nLab Elements of Mathematics

Related entries

Elements of Mathematics (French: Éléments de mathématique) is a series of books by Nicolas Bourbaki.

It is named after Euclid‘s Elements (Στοιχεῖα).


Most of these books were quite influential, some of them especially so.

In particular, Bourbaki’s presentation of multilinear algebra in Chapter III of the second book (Algèbre) was the first detailed expository presentation of the Grassmann algebra.

Another influential book was Groupes et algèbres de Lie, its presentation of root systems and related topics in Chapter 4–6 was the first of its kind.

Some criticisms raised against this series:

  • Almost complete absence of categories (a deliberate choice);

  • Théorie des ensembles receives a lot of criticism for its somewhat nonstandard treatment of logic, as well as the rather awkward notion of a structure, which occupies a similar niche to categories.

  • The use of Daniell’s approach in Intégration, mostly ignoring abstract measure spaces.

  • Chapter 10 of Algèbre (homological algebra) only covers the very classical results, (intentionally) ignoring derived categories.

category: reference

Last revised on May 18, 2022 at 16:32:29. See the history of this page for a list of all contributions to it.