The greatest mathematician who never was

Have you heard of Nicolas Bourbaki? I hadn’t but David Gunderman writes that “he made fundamental contributions to important mathematical fields such as set theory and functional analysis.” But the problem is that he never existed. So what happened?

He first appeared in 1934 in Paris.

World War I had wiped out a generation of French intellectuals. As a result, the standard university-level calculus textbook had been written more than two and half decades before and was out of date.

Newly minted professors André Weil and Henri Cartan wanted a rigorous method to teach Stokes’ theorem, a key result of calculus. After realizing that others had similar concerns, Weil organized a meeting. It took place December 10, 1934 at a Parisian café called Capoulade.

The nine mathematicians in attendance agreed to write a textbook “to define for 25 years the syllabus for the certificate in differential and integral calculus by writing, collectively, a treatise on analysis,” which they hoped to complete in just six months.

As a joke, they named themselves after an old French general who had been duped in the Franco-Prussian war.

As they proceeded, their original goal of elucidating Stokes’ theorem expanded to laying out the foundations of all mathematics. Eventually, they began to hold regular Bourbaki “conferences” three times a year to discuss new chapters for the treatise.

Top mathematicians from across Europe, intrigued by the group’s work and style, joined to augment the group’s ranks. Over time, the name Bourbaki became a collective pseudonym for dozens of influential mathematicians spanning generations, including Weil, Dieudonne, Schwartz, Borel, Grothendieck and many others.

Mathematicians have made a plethora of important contributions under Bourbaki’s name.

To name a few, the group introduced the null set symbol; the ubiquitous terms injective, surjective, bijective; and generalizations of many important theorems, including the Bourbaki-Witt theorem, the Jacobson-Bourbaki theorem and the Bourbaki-Banach-Alaoglu theorem.

Mathematicians and scientists can sometimes have a weird sense of humor.


  1. says

    Bourbaki stands as an example of how mathematicians are different.

    In most disciplines which Publish, authors are very persnickety about the order of names, font sizes, and so on. Mathematicians (at least up until recently) have listed authors relentlessly alphabetically. And then we have Bourbaki, where important published results are simply attributed to Bourbaki.

    I can’t explain it, but it was always one of my favorite aspects of the culture.

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