ESHS/HSS Annual Meeting

Bourbaki's 'redactions'. Reconstructing values of intelligibility from drafts of expository material

• In Event: Mathematics in Manuscripts 2

English Abstract

The Bourbaki group, together with the massive /Éléments de mathématique/ textbook its members authored collectively from the mid-1930s, have become emblematic of a certain kind of mathematical modernity. In particular, the group's distinctive (and sometimes controversial) style of exposition has had a large impact on the teaching and writing of pure mathematics in the second half of the 20th century. The standard way of portraying Bourbaki's writing choices is to emphasize the group's commitment to prove theorems in the most general setting possible (for instance, if a theorem is true not only of real numbers, but also of other mathematical objects, the group would typically provide an abstract, general proof first and only then derive the result for real numbers as a special case). This talk will discuss how, by drawing on the archives of the group—and in particular on the numerous successive drafts of chapters of the /Éléments/ that they contain—one can paint a richer picture of the values driving Bourbaki's expository choices. More specifically, I suspect that part of the group's aura relies on a feature of their textbooks that is harder to pin down than their mere generality, namely peculiar virtues of clarity of the proofs. The talk will argue that an examination of the archives reveals a sustained, though often implicit effort to make proofs, in some sense, economical and conceptually transparent, including by choosing definitions accordingly, even at the expense of other expository values.

Author

• David Waszek