Near the middle of the 20th century, Nicolas Bourbaki published several mathematics texts in areas such as Set Theory, Algebra, Topology, Functions of a Real Variable, etc. These texts had a profound impact on the mathematical landscape of the day and their affect is felt to this day. Many of the readers of this blog may remember the introduction of the “New Math” where the fundamental concepts of mathematics were built from the basic concepts in set theory. So what’s so significant about Bourbaki? How about the fact that he never existed. He is a fictional character invented by a group of French mathematicians who adopted the name Bourbaki from a French general of Greek origin, who lost a significant battle to the Prussians. That’s right, publications, major mathematical contributions, all made by a group hiding behind the allonym, Nicolas Bourbaki. What’s even more interesting is that for some time, the fact that Bourbaki was fictional was not known to the general mathematical community.

The first Bourbaki congress, July 1935. From left to right, back row: Henri Cartan, René de Possel, Jean Dieudonné, André Weil, university lab technician, seated: Mirlès, Claude Chevalley, Szolem Mandelbrojt.

One of the primary founders was André Weil who, along with the rest of the founders, was quite fond of the practical joke. Originally this group was founded in order to author an improved Calculus/Analysis text. Eventually, their goal expanded to basically re-develop the whole of mathematical theory around the premise of greater rigor.

For a time, the group was very secretive. Once the secret got out, it spread fairly slowly. Bourbaki was already making waves in the mathematical community. Even when most of the French were aware of the fictional nature of the Bourbaki character, they wondered if the Americans were aware. At one point, Weil sent an application to the American Mathematical Society requesting membership. The group had gone so far as to counterfeit official documents and create an imaginary life for Nicolas Bourbaki. Nevertheless, the president of the AMS at the time had become aware of the Bourbaki “group” and sent a “tongue-in-cheek” reply saying that he understood that the application was not from an individual and that they would have to pay the *substantially* higher institutional member dues.

For more information on Bourbaki, check out some of the following links:

- Nicolas Bourbaki – Wikipedia, the free encyclopedia
- PlanetMath: Bourbaki , Nicolas
- Twenty-Five Years with Nicolas Bourbaki , 1949-1973 (pdf)