Bourbaki group

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935. With the goal of grounding all of mathematics on set theory, the group strove for rigour and generality. Their work led to the discovery of several concepts and terminologies still used, and influenced modern branches of mathematics.

While there is no one person named Nicolas Bourbaki, the Bourbaki group, officially known as the Association des collaborateurs de Nicolas Bourbaki (Association of Collaborators of Nicolas Bourbaki), has an office at the École Normale Supérieure in Paris.

In 1934, young French mathematicians from various French universities felt the need to form a group to jointly produce textbooks that they could all use for teaching. André Weil organized the first meeting on 10 December 1934 in the basement of a Parisian grill room, while all participants were attending a conference in Paris.

Bourbaki's main work is the Elements of Mathematics (Éléments de mathématique) series. This series aims to be a completely self-contained treatment of the core areas of modern mathematics. Assuming no special knowledge of mathematics, it takes up mathematics from the very beginning, proceeds axiomatically and gives complete proofs.

and later

The book Variétés différentielles et analytiques was a fascicule de résultats, that is, a summary of results, on the theory of manifolds, rather than a worked-out exposition. The (still incomplete) volume on spectral theory (Théories spectrales) from 1967 was for almost four decades the last new book to be added to the series. After that several new chapters to existing books as well as revised editions of existing chapters appeared until the publication of chapters 8-9 of Commutative Algebra in 1983. Then a long break in publishing activity occurred, leading many to suspect the end of the publishing project. However, chapter 10 of Commutative Algebra appeared in 1998, and after another long break a completely re-written and expanded chapter 8 of Algèbre was published in 2012. More importantly, the first four chapters of a completely new book on algebraic topology were published in 2016. The new material from 2012 and 2014 address some references to forthcoming books in the book on Lie Groups and Algebras; there remain other such references (some very precise) to expected additional chapters of the book spectral theory.

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