalyst Jacques Lacan.

A bit more on that book you can read in the topos of unconsciousness. For another take on this you can visit the blog of l’homme quantique – Sur les traces de Lévi-Strauss, Lacan et Foucault, filant comme le sable au vent marin…. There is a series of posts dedicated to the reading of ‘A l’ombre de Grothendieck et de Lacan’:

Alain Connes isn’t the first (former) Bourbaki-member to write a book together with a Lacan-disciple.

In 1984, Henri Cartan (one of the founding fathers of Bourbaki) teamed up with the French psychoanalyst (and student of Lacan) Jean-Francois Chabaud for “Le Nœud dit du fantasme – Topologie de Jacques Lacan”.

(Chabaud on the left, Cartan on the right, Cartan’s wife Nicole in the mddle)

“Dans cet ouvrage Jean François Chabaud, psychanalyste, effectue la monstration de l’interchangeabilité des consistances de la chaîne de Whitehead (communément nommée « Noeud dit du fantasme » ou du « Non rapport sexuel » dans l’aire analytique), et peut ainsi se risquer à proposer, en s’appuyant sur les remarques essentielles de Jacques Lacan, une écriture du virage, autre nom de la passe. Henri Cartan (1904-2008), l’un des Membres-fondateur de N. Bourbaki, a contribué à ce travail avec deux réflexions : la première, considère cette monstration et l’augmente d’une présentation ; la seconde, traite tout particulièrement de l’orientation des consistances. Une suite de traces d’une séquence de la chaîne précède ce cahier qui s’achève par : « L’en-plus-de-trait », une contribution à l’écriture nodale.”

Lacan was not only fascinated by the topology of surfaces such as the crosscap (see the topos of unconsciousness), but also by the theory of knots and links.

The Borromean link figures in Lacan’s world for the Real, the Imaginary and the Symbolic. The Whitehead link (that is, two unknots linked together) is thought to be the knot (sic) of phantasy.

In 1986, there was the exposition “La Chaine de J.H.C. Whitehead” in the
Palais de la découverte in Paris (from which also the Chabaud-Cartan picture above is taken), where la Salle de Mathématiques was filled with different models of the Whitehead link.

In 1988, the exposition was held in the Deutches Museum in Munich and was called “Wandlung – Darstellung der topologischen Transformationen der Whitehead-Kette”

The set-up in Munich was mathematically more interesting as one could see the link-projection on the floor, and use it to compute the link-number. It might have been even more interesting if the difference in these projections between two subsequent models was exactly one Reidemeister move

You can view more pictures of these and subsequent expositions on the page dedicated to the work of Jean-Francois Chabaud: La Chaîne de Whitehead ou Le Nœud dit du fantasme Livre et Expositions 1980/1997.

Part of the first picture featured also in the Hommage to Henri Cartan (1904-2008) by Michele Audin in the Notices of the AMS. She writes (about the 1986 exposition):

“At the time, Henri Cartan was 82 years old and retired, but he continued to be interested in mathematics and, as one sees, its popularization.”

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Bourbaki, Brassens, Hula Hoops and Coconuts

More than ten years ago, when I ran a series of posts on pre-WW2 Bourbaki congresses, I knew most of the existing B-literature. I’m afraid I forgot most of it, thereby missing opportunities to spice up a dull post (such as yesterday’s).

Right now, I need facts about the infamous ACNB and its former connection to Nancy, so I reread Liliane Beaulieu’s Bourbaki a Nancy:

(page 38) : “Like a theatrical canvas, “La Tribu” often carries as its header a subtitle, the product of its editor’s imagination, which brings out the theme of the congress, if necessary. There is thus a “De Nicolaıdes” congress in Nancy, “Du banc public” (reference to Brassens) that of the “Universites cogerees” (in October 68, at the time of co-management).”

The first La Ciotat congress (February 27 to March 6, 1955) was called ‘the congress of the public bench’ (‘banc public’ in French) where Serre and Cartan tried to press Bourbaki to opt for the by now standard approach to varieties (see yesterday), and the following Chicago-congress retaliated by saying that there were also public benches nearby, but of little use.

What I missed was the reference to French singer-songwriter George Brassens. In 1953, he wrote, composed and performed Bancs Public (later called ‘Les Amoureux des bancs publics’).

If you need further evidence (me, I’ll take Liliane’s word on anything B-related), here’s the refrain of the song:

“Les amoureux qui s’bécotent sur les bancs publics,
Bancs publics, bancs publics,
En s’foutant pas mal du regard oblique
Des passants honnêtes,
Les amoureux qui s’bécotent sur les bancs publics,
Bancs publics, bancs publics,
En s’disant des “Je t’aime'” pathétiques,
Ont des p’tits gueules bien sympathiques!

(G-translated as:
‘Lovers who smooch on public benches,
Public benches, public benches,
By not giving a damn about the sideways gaze
Honest passers-by,
The lovers who smooch on the public benches,
Public benches, public benches,
Saying pathetic “I love you” to each other,
Have very nice little faces!‘)

Compare this to page 3 of the corresponding “La Tribu”:

“Geometrie Algebrique : elle a une guele bien sympathique.”

(Algebraic Geometry : she has a very nice face)

More Bourbaki congresses got their names rather timely.

In the summer of 1959 (from June 25th – July 8th) there was a congress in Pelvout-le-Poet called ‘Congres du cerceau’.

‘Cerceau’ is French for Hula Hoop, whose new plastic version was popularized in 1958 by the Wham-O toy company and became a fad.

(Girl twirling Hula Hoop in 1958 – Wikipedia)

The next summer it was the thing to carry along for children on vacation. From the corresponding “La Tribu” (page 2):

“Le congres fut marque par la presence de nombreux enfants. Les distractions s’en ressentirent : baby-foot, biberon de l’adjudant (tres concurrence par le pastis), jeu de binette et du cerceau (ou faut-il dire ‘binette se jouant du cerceau’?) ; un bal mythique a Vallouise faillit faire passer la mesure.”
(try to G-translate it yourself…)

Here’s another example.

The spring 1949 congress (from April 13th-25th) was held at the Abbey of Royaumont and was called ‘le congres du cocotier’ (the coconut-tree congress).

From the corresponding “La Tribu 18”:

“Having absorbed a tough guinea pig, Bourbaki climbed to the top of the Royaumont coconut tree, and declared, to unanimous applause, that he would only rectify rectifiable curves, that he would treat rational mechanics over the field $\mathbb{Q}$, and, that with a little bit of vaseline and a lot of patience he would end up writing the book on algebraic topology.”

The guinea pig that congress was none other than Jean-Pierre Serre.

A year later (from April 5th-17th 1950) there was another Royaumont-congress called ‘le congres de la revanche du cocotier’ (the congress of the revenge of the coconut-tree).

From the corresponding La Tribu 22:

“The founding members had decided to take a dazzling revenge on the indiscipline young people; mobilising all the magical secrets unveiled to them by the master, they struck down the young people with various ailments; rare were those strong enough to jump over the streams of Royaumont.”

Here’s what Maurice Mashaal says about this in ‘Bourbaki – a secret society of mathematicians’ (page 113):

“Another prank among the members was called ‘le cocotier’ (the coconut tree). According to Liliane Beaulieu, this was inspired by a Polynesian custom where an old man climbs a palm tree and holds on tightly while someone shakes the trunk. If he manages to hold on, he remains accepted in the social group. Bourbaki translated this custom as the following: some members would set a mathematical trap for the others. If someone fell for it, they would yell out ‘cocotier’.”

May I be so bold as to suggest that perhaps this sudden interest in Polynesian habits was inspired by the recent release of L’ile aux cocotiers (1949), the French translation of Robert Gibbing’s book Coconut Island?

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Le Guide Bourbaki : La Ciotat (2)

Rereading the Grothendieck-Serre correspondence I found a letter from Serre to Grothendieck, dated October 22nd 1958, which forces me to retract some claims from the previous La Ciotat post.

Serre writes this ten days after the second La Ciotat-congress (La Tribu 46), held from October 5th-12th 1958:

“The Bourbaki meeting was very pleasant; we all stayed in the home of a man called Guérin (a friend of Schwartz’s – a political one, I think); Guérin himself was in Paris and we had the whole house to ourselves. We worked outside most of the time, the weather was beautiful, we went swimming almost every day; in short, it was one of the best meetings I have ever been to.”

So far so good, we did indeed find Guérin’s property ‘Maison Rustique Olivette’ as the location of Bourbaki’s La Ciotat-congresses. But, Serre was present at both meetings (the earlier one, La Tribu 35, was held from February 27th – March 6th, 1955), so wouldn’t he have mentioned that they returned to that home when both meetings took place there?

From La Tribu 35:

“The Congress was held “chez Patrice”, in La Ciotat, from February 27 to March 6, 1955. Present: Cartan, Dixmier, Koszul, Samuel, Serre, le Tableau (property, fortunately divisible, of Bourbaki).”

In the previous post I mentioned that there was indeed a Hotel-Restaurant “Chez Patrice” in La Ciotat, but mistakingly assumed both meetings took place at Guérin’s property.

Can we locate this place?

On the backside of this old photograph

we read:

“Chez Patrice”
seul au bord de la mer
Hotel Restaurant tout confort
Spécialités Provençales
Plage privée Parc auto
Ouvert toute l’année
Sur la route de La Ciota-Bandol
Tel 465
La Ciota (B.-d.-R.)

So it must be on the scenic coastal road from La Ciotat to Bandol. My best guess is that “Chez Patrice” is today the one Michelin-star Restaurant “La Table de Nans”, located at 126 Cor du Liouquet, in La Ciotat.

Their website has just this to say about the history of the place:

“Located in an exceptional setting between La Ciotat and Saint Cyr, the building of “l’auberge du Revestel” was restored in 2016.”

And a comment on a website dedicated to the nearby Restaurant Roche Belle confirms that “Chez Patrice”, “l’auberge du Revestel” and “table de Nans” were all at the same place:

“Nous sommes locaux et avons découverts ce restaurant seulement le mois dernier (suite infos copains) alors que j’ai passé une partie de mon enfance et adolescence “chez Patrice” (Revestel puis chez Nans)!!!”

I hope to have it right this time: the first Bourbaki La Ciotat-meeting in 1955 took place “Chez Patrice” whereas the second 1958-congress was held at ‘Maison Rustique Olivette’, the property of Schwartz’s friend Daniel Guérin.

Still, if you compare Serre’s letter to this paragraph from Schwartz’s autobiography, there’s something odd:

“I knew Daniel Guérin very well until his death. Anarchist, close to Trotskyism, he later joined Marceau Prevert’s PSOP. He had the kindness, after the war, to welcome in his property near La Ciotat one of the congresses of the Bourbaki group. He shared, in complete camaraderie, our life and our meals for two weeks. I even went on a moth hunt at his house and caught a death’s-head hawk-moth (Acherontia atropos).”

Schwartz was not present at the second La Ciotat-meeting, and he claims Guérin shared meals with the Bourbakis whereas Serre says he was in Paris and they had the whole house to themselves.

Moral of the story: accounts right after the event (Serre’s letter) are more trustworthy than later recollections (Schwartz’s autobiography).

Dear Collaborators of Nicolas Bourbaki, please make all Bourbaki material (Diktat, La Tribu, versions) publicly available, certainly those documents older than 50 years.

Perhaps you can start by adding the missing numbers 36 and 49 to your La Tribu: 1940-1960 list.

Thank you!

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Le Guide Bourbaki : Celles-sur-Plaine

Bourbaki held His Spring-Congresses between 1952 and 1954 in Celles-sur-Plaine in the Vosges department.

  • La Tribu 27, ‘Congres croupion des Vosges’ (March 8th-16th, 1952)
  • La Tribu 30, ‘Congres nilpotent’ (March 1st-8th, 1953)
  • La Tribu 33, ‘Congres de la tangente’ (March 28th-April 3rd, 1954)

As we can consult the Bourbaki Diktat of the first two meetings, there is no mystery as to their place of venue. From Diktat 27:

“The Congress of March 1952 will be held as planned in Celles-sur-Plaine (Vosges) at the Hotel de la Gare, from Sunday March 9 at 2 p.m. to Sunday March 16 in the evening. A train leaves Nancy on Sunday morning at 8:17 a.m., direction Raon-l’Etappe, where we arrive at 9:53 a.m.; from there a bus leaves for Celles-sur-Plaine (11 km away) at 10 am. Please bring big shoes for the walks (there will probably be a lot of snow on the heights).”

Even though few French villages have a train station, most have a ‘Place de la Gare’, indicating the spot where the busses arrive and leave. Celles-sur-Plaine is no exception, and one shouldn’t look any further to find the ‘Hotel de la Gare’.

This Hotel still exists today, but is now called ‘Hotel des Lacs’.

At the 1952 meeting, Grothendieck is listed as a ‘visitor’ (he was a guinea-pig earlier and would only become a Bourbaki-member in 1955). He was invited to settle disputes over the texts on EVTs (Topological Vector Spaces). In the quote below from La Tribu 27 ‘barrel’ refers of course to barreled space:

“But above all a drama was born from the laborious delivery of the EVTs. Eager to overcome the reluctance of the opposition, the High Commissioner attempted a blackmail tactic: he summoned Grothendieck! He hoped to frighten the Congress members to such an extent that they would be ready to swallow barrel after barrel for fear of undergoing a Grothendieckian redaction. But the logicians were watching: they told Grothendieck that, if all the empty sets are equal, some at least are more equal than others; the poor man went berserk, and returned to Nancy by the first train.”

The 1953 meeting also had a surprise guest, no doubt on Weil’s invitation, Frank Smithies, who we remember from the Bourbaki wedding joke.

Frank Smithies seated in the middle, in between Ralph Boas (left) and Andre Weil (right) at the Red Lion, Grantchester in 1939.

At the 1954 meeting we see a trace of Bourbaki’s efforts to get a position for Chevalley at the Sorbonne.

“Made sullen by the incessant rain, and exhausted by the electoral campaigns of La Sorbonne and the Consultative Committee, the faithful poured out their indecisive bile on the few drafts presented to them, and hardly took any serious decisions.”

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Charlie Hebdo on Grothendieck

Charlie Hebdo, the French satirical weekly newspaper, victim of a terroristic raid in 2015, celebrates the 30th anniversary of its restart in 1992 (it appeared earlier from 1969 till 1981).

Charlie’s collaborators have looked at figures who embody, against all odds, freedom, and one of the persons they selected is Alexandre Grothendieck, ‘Alexandre Grothendieck – l’équation libertaire’. Here’s why

“A Fields Medal winner, ecology pioneer and hermit, he threw honours, money and his career away to defend his ideas.”

If you want to learn something about Grothendieck’s life and work, you’d better read the Wikipedia entry than this article.

Some of the later paragraphs are even debatable:

“But at the end of his life, total derailment, he gets lost in the meanders of madness. Is it the effect of desperation? of too much freedom? or the abuse of logic (madness is not uncommon among mathematicians, from Kürt Godel to Grigori Perelman…)? The rebel genius withdraws to a village in the Pyrenees and refuses all contact with the outside world.”

“However, he silently continues to do math. Upon his death in 2014, thousands of pages will be discovered, of which the mathematician Michel Demazure estimates that “it will take fifty years to transform [them] into accessible mathematics”.”

If you want to read more on these ‘Grothendieck gribouillis’, see here, here, here, here, here, and here.

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Le Guide Bourbaki : La Ciotat

Two Bourbaki-congresses were organised at the Côte d’Azur, in La Ciotat, claiming to have one of the most beautiful bays in the world.

  • La Tribu 35, ‘Congres du banc public’ (February 27th – March 6th, 1955)
  • La Tribu 46, ‘Congres du banquet auxiliaire’ (October 5th-12th, 1958)

As is the case for all Bourbaki-congresses after 1953, we do not have access to the corresponding Diktat, making it hard to find the exact location.

The hints given in La Tribu are also minimal. In La Tribu 34 there is no mention of a next conferences in La Ciotat, in La Tribu 45 we read on page 11:

“October Congress: It will take place in La Ciotat, and will be a rump congress (‘congres-croupion’). On the program: Flat modules, Fiber carpets, Schwartz’ course in Bogota, Chapter II and I of Algebra, Reeditions of Top. Gen. III and I, Primary decomposition, theorem of Cohen and consorts, Local categories, Theorems of Ad(o), and (ritually!) abelian varieties.”

La Tribu 35 itself reads:

“The Congress was held “chez Patrice”, in La Ciotat, from February 27 to March 6, 1955.
Presents: Cartan, Dixmier, Koszul, Samuel, Serre, le Tableau (property, fortunately divisible, of Bourbaki).
The absence, for twenty-four hours, of any founding member, created a euphoric climate, consolidated by the aioli, non-cats, and sunbathing by the sea. We will ask Picasso for a painting on the theme ‘Bourbaki soothing the elements’. However, some explorations were disturbed by barbed wire, wardens, various fences, and Samuel, blind with anger, declared that he could not find ‘la patrice de massage’.”

The last sentence seems to indicate that the clue “chez Patrice” is a red herring. There was, however, a Hotel-Restaurant Chez Patrice in La Ciotat.

But, we will find out that the congress-location was elsewhere. (Edit August 4th : wrong see the post La Ciotat (2).

As to that location, La Tribu 46 has this to say:

“The Congress was held in a comfortable villa, equipped with a pick-up, rare editions, tasty cuisine, and a view of the Mediterranean. In the deliberation room, Chevalley claimed to see 47 fish (not counting an object, in the general shape of a sea serpent which served as an ashtray); this prompted him to bathe; but, indisposed by a night of contemplation in front of Brandt’s groupoid, he pretended to slip all his limbs into the same hole in Bruhat’s bathing suit.”

Present in 1958 were : Bruhat, Cartan, Chevalley, Dixmier, Godement, Malgrange
and Serre.

So far, we have not much to go on. Luckily, there are these couple of sentences in Laurent Schwartz’ autobiography Un mathématicien aux prises avec le siècle:

“I knew Daniel Guérin very well until his death. Anarchist, close to Trotskyism, he later joined Marceau Prevert’s PSOP. He had the kindness, after the war, to welcome in his property near La Ciotat one of the congresses of the Bourbaki group. He shared, in complete camaraderie, our life and our meals for two weeks. I even went on a moth hunt at his house and caught a death’s-head hawk-moth (Acherontia atropos).”

Daniel Guérin is known for his opposition to Nazism, fascism, capitalism, imperialism and colonialism. His revolutionary defense of free love and homosexuality influenced the development of queer anarchism.

Now we’re getting somewhere.

But there are some odd things in Schwartz’ sentences. He speaks of ‘two weeks’ whereas both La Ciotat-meetings only lasted one week. Presumably, he takes the two together, so both meetings were held at Guérin’s property.

Stranger seems to be that Schwartz was not present at either congress (see above list of participants). Or was he? Yes, he was present at the first 1955 meeting, masquerading as ‘le Tableau’. On Bourbaki photos, Schwartz is often seen in front of their portable blackboard, as we’ve seen in the Pelvoux-post. Here’s another picture from that 1951-conference with Weil and Schwartz discussing before ‘le tableau’. (Edit August 12th : wrong, La Tribu 37 lists both Schwartz and ‘Le Tableau’ among those present).

Presumably, Bourbaki got invited to La Ciotat via Schwartz’ connection with Guérin in 1955, and there was a repeat-visit three years later.

But, where is that property of Daniel Guérin?

I would love to claim that it is La Villa Deroze, (sometimes called the small Medici villa in La Ciotat), named after Gilbert Deroze. From the website:

“Gilbert Deroze’s commitment to La Ciotat (he will be deputy mayor in 1947) is accompanied by a remarkable cultural openness. The house therefore becomes a place of hospitality and artistic and intellectual convergence. For example, it is the privileged place of reception for Daniel Guérin, French revolutionary writer, anti-colonialist, activist for homosexual emancipation, theoretician of libertarian communism, historian and art critic. But it also receives guests from the place that the latter had created nearby, the Maison Rustique Olivette, a real center of artistic residence which has benefited in particular from the presence of Chester Himes, Paul Célan, the “beat” poet Brion Gysin, or again of the young André Schwarz-Bart.”

Even though the Villa Deroze sometimes received guests of Guérin, this was not the case for Bourbaki as Schwartz emphasises that the congress took place in Guérin’s property near La Ciotat, which we now have identified as ‘Maison (or Villa) Rustique Olivette’.

From the French wikipedia entry on La Ciotat:

“In 1953 the writer Daniel Guérin created on the heights of La Ciotat, Traverses de la Haute Bertrandière, an artists’ residence in his property Rustique Olivette. In the 1950s, he notably received Chester Himes, André Schwartz-Bart, in 1957, who worked there on his book The Last of the Righteous, Paul Celan, Brion Gysin. Chester Himes returned there in 1966 and began writing his autobiography there.”

Okay, now we’re down from a village (La Ciotat) to a street (Traverses de la Haute Bertrandière), but which of these fabulous villas is ‘Maison Rustique Olivette’?

I found one link to a firm claiming to be located at the Villa Rustique Olivette, and giving as its address: 130, Traverses de la Haute Bertrandière.

If this information is correct, we have now identified the location of the two last Bourbaki congress in La Ciotat as ‘Maison Rustique Olivette’,

with coordinates 43.171122, 5.597150.

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Grothendieck’s haircut

Browsing through La Tribu (the internal report of Bourbaki-congresses), sometimes you’ll find an answer to a question you’d never ask?

Such as: “When did Grothendieck decide to change his looks?”

Photo on the left is from 1951 taken by Paulo Ribenboim, on a cycling tour to Pont-a-Mousson (between Nancy and Metz). The photo on the right is from 1965 taken by Karin Tate.

From La Tribu 43, the second Bourbaki-congress in Marlotte from October 6th-11th 1957:

“The congress gave an enthusiastic welcome to Yul Grothendieck, who arrived in his Khrushchev haircut, in order to enjoy more comfortably the shadow of the sputniks. Seized with jealousy, Dixmier and Samuel rushed to the local hairdresser, who was, alas, quite unable to imitate this masterpiece.”

This Marlotte-meeting was called ‘Congres de la deuxieme lune’, because at their first congress in Marlotte, the hotel-owner thought this group of scientists was preparing for a journey to the moon. Bourbaki was saddened to find out that ownership of the ‘Hotel de la mare aux fées’ changed over the two years between meetings, for He hoped to surprise her with a return visit just at the time the first Sputnik was launched (October 4th, 1957).

Given the fact that the 1957-summer Bourbaki-congress lasted until July 7th, and that most of the B’s may have bumped into G over the summer, I’d wager that the answer to this most important of questions is: late summer 1957.

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