Search Results for “bourbaki” – Page 19

Map of the Parisian mathematical scene 1933-39

Published January 9, 2015 by lievenlb

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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”

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’…

Oulipo’s use of the Tohoku paper

Published July 17, 2014 by lievenlb

Many identify the ‘Tohoku Mathematical Journal’ with just one paper published in it, affectionately called the Tohoku paper: “Sur quelques points d’algèbre homologique” by Alexander Grothendieck.

In this paper, Grothendieck reshaped homological algebra for Abelian categories, extending the setting of Cartan-Eilenberg (their book and the paper both appeared in 1957). While working on the Tohoku paper in Kansas, Grothendieck did not have access to the manuscript of the 1956 book of Cartan-Eilenberg, about which he heard from his correspondence with Serre.

Concerning the title, an interesting suggestion was made by Mathieu Bélanger in his thesis “Grothendieck et les topos: rupture et continuité dans les modes d’analyse du concept d’espace topologique”, (footnote 18 on page 164):

“There is a striking resemblance between the title of the Grothendieck’s article “Sur quelques points d’algèbre homologique”, and that of Fréchet‘s thesis “Sur quelques points d’analyse fonctionelle”. Why? Grothendieck remains silent about it. Perhaps he saw a methodological similarity between the introduction, by Fréchet, of abstract spaces in order to develop the foundations of functional calculus and that of the Abelian categories he needed to clarify the homological theory. Compared with categories of sets, groups, topological spaces, etc. that were used until then, Abelian categories are in effect abstract categories.”

But, what does this have to do with the literary group OuLiPo (ouvroir de littérature potentielle, ‘workshop of potential literature’)?

Oulipo was founded in 1960 by Raymond Queneau and François Le Lionnais. Other notable members have included novelists Georges Perec and Italo Calvino, poets Oskar Pastior, Jean Lescure and poet/mathematician Jacques Roubaud.

Several members of Oulipo were either active mathematicians or at least had an interest in mathematics. Sometimes, Oulipo is said to be the literary answer to Bourbaki. The group explored new ways to create literature, often with methods coming from mathematics or programming.

One such method is described in “Chimères” by Le Lionnais:

One takes a source text A. One ’empties’ it, that is, one deletes all nouns, adjectives and verbs, but marks where they were in the text. In this way we have ‘prepared’ the text.

Next we take three target texts and make lists of words from them, K the list of nouns of the first, L the list of adjectives of the second and M the list of verbs of the third. Finally, we fill the empty spaces in the source text by words from the target lists, in the order that they appeared in the target texts.

In the example Le Lionnais gives, the liste M is the list of all verbs appearing in the Tohoku paper.

71 search results for "bourbaki"

Map of the Parisian mathematical scene 1933-39

On categories, go and the book $\in$

Oulipo’s use of the Tohoku paper