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Witicisms and memorializing games of N. Bourbaki. (Jeux d’esprit et jeux de mémoire chez N. Bourbaki.) (French) Zbl 1005.01009

Abir-Am, Pnina G. (ed.), La mise en mémoire de la science. Pour une ethnographie historique des rites commémoratifs. Amsterdam: Éditions des Archives Contemporaines (EAC). Hist. Sci. Tech. Méd. 75-123 (1998).
A group of prominent French mathematicians (“the founders”) associated with the “École normale supérieure” decided to form, in 1934/35, an informal (and somewhat secretive) society named Nicolas Bourbaki. Their initial goal was to transform and put order into teaching of university mathematics in France and replace the long used treatise in analysis by Éduard Goursat, by a more modern work cooperated on and written collectively. The result of their labors is the world famous treatise named “Éléments de mathématique” that presents different mathematical theories in a unique, rigorous, axiomatic exposition in volumes on set theory, algebra, general topology, theory of integration, theory of functions of real variables, topological vector spaces, Lie groups and algebras, commutative algebra, spectral theory, differentiable and analytic varieties; historical notes have been collected into a separate volume.
Bourbaki proved to be one of a few distinct phenomena of the twentieth century mathematics (another example being a great development of the Soviet-era mathematics in Russia), a brand name as well as a unique style. It is no surprise thus that this paper looks into some folklore of Bourbaki as exposed through humor and jokes that was an inseparable part of the group’s activities. The author has for her sources some former members or their families and an internal publication of the group called “La Tribu” (“The Tribe” – an “ecumenical, aperiodic, Bourbakian bulletin”). This was published on the occasion of every Bourbaki congress (the meetings took place three times per year after WWII). Just as with theatrical plays, the title would have a subtitle characteristic to the congress in question; such are titles that are at the same time plays with words, usually lost in translations: “The congress of motorization of the trotting donkey,” (related to an expression Pierre Samuel utilized in polishing up the proofs) “The congress of three flat angles,” “Intermittent discussions that nevertheless terminated.” There would be an introductory part about the congress and the participants, followed by a mathematical content of the congress; thus reads one (in 1952): Present: Cartan, Chevalley, Delsarte, Dieudonné, Dixmier, Godement, Sammy, Samuel, Schwartz, Serre, Weil; Noble foreign visitors (play with words – in French “étranger” means ‘foreign’ and ‘strange’, but also ‘irrelevant’): Borel, De Rham, Hochschild; Figures: 7 females (wives), 9 children, 4 automobiles, 2 perambulators, 2 baby carriages, some cats, an éclair. When André Weil, the group’s elder, approached Élie Cartan (whose brother Henri was a Bourbakian) to publish a note in Comptes Rendus the editor asked for a biography of the author, Weil wrote that the author Bourbaki is an old professor at the Royal University of Besse-on-Poldévie whom he knows and meets in cafes, etc. Poldévie is an imaginary state invented by Alain Mellet and his colleagues of ‘L’Action française.’ Thus the first Bourbaki paper seems to be “On a theorem of Carathéodory and the measure on topological spaces” in C. R. Acad. Sci. 201, 1309-1311 (1935; Zbl 0013.15503). Note that collective publication did not prevent individual members from publishing works under their own name…
One learns that Alexandre Grothendieck claimed that “if all empty sets are equal, certainly some are more equal than the others;” one also learns of an expression adopted by many from André Weil: “With a little bit of Vaseline and a lot of patience…,” or “With a little bit of patience and a lot of Vaseline…” Every member would revise drafts of the group’s current work, which would be then examined and criticized by the peers. Some of the humor and the flavor of the individual authors can be traced in the final product by a careful observer. The comments found on these revisions are merciless in its humorous critiques. Comments about colleagues’ work: “phobic,” “purely chimerical,” “inconsequential,” “foolish”, “You do not know anything, you do not understand,” “scurrilous hot air”, “worn-out” ideas and regurgitations that beg the reviewer “not to bother Bourbaki any more.”
One also learns of some character traits of some members that earned them appropriate nicknames: Henri Cartan was named a “mosquito” for his constant stinging and stubbornness; his habit to correct even slightest typographical errors of his colleagues resulted in calls to change his career into a “professor of orthography.” Claude Chevalley is a radical, a visionary, a “metaphysician” who tends to sink Bourbaki affairs in the game of Go. He also had a tendency to forget what position he is defending, sometimes defending the opposite position with same resolve the next day – a trait he shared among other things with Dieudonné. Jean Dieudonné is a giant who thunders, stings the angry saints and threatens to resign for any or for no reason (sometimes premeditated moves). Samuel “Sammy” Eilenberg earned a nickname of a “Grand Functor” who through pushing of his projects for publication in Bourbaki was characterized to be like a merchant of rugs. Laurent Schwartz is a Trotskyite who aspires to succeed Stalin.
There are many other aspects treated in this article, such as Bourbaki poems, spicy language, imitation of current personalities, treated in this paper which was published in a publication on ethnography. The author argues that this Bourbaki burlesque fulfills at the same time a function of identification and reference. The humor created a community of thought among the members of Bourbaki – a \`\` culture of Bourbaki,” that aided in one way or the other the splendid accomplishments that make up Bourbaki’s legacy.
An interested reader can find more on the story of Bourbaki by looking into the following Zentralblatt reviews: A. Weil, Souvenirs d’apprentissage. Vita Mathematica 6, Birkhäuser (1991; Zbl 0733.01024), P. Colmez (ed.) and J.-P. Serre (ed.), Correspondance Grothendieck-Serre. Documents Mathématiques (Paris). 2. Paris: x. 228 p. (2001; Zbl 0986.01019), J.-P. Serre, Exposés de séminaires. 1950-1999. Reprints. Documents Mathématiques (Paris). 1. Paris (2001; Zbl 1005.01014).
For the entire collection see [Zbl 0983.00019].

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
01A60 History of mathematics in the 20th century
01A72 Schools of mathematics
01A65 Development of contemporary mathematics
01A80 Sociology (and profession) of mathematics
01A99 History of mathematics and mathematicians

Biographic References:

Bourbaki, Nicolas

Software:

Mathematica
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