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Inside the Secret Math Society Known Simply as Nicolas Bourbaki
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Abstractions blog
Inside the Secret Math Society Known Simply as Nicolas Bourbaki
By
Kevin Hartnett
November 9, 2020
For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.
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Some of the founding members of the secretive math group Nicolas Bourbaki include Henri Cartan (standing, leftmost), André Weil (standing, second from right) and Szolem Mandelbrojt (seated, rightmost).
Nicolas Bourbaki
Introduction
By Kevin Hartnett
Contributing Writer
November 9, 2020
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Antoine Chambert-Loir’s initiation into one of math’s oldest secret societies began with a phone call. “They told me Bourbaki would like me to come and see if I’d work with them,” he said.
Chambert-Loir accepted, and for a week in September 2001 he spent seven hours a day reading math texts out loud and discussing them with the members of the group, whose identities are unknown to the rest of the world.
He was never officially asked to join, but on the last day he was given a long-term task — to finish a manuscript the group had been working on since 1975. When Chambert-Loir later received a report on the meeting he saw that he was listed as a “membrifié,” indicating he was part of the group. Ever since, he’s helped advance an almost Sisyphean tradition of math writing that predates World War II.
The group is known as “Nicolas Bourbaki” and is usually referred to as just Bourbaki. The name is a collective pseudonym borrowed from a real-life 19th-century French general who never had anything to do with mathematics. It’s unclear why they chose the name, though it may have originated in a prank played by the founding mathematicians as undergraduates at the École Normale Supérieure (ENS) in Paris.
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“There was some custom to play pranks on first-years, and one of those pranks was to pretend that some General Bourbaki would arrive and visit the school and maybe give a totally obscure talk about mathematics,” said Chambert-Loir, a mathematician at the University of Paris who has acted as a spokesperson for the group and is its one publicly identified member.
Bourbaki began in 1934, the initiative of a small number of recent ENS alumni. Many of them were among the best mathematicians of their generation. But as they surveyed their field, they saw a problem. The exact nature of that problem is also the subject of myth.
In one telling, Bourbaki was a response to the loss of a generation of mathematicians to World War I, after which the group’s founders wanted to find a way to preserve what math knowledge remained in Europe.
“There is a story that young French mathematicians were not seen as a government priority during [the] First World War and many were sent to war and died there,” said Sébastien Gouëzel of the University of Rennes, who is not publicly identified with the group but, like many mathematicians, is familiar with its activities.
In a more prosaic but probably also more likely rendering, the original Bourbaki members were simply dissatisfied with the field’s textbooks and wanted to create better ones. “I think at the beginning it was just for that very concrete matter,” Chambert-Loir said.
Nicolas Bourbaki
Whatever their motivation, the founders of Bourbaki began to write. Yet instead of writing textbooks, they ended up creating something completely novel: free-standing books that explained advanced mathematics without reference to any outside sources.
The first Bourbaki text was meant to be about differential geometry, which reflected the tastes of some of the group’s early members, luminaries like Henri Cartan and André Weil. But the project quickly expanded, since it’s hard to explain one mathematical idea without involving many others.
“They realized that if they wanted to do this cleanly, they needed [ideas from other areas], and Bourbaki grew and grew into something huge,” Gouëzel said.
The most distinctive feature of Bourbaki was the writing style: rigorous, formal and stripped to the logical...