Nicolas Bourbaki

In 1934, André Weil and Henri Cartan, both young professors of mathematics at the University of Strasbourg, would frequently, when discussing the calculus courses, they were teaching, deplore the textbooks available, all of which they considered antiquated and inadequate. Weil eventually suggested getting in touch with several of their fellow alumni of the École Normale Supérieure who were teaching similar courses in provincial universities around France, inviting them to collaborate on a new analysis textbook. The complete work was expected to total 1000 to 1200 pages, with the first volumes ready about 6 months after the project began. Thus began 1 of the most flabbergasting examples of “mission creep” in human intellectual history, which set the style for much of mathematics publication and education in subsequent decades. Working collectively and publishing under the pseudonym “Nicolas Bourbaki” (after the French general in the Franco-Prussian War Charles Denis Bourbaki), the “analysis textbook” to be assembled by a small group over a few years grew into a project spanning more than 60 years and 10 books, most of multiple volumes, totaling more than 7000 pages, systematizing the core of mathematics in a relentlessly abstract and austere axiomatic form. Although Bourbaki introduced new terminology, some of which has become commonplace, there is no new mathematics in the work: it is a presentation of pre-existing mathematical work as a pedagogical tool and toolbox for research mathematicians. (This is not to say that the participants in the Bourbaki project did not do original work—in fact, they were among the leaders in mathematical research in their respective generations. But their work on the Bourbaki opus was a codification and grand unification of the disparate branches of mathematics into a coherent whole. In fact, so important was the idea that mathematics was a unified tree rooted in set theory that the Bourbaki group always used the word mathématique, not mathématiques.)

Leave a comment