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Nicolas Bourbaki

       Nicolas Bourbaki

Nicolas Bourbaki (1935) is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics. The original goal of the group had been to compile an improved mathematical analysis text, but it was soon decided that a more comprehensive treatment of all of mathematics was necessary. There was no official status of membership, and at the time the group was quite secretive and also fond of supplying disinformation. Regular meetings were scheduled, during which the whole group would vigorously discuss every proposed line of every book. Members had to resign by age 50.
       Through the years members of the group through were: Alexander Grothendieck, André Weil, Charles Ehresmann, Claude Chevalley, Henri Cartan, Hyman Bass, Jean Coulomb, Jean Delsarte, Jean Dieudonné, Jean-Louis Koszul, Jean-Pierre Serre, Laurent Schwartz, René de Possel, Roger Godement, Samuel Eilenberg, Serge Lang and Szolem Mandelbrojt.
       Although ‘Nicolas Bourbaki’ is an invented personage, the Bourbaki group is officially known as the ‘Association des collaborateurs de Nicolas Bourbaki’ [Association of Collaborators of Nicolas Bourbaki], and has an office at the École Normale Supérieure in Paris.
        It is rather surprising that members of the group seemed a little unsure of exactly where the name had come from. Certainly the name came from General Charles Soter Bourbaki was a French general who had fought in the Franco-Prussian war (1870–1871). When André Weil was a first year student at the École Normale Supérieur a lecture was announced which all first year students were encouraged to attend. The lecturer was Raoul Husson, a senior student, who disguised himself as a distinguished venerable mathematician. To appear the part he put on a false beard and delivered the lecture in a heavy foreign accent. He presented a series of theorems, all completely wrong, each attributed to a different fake mathematician. The names for the theorems were taken from French generals, and the final and most ridiculous theorem he presented he had named ‘Bourbaki's theorem’, taking the name from General Bourbaki. The humour of this was so enjoyed by all members of the group designing the Analysis Treatise that they adopted the name Bourbaki. It would appear that Nicolas was a classical reference to an ancient Greek hero from whom General Bourbaki was descended. (There was certainly also a reference to Greek mathematics, Bourbaki being of Greek extraction. It is a valid reading to take the name as implying a transplantation of the tradition of Euclid to a France of the 1930s, with soured expectations.)
       Another example of the humour of the members regarding the pseudonym, is their response to an article written by R.P. Boas, editor of Mathematical Reviews. Boas explains that Nicolas Bourbaki is the pseudonym for a group of young French mathematicians. Soon thereafter the publisher of Boas' article received a letter from Nicolas Bourbaki in which he objected in strong terms that his existence was drawn into question. Bourbaki then continued in his letter explaining that the BOAS was nothing but a pseudonym for the editors of Mathematical Reviews.

‘Nicolas Bourbaki’, The MacTutor History of Mathematics archive, retrieved 3 August 2013
‘Nikolas Bourbaki’, Wikipedia, retrieved 12 October 2013

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