Mathematical collective

Since 1939 an author named Nicolas Bourbaki has published a series of volumes on pure mathematics. But Bourbaki does not exist.

1938 Bourbaki collective
Unknown author, Public domain, via Wikimedia Commons

Éléments de Mathématique is a series of textbooks that dig deeply into pure mathematics: algebra, topology, set theory, and so on. In the tradition of Euclid’s Elements and Whitehead and Russell’s Principia Mathematica, it tries to give a comprehensive and structured overview of mathematics.

Unlike those two works, Éléments de Mathématique is a work in progress. The first volumes came out in 1939. The most recent volume was published in 2016. All of those volumes have the same author: Nicolas Bourbaki. And, of course, Bourbaki is not a real person.

Well, there was a Bourbaki: Charles-Denis Bourbaki was a 19th century French general who suffered a spectacular defeat in the Franco-Prussian War. What did he have to do with mathematics? Not a lot. Many of France’s best and brightest students (including those of mathematics) went to the front lines in the early 20th century, and some did not come home again, so when a student named Raoul Husson needed a pseudonym for a prank Bourbaki was the name that jumped to his mind.

The prank was a good one. In 1923, Husson was a student at the École Normale Supérieure, a “grande école” in Paris. (Side note: grande écoles are related to, but distinct from, universities. Entry is selective and highly competitive.) Husson wore a fake beard to a conference and presented a fake and intentionally baffling mathematical theorem. The name he chose? The Bourbaki theorem.

From then on, Bourbaki became an in-joke amongst aspiring mathematicians. André Weil, teaching in India, encouraged the mathematician Damodar Kosambi to allude to the fictional Bourbaki as a way of impressing and bamboozling a problematic colleague. When Weil returned to France, he and five other mathematicians began work on a “collective textbook” that would support their mathematics teaching. And, in keeping with the collective nature of that work, they credited that work – the Éléments de Mathématique – to one Nicolas Bourbaki.

The collective pseudonym stuck, and while the makeup of the writing group has changed a lot in the last eighty years the work and the name continue. Today Bourbaki has a newsletter, a seminar series, and a lot of admirers.

(End note: the mathematics community seems to enjoy their communal pseudonyms: John Rainwater, Blanche Descartes, Arthur Besse, and G. W. Peck have all authored significant mathematical publications despite all being fictional.)

[Thanks to an anonymous reader who asked to be identified as Nicolas Bourbaki Jr.]

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