Dispelling a Myth: Questions and Answers about Bourbaki’s Early Work, 1934–1944

Abstract

The group of mathematicians who wrote the treatise Éléments de mathématique under the assumed name “N. Bourbaki” inspired and created legends and controversies. This paper retraces Bourbaki’s initial goals and analyzes some of the first written outlines for the treatise. This account answers some questions about the team’s original visions. It shows how Bourbaki set out to write a treatise of analysis that could serve various purposes, some of which pertained to research and others to the teaching of mathematics. Bourbaki’s first outlines covered much classical analysis, including the range of topics found in the then current French Cours d’analyse. While Bourbaki intended to recast these subjects in a more modern setting, it was not immediately obvious to the group what particular setting would be appropriate. Other features of Bourbaki’s early outlines include the scarcity of set theory, algebra and topology, along with a marked conservativeness in the treatment of these subjects. From this perspective, the paper argues that Bourbaki’s treatise did not arise from a ready-made, architectural and unitary vision of mathematics which the members of the group would have shared at the outset. Rather, any coherent doctrine that may eventually be attributed to Bourbaki was the outcome of painstaking reworkings and discussions.