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Tag: bourbaki

On categories, go and the book $\in$

Published July 24, 2014 by lievenlb

A nice interview with Jacques Roubaud (the guy responsible for Bourbaki’s death announcement) in the courtyard of the ENS. He talks about go, categories, the composition of his book $\in$ and, of course, Grothendieck and Bourbaki.

Clearly there are pop-math books like dedicated to $\pi$ or $e$, but I don’t know just one novel having as its title a single mathematical symbol : $\in$ by Jacques Roubaud, which appeared in 1967.

The book consists of 361 small texts, 180 for the white stones and 181 for the black stones in a game of go, between Masami Shinohara (8th dan) and Mitsuo Takei (2nd Kyu). Here’s the game:

In the interview, Roubaud tells that go became quite popular in the mid sixties among French mathematicians, or at least those in the circle of Chevalley, who discovered the game in Japan and became a go-envangelist on his return to Paris.

In the preface to $\in$, the reader is invited to read it in a variety of possible ways. Either by paying attention to certain groupings of stones on the board, the corresponding texts sharing a common theme. Or, by reading them in order of how the go-game evolved (the numbering of white and black stones is not the same as the texts appearing in the book, fortunately there’s a conversion table on pages 153-155).

Or you can read them by paragraph, and each paragraph has as its title a mathematical symbol. We have $\in$, $\supset$, $\Box$, Hilbert’s $\tau$ and an imagined symbol ‘Symbole de la réflexion’, which are two mirrored and overlapping $\in$’s. For more information, thereader should consult the “Dictionnaire de la langue mathématique” by Lachatre and … Grothendieck.

According to the ‘bibliographie’ below it is number 17 in the ‘Publications of the L.I.T’.

Other ‘odd’ books in the list are: Bourbaki’s book on set theory, the thesis of Jean Benabou (who is responsible for Roubaud’s conversion from solving the exercises in Bourbaki to doing work in category theory. Roubaud also claims in the interview that category theory inspired him in the composition of the book $\in$) and there’s also Guillaume d’Ockham’s ‘Summa logicae’…

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Grothendieck’s Café

Published July 1, 2014 by lievenlb

“A story says that in a Paris café around 1955 Grothendieck asked his friends “what is a scheme?”. At the time only an undefined idea of “schéma” was current in Paris, meaning more or less whatever would improve on Weil’s foundations.” (McLarty in The Rising Sea)

Finding that particular café in Paris, presumably in the 5th arrondissement, seemed like looking for a needle in a haystack.

Until now.

In trying to solve the next riddle in Bourbaki’s death announcement:

A reception will be held at the Bar ‘The Direct Products’, at the crossroads of the Projective Resolutions (formerly Koszul square)

I’ve been reading Mathematics, a novel by Jacques Roubaud (the guy responsible for the announcement) on Parisian math-life in the 50ties and 60ties.

It turns out that the poor Bourbakistas had very little choice if they wanted to have a beer (or coffee) after attending a seminar at the IHP.

On page 114, Roubaud writes:

“Père Plantin presided over his bar, which presided over the Lhomond/Ulm street corner. It is an obvious choice. rue Pierre-et-Marie-Curie had no bars; rue d’Ulm had no bars in eyeshot either. If we emerged, as we did, on this side of the Institut Henri Poincaré (for doing so on the other side would have meant fraternizing with the Spanish and Geography students in the cafés on rue Saint-Jacques, which was out of the question), we had no choice. Café Plantin had a hegemony.”

It is unclear to me whether Plantin was once actually the name of the café, or that it’s just Roubaud’s code-word for it. At other places in the book, e.g. on pages 82 and 113, he consistently writes “Plantin”, between quotes.

Today, the café on the crossroads of rue d’Ulm (where the Ecole Normal Superieure is located) and de rue Lhomond is the Interlude Café

and here’s what Roubaud has to say about it, or rather about the situation in 1997, when the French version of his book was published:

“the thing that would currently be found at the very same corner of rues Lhomond/Ulm would not be what I am here terming “Plantin”.”

So, we can only hope that the Café ‘Aux Produits Directs’ was a lot cosier, way back then.

But let us return to Grothendieck’s “What is a scheme?” story.

Now that we have a fair idea of location, what about a possible date? Here’s a suggestion: this happened on monday december 12th, 1955, and, one of the friends present must have been Cartier.

Here’s why.

The very first time the word “schéma” was uttered, in Paris, at an official seminar talk, was during the Cartan seminar of 1955/56 on algebraic geometry.

The lecturer was Claude Chevalley, and the date was december 12th 1955.


I’m fairly certain Grothendieck and Cartier attended and that Cartier was either briefed before or understood the stuff at once (btw. he gave another talk on schemes, a year later at the Chevalley seminar).

A couple of days later, on december 15th, Grothendieck sends a letter to his pal Serre (who must have been out of Paris for otherwise they’d phone each other) ending with:



Note the phrase: I am exploiting him most profitably. Yes, by asking him daft questions over a pint at Café “Plantin”…

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16 ways to capture a lion (in 1938)

Published February 13, 2013 by lievenlb

A classic among mathematical jokes is the paper in the August/September 1938 issue of the American Mathematical Monthly “A contribution to the mathematical theory of big game hunting” by one Hector Petard of Princeton who would marry, one year later, Nicolas Bourbaki’s daughter Betti.

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There are two main sources of information on the story behind this paper. There are Frank Smithies’ “Reminiscences of Ralph Boas” in the book Lion Hunting & Other Mathematical Pursuits and the transcript of an interview with John Tukey and Albert Tucker at Princeton University on 11 April 1984, part of the oral-history project on the Princeton mathematics community in the 1930s.

Smithies recalls being part of a lively group of people in Princeton during the academic year 1937/38 including Arthur Brown, Ralph Traber, Lyman Spitzer, Hugh Dowker, John Olmsted, Henry Walman, George Barnard, John Tukey, Mort Kanner (a physicist), Dick Jameson (a linguist) and Ralph Boas. Smithies writes:

“At some time that winter we were told about the mathematical methods for lion-hunting that have been devised in Gottingen, and several of us came up with new ones; who invented which method is now lost to memory. Ralph (Boas) and I decided to write up all the methods known to us, with a view to publication, conforming as closely as we could to the usual style of a mathematical paper. We choose H. Petard as a pseudonym (“the engineer, hoist with his own petard”; Hamlet, Act III, Scene IV), and sent the paper to the Americal Mathematical Monthly, over the signature of E. S. Pondiczery.”

Pondiczery was Princeton’s answer to Nicolas Bourbaki, and in the interview John Tukey recalls from (sometimes failing) memory:

“Well, the hope was that at some point Ersatz Stanislaus Pondiczery at the Royal Institute of Poldavia was going to be able to sign something ESP RIP. Then there’s the wedding invitation done by the Bourbakis. It was for the marriage of Betti Bourbaki and Pondiczery. It was a formal wedding invitation with a long Latin sentence, most of which was mathematical jokes, three quarters of which you could probably decipher. Pondiczery even wrote a paper under a pseudonym, namely “The Mathematical Theory of Big Game Hunting” by H. Petard, which appeared in the Monthly. There were also a few other papers by Pondiczery.”

Andrew Tucker then tells the story of the paper’s acceptance:

“Moulton, the editor of the Monthly at that time, wrote to me saying that he had this paper and the envelope was postmarked Princeton and he assumed that it was done by some people in math at Princeton. He said he would very much like to publish the paper, but there was a firm policy against publishing anything anonymous. He asked if I, or somebody else that he knew and could depend on, would tell him that the authorship would be revealed if for any reason it became legally necessary. I did not know precisely who they were, but I knew that John [Tukey] was one of them. He seemed to be in the thick of such things. John agreed that I could accept Moulton’s terms. I sent a letter with this assurance to Moulton and he went ahead and published it.”

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