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Bourbaki Congress, in 1938.
Considered one of the greatest mathematicians of all time, Nicolas Bourbaki was nothing more than a pseudonym adopted by a group of great mathematicians, who revolutionized mathematics as we know it.
The mathematician Nicolas Bourbaki He is among the greatest mathematicians of the 20th century. Currently unknown, he was probably the last mathematician to master almost all aspects of this science.
He made fundamental contributions to important mathematical fields such as set theory and functional analysis.
There’s just one small problem: Nicolas Bourbaki never existed.
Although it is now widely accepted that there never was a Nicolas Bourbaki, there is evidence to the contrary. For example, there are wedding announcements for his daughter Betty, a baptismal certificate in her name, and an impressive family lineage dating back to an ancestor Napoleon raised as his own son.
Even the mathematical community was fooled for some time, mathematician David Gunderman said in 2019 in an article on .
When Ralph Boaseditor of the magazine Mathematical Reviews, revealed that Bourbaki was a pseudonymwas immediately refuted by Bourbaki himself, who in a letter counterattacked, saying that BOAS was, in fact, just an acronym for the surnames of the magazine’s editors.
It is said that while visiting Finland at the start of World War II, the French mathematician Andrew Weil was investigated for espionage.
Authorities found suspicious documents in his possession: a fake ID, a set of business cards and even invitations from the Russian Academy of Sciences — all in the name of Bourbaki. Supposedly, Weil was only released after an officer recognized him as a “prominent mathematician”.
Who was Bourbaki?
If Bourbaki never existed, who (or what) — was he? The name Nicolas Bourbaki first appeared in a place shaken by turbulence at a volatile moment in history: Paris, in 1934.
A First World War destroyed a generation of French intellectuals. As a result, the standard college calculus textbook had been written more than two and a half decades earlier and was out of date.
Newly licensed professors André Weil and Henri Cartan wanted a rigorous method for teaching Stokes’ theorem. After realizing that others had similar concerns, Weil organized a meeting. It happened on December 10, 1934 in a Parisian café called Capoulade.
Café Capoulade, in 1943.
The nine mathematicians present agreed to write a book “to define for 25 years the study plan for the certificate in differential and integral calculus, collectively writing an analytical treatise”, which they hoped to complete in just six months.
As a joke, they named their group after name of an ancient French general who had been deceived in the Franco-Prussian war: Bourbaki.
As they proceeded, their original goal of elucidating Stokes’ theorem expanded to establish the foundations of all mathematics. Eventually, they began holding regular “conferences” three times a year to discuss new chapters for the treaty.
Leading mathematicians from across Europe, intrigued by the group’s work and style, joined together to swell the group’s ranks. Over time, the name Bourbaki became a collective pseudonym for dozens of influential mathematicians of several generations, including Weil, Dieudonne, Schwartz, Borel, Grothendieck and many others.
Since then, the group, which has added new members over time, has proven to have a profound impact on mathematics, certainly rivaling any of its individual contributors.
Deep impact
Mathematicians made a multitude of important contributions under the name Bourbaki.
To name a few, the group introduced the null set symbol; the terms of injective, surjective and bijective functions; and generalizations of many important theorems, including the Bourbaki-Witt theorem, the Jacobson-Bourbaki theorem, and the Bourbaki-Banach-Alaoglu theorem.
His text, “Elements of Mathematics”, has more than 6,000 pages and provides a “solid foundation for the entire body of modern mathematics”according to mathematician Barbara Pieronkiewicz.
Bourbaki’s influence is still alive and well. Now, in “his” eightieth year of research, in 2016, he published the 11th volume of “Elements of Mathematics”. The Bourbaki group, with its ever-changing roster of members, still holds seminars at the University of Paris.
In part thanks to the breadth and importance of his mathematical contributions, and also because, ageless, immutable and operating in many places at once, “he” seems to defy the very laws of physics — and Bourbaki’s mathematical prowess. will probably never be equaled.
