**Nicolas Bourbaki** is the pseudonym of a group of (mainly) French mathematicians who publish an authoritative account of contemporary mathematics.

- By the summer of 1935 the group had decided that they would write under the name Nicolas Bourbaki.
- Certainly the name came from General Charles Soter Bourbaki was a French general who had fought in the Franco-Prussian war of 1870-71.
- The names for the theorems were taken from French generals, and the final and most ridiculous theorem he presented he had named "Bourbaki's theorem", taking the name from General Bourbaki.
- The humour of this was so enjoyed by all members of the group designing the Analysis Treatise that they adopted the name Bourbaki.
- It would appear that Nicolas was a classical reference to an ancient Greek hero from whom General Bourbaki was descended.
- Boas explained to his readers that Nicolas Bourbaki was the pseudonym for a group of young French mathematicians.
- Soon after, the publisher of Boas's article received a strongly worded letter from Nicolas Bourbaki objecting violently that his right to exist had been questioned.
- Further, Bourbaki's letter put forward the theory that BOAS was simply a pseudonym for the editors of Mathematical Reviews.
- The first Bourbaki Congress was held at Besse-en-Chandesse in July 1935.
- Descriptions of these congresses by founder members of Bourbaki are fascinating.
- There were, however, some clear decisions taken by the Bourbaki group on how to present mathematics which set the pattern for how the whole work would develop.
- Also it was decided that Bourbaki would never generalise from special cases but would always deduce special cases from the most general.
- But that is not Bourbaki's intention.
- For Bourbaki, a general concept is useful only if it is applicable to a number of more special problems and really saves time and effort.
- If Bourbaki members considered it their duty to work out everything from the ground up, they did so with the hope of placing in the hands of future mathematicians an instrument that would make their work easier and enable them to advance further.
- Already in 1935 Bourbaki had taken the decision to produce a series of books which were linearly ordered in the sense that no reference could be made except to books earlier in the linear progression.
- Also no references could be made to material outside Bourbaki, for the group wanted to construct mathematics from scratch within their work.
- It took much longer than the members of Bourbaki had imagined in 1935 for the first material to be published, which did not happen until 1939.
- The absence of the "s" was of course quite intentional, one way for Bourbaki to signal its belief in the unity of mathematics.
- We discuss this second phase in the article Bourbaki: the post-war years.
- In particular Roger Godement, Pierre Samuel, Jacques Dixmier and Jean-Pierre Serre joined Bourbaki in the late 1940's.
- Armand Borel first became acquainted with the Bourbaki team in 1949.
- A Bourbaki member is supposed to take an interest in everything he hears.
- These chapters set up the basic properties of integration theory which, as far as Bourbaki is concerned, means integration on locally compact spaces.
- The "third generation" of Bourbaki members joined around the time that the project to produce the six books was well on its way to completion.
- Bourbaki will always remain young and lively; like mankind he renews himself constantly.
- These newcomers found their own way to Bourbaki.
- You can think of the first books of Bourbaki as an encyclopaedia of mathematics, containing all the necessary information.
- Not at all - in fact right from the beginning members of Bourbaki had more grandiose ideas than simply the six planned books.
- However, mathematics had grown enormously, the mathematical landscape had changed considerably, in part through the work of Bourbaki, and it became clear we could not go on simply following the traditional pattern.
- These basic principles had required Bourbaki to build everything in a linear fashion without references to outside sources.
- Would Bourbaki then split up into smaller units each responsible for an advanced topic?
- Grothendieck, although a third generation member, was fully committed to providing full foundations in accepted "Bourbaki generality" for the advanced topics.
- There was another problem which constantly bothered Bourbaki members.
- Although Bourbaki held back from the ultimate goal of writing down the whole of mathematics in their linear development, realising that this was just not feasible, nevertheless they still embarked on a programme which was impossibly ambitious.
- For many the chapters on Lie groups and Lie algebras are Bourbaki's finest achievements.
- Bourbaki could not find a new outlet, because they had a dogmatic view of mathematics: everything should be set inside a secure framework.
- There was another problem for Bourbaki in the 1970s which was unrelated to mathematics.
- The founders of Bourbaki had a rule that members should retire at fifty.
- Cartier has suggested that perhaps it would be appropriate for Bourbaki to retire at fifty.
- This did not happen and Bourbaki is now seventy.
- There may not now be a need for this, and one reason that there is no need is of course the way that Bourbaki has shaken up the world of mathematics.
- Some love the approach, some hate it, but one cannot deny Bourbaki's influence.

Born 1935, Paris, France View two larger pictures.

View full biography at MacTutor

Analysis, Geometry

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive