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Tag: bourbaki

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 : 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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Le Guide Bourbaki : Royaumont

At least six Bourbaki-congresses were held in ‘Royaumont’:

  • La Tribu 18 : ‘Congres oecumenique du cocotier’, April 13th-25th 1949
  • La Tribu 22 : ‘Congres de la revanche du cocotier’, April 5th-17th 1950
  • La Tribu without number : ‘Congres de l’horizon’, October 8th-15th 1950
  • La Tribu 26 : ‘Congres croupion’, October 1st-9th 1951
  • La Tribu 31 : ‘Congres de la revelation du reglement’, JUne 6th-19th 1953
  • La Tribu 32 : ‘Congres du coryza’, October 2nd-9th 1953

All meetings were pre-1954, so the ACNB generously grants us all access to the corresponding Bourbaki Diktats. From Diktat 31:

“The next congress will be held at the Abbey of Royaumont, from Saturday June 6th (not from June 5th as planned) to Saturday June 20th.
We meet at 10 a.m., June 6 at the Gare du Nord before the ticket-check. Train to Viarmes (change at Monsoult at 10.35 a.m.). Do not bring a ticket: one couch can transport 4 delegates.
Bring the Bible according to the following distribution:
Cartan: livre IV. Dixmier: Alg. 3, livre VI. Godement: Alg.4-5, Top. 1-2. Koszul: Top. 5-6-7-8-9. Schwartz: Top. 10, Alg. 1-2. Serre: Top. 3-4, livre V. Weil: Alg. 6-7, Ens. R.”

Royaumont Abbey is a former Cistercian abbey, located near Asnières-sur-Oise in Val-d’Oise, approximately 30 km north of Paris, France.

How did Bourbaki end up in an abbey? From fr.wikipedia Abbaye de Royaumont:

In 1947, under the direction of Gilbert Gadoffre, Royaumont Abbey became the “International Cultural Center of Royaumont”, an alternative place to traditional French university institutions. During the 1950s and 1960s, the former abbey became a meeting place for intellectual and artistic circles on an international scale, with numerous seminars, symposiums and conferences under the name “Cercle culturel de Royaumont”. Among its illustrious visitors came Nathalie Sarraute, Eugène Ionesco, Alain Robbe-Grillet, Vladimir Jankélévitch, Mircea Eliade, Witold Gombrowicz, Francis Poulenc and Roger Caillois.

And… less illustrious, at least according to the French edition of Wikipedia, the Bourbaki-gang.

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Le Guide Bourbaki : Marlotte

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.

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The (somewhat less) Secret Bourbaki Archive

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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Princeton’s own Bourbaki

In the first half of 1937, Andre Weil visited Princeton and introduced some of the postdocs present (notably Ralph Boas, John Tukey, and Frank Smithies) to Poldavian lore and Bourbaki’s early work.

In 1935, Bourbaki succeeded (via father Cartan) to get his paper “Sur un théorème de Carathéodory et la mesure dans les espaces topologiques” published in the Comptes Rendus des Séances Hebdomadaires de l’Académie des Sciences.

Inspired by this, the Princeton gang decided to try to get a compilation of their mathematical ways to catch a lion in the American Mathematical Monthly, under the pseudonym H. Petard, and accompanied by a cover letter signed by another pseudonym, E. S. Pondiczery.

By the time the paper “A contribution to the mathematical theory of big game hunting” appeared, Boas and Smithies were in cambridge pursuing their postdoc work, and Boas reported back to Tukey: “Pétard’s paper is attracting attention here,” generating “subdued chuckles … in the Philosophical Library.”

On the left, Ralph Boas in ‘official’ Pondiczery outfit – Photo Credit.



The acknowledgment of the paper is in true Bourbaki-canular style.

The author desires to acknowledge his indebtedness to the Trivial Club of St. John’s College, Cambridge, England; to the M.I.T. chapter of the Society for Useless Research; to the F. o. P., of Princeton University; and to numerous individual contributors, known and unknown, conscious and unconscious.

The Trivial Club of St. John’s College probably refers to the Adams Society, the St. John’s College mathematics society. Frank Smithies graduated from St. John’s in 1933, and began research on integral equations with Hardy. After his Ph. D., and on a Carnegie Fellowship and a St John’s College studentship, Smithies then spent two years at the Institute for Advanced Study at Princeton, before returning back ‘home’.

In the previous post, I assumed that Weil’s visit to Cambridge was linked to Trinity College. This should probably have been St. John’s College, his contact there being (apart from Smithies) Max Newman, a fellow of St. John’s. There are two letters from Weil (summer 1939, and summer 1940) in the Max Newman digital library.



The Eagle Scanning Project is the online digital archive of The Eagle, the Journal of St. John’s College. Last time I wanted to find out what was going on, mathematically, in Cambridge in the spring of 1939. Now I know I just had to peruse the Easter 1939 and Michaelmas 1939 volumes of the Eagle, focussing on the reports of the Adams Society.

In the period Andre Weil was staying in Cambridge, they had a Society Dinner in the Music Room on March 9th, a talk about calculating machines (with demonstration!) on April 27th, and the Annual Business Meeting on May 11th, just two days before their punting trip to Grantchester,



The M.I.T. chapter of the Society for Useless Research is a different matter. The ‘Useless Research’ no doubt refers to Extrasensory Perception, or ESP. Pondiczery’s initials E. S. were chosen with a future pun in mind, as Tukey said in a later interview:

“Well, the hope was that at some point Ersatz Stanislaus Pondiczery at the Royal Institute of Poldavia was going to be able to sign something ESP RIP.”

What was the Princeton connection to ESP research?

Well, Joseph Banks Rhine conducted experiments at Duke University in the early 1930s on ESP using Zener cards. Amongst his test-persons was Hubert Pearce, who scored an overall 40% success rate, whereas chance would have been 20%.



Pearce and Joseph Banks Rhine (1932) – Photo Credit

In 1936, W. S. Cox tried to repeat Rhine’s experiment at Princeton University but failed. Cox concluded “There is no evidence of extrasensory perception either in the ‘average man’ or of the group investigated or in any particular individual of that group. The discrepancy between these results and those obtained by Rhine is due either to uncontrollable factors in experimental procedure or to the difference in the subjects.”

As to the ‘MIT chapter of the society for useless research’, a chapter usually refers to a fraternity at a University, but I couldn’t find a single one on the list of MIT fraternities involved in ESP, now or back in the late 1930s.

However, to my surprise I found that there is a MIT Archive of Useless Research, six boxes full of amazing books, pamphlets and other assorted ‘literature’ compiled between 1900 and 1940.

The Albert G. Ingalls pseudoscience collection (its official name) comprises collections of books and pamphlets assembled by Albert G. Ingalls while associate editor of Scientific American, and given to the MIT Libraries in 1940. Much of the material rejects contemporary theories of physical sciences, particularly theoretical and planetary physics; a smaller portion builds upon contemporary science and explores hypotheses not yet accepted.

I don’t know whether any ESP research is included in the collection, nor whether Boas and Tukey were aware of its existence in 1938, but it sure makes a good story.

The final riddle, the F. o. P., of Princeton University is an easy one. Of course, this refers to the “Friends of Pondiczery”, the circle of people in Princeton who knew of the existence of their very own Bourbaki.

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the Bourbaki code revisited

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

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

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



Bourbaki at Beauvallon 1938 – Photo Credit

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



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

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

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

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Map of the Parisian mathematical scene 1933-39

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Michele Audin has written a book on the history of the Julia seminar (hat tip +Chandan Dalawat via Google+).

The “Julia Seminar” was organised between 1933 and 1939, on monday afternoons, in the Darboux lecture hall of the Institut Henri Poincare.

After good German tradition, the talks were followed by tea, “aimablement servi par Mmes Dubreil et Chevalley”.

A perhaps surprising discovery Audin made is that the public was expected to pay an attendance fee of 50 Frs. (approx. 32 Euros, today), per year. Fortunately, this included tea…

The annex of the book contains the lists of all people who have paid their dues, together with their home addresses.

The map above contains most of these people, provided they had a Parisian address. For example, Julia himself lived in Versailles, so is not included.

As are several of the first generation Bourbakis: Dieudonne lived in Rennes, Henri Cartan and Andre Weil in Strasbourg, Delsarte in Nancy, etc.

Still, the lists are a treasure trove of addresses of “les vedettes” (the professors and the people in the Bourbaki-circle) which have green markers on the map, and “les figurants” (often PhD students, or foreign visitors of the IHP), the blue markers.

Several PhD-students gave the Ecole Normale Superieure (btw. note the ‘je suis Charlie’-frontpage of the ENS today jan.9th) in the rue d’Ulm as their address, so after a few of them I gave up adding others.

Further, some people changed houses over this period. I will add these addresses later on.

The southern cluster of markers on Boulevard Jourdan follows from the fact that the university had a number of apartment blocks there for professors and visitors (hat tip Liliane Beaulieu).

A Who’s Who at the Julia seminar can be found in Audin’s book (pages 154-167).

Reference:

Michele Audin : “Le seminaire de mathematiques 1933-1939, premiere partie: l’histoire”

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