An Introduction to Nicolas Bourbaki, One of the Most Influential Mathematicians of All Time … Who Never Actually Lived

By Colin Marshall

In 20th-century mathematics, the renowned name of Nicolas Bourbaki stands alone in its class — the class, that is, of renowned mathematical names that don’t actually belong to real people. Bourbaki refers not to a mathematician, but to mathematicians; a whole secret society of them, in fact, who made their name by collectively composing Elements of Mathematic. Not, mind you, Elements of Mathematics: “Bourbaki’s Elements of Mathematic — a series of textbooks and programmatic writings first appearing in 1939—pointedly omitted the ‘s’ from the end of ‘Mathematics,'” writes JSTOR Daily’s Michael Barany, “as a way of insisting on the fundamental unity and coherence of a dizzyingly variegated field.”

That’s merely the tip of Bourbaki’s iceberg of eccentricities. Formed in 1934 “by alumni of the École normale supérieure, a storied training ground for French academic and political elites,” this group of high-powered mathematical minds set about rectifying their country’s loss of nearly an entire generation of mathematicians in the First World War. (While Germany had kept its brightest students and scientists out of battle, the French commitment to égalité could permit no such favoritism.) It was the pressing need for revised and updated textbooks that spurred the members of Bourbaki to their collaboratively pseudonymous, individually anonymous work.

“Yet instead of writing textbooks,” explains Quanta‘s Kevin Hartnett, “they ended up creating something completely novel: free-standing books that explained advanced mathematics without reference to any outside sources.” The most distinctive feature of this already unusual project “was the writing style: rigorous, formal and stripped to the logical studs. The books spelled out mathematical theorems from the ground up without skipping any steps — exhibiting an unusual degree of thoroughness among mathematicians.”  Not that Bourbaki lacked playfulness: “In fanciful and pun-filled narratives shared among one another and alluded to in outward-facing writing,” adds Barany, “Bourbaki’s collaborators embedded him in an elaborate mathematical-political universe filled with the abstruse terminology and concepts of modern theories.”

You can get an animated introduction to Bourbaki, which survives even today as a still-prestigious and at least nominally secret mathematical society, in the TED-Ed lesson above. In the decades after the group’s founding, writes lesson author Pratik Aghor, “Bourrbaki’s publications became standard references, and the group’s members took their prank as seriously as their work.” Their commitment to the front was total: “they sent telegrams in Bourbaki’s name, announced his daughter’s wedding, and publicly insulted anyone who doubted his existence. In 1968, when they could no longer maintain the ruse, the group ended their joke the only way they could: they printed Bourbaki’s obituary, complete with mathematical puns.” And if you laugh at the mathematical pun with which Aghor ends the lesson, you may carry a bit of Bourbaki’s spirit within yourself as well.

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Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.