Bourbaki Mathematics

As per request, today I will be talking about Nicolas Bourbaki. While there is no one person named Nicolas Bourbaki, this name was used as a collective pseudonym by a group of, mainly French, mathematicians in the 20th century to publish a series of books, beginning in 1935, with the aim of basing all mathematics on set theory in order to gain rigour and generality.

The Bourbaki group began in 1934, when French mathematicians from a range of French universities joined together in order to produce textbooks, which they could then use for teaching. Bourbaki’s main work is the the series of books entitled ‘Elements of Mathematics’. This series aimed to be a “self-contained treatment of the core areas of modern mathematics”. It made no assumptions on the knowledge of mathematics, and attempted to construct axioms to then give proofs.

The Bourbaki group had a great influence on mathematics. Not only did they establish the notation for empty sets and define the terms injective, surjective and bijective, but also their emphasis on rigour was highly celebrated by mathematicians:

“Our time is witnessing the creation of a monumental work: an exposition of the whole of present day mathematics. Moreover this exposition is done in such a way that the common bond between the various branches of mathematics become clearly visible, that the framework which supports the whole structure is not apt to become obsolete in a very short time, and that it can easily absorb new ideas.” 

-Emil Artin

However, there was some hostility towards their work from classical analysts who did not approve of their abstract approach to mathematics.

So who was part of the Bourbaki group?Bourbaki_congress1938.png

Although it is hard to ascertain exactly who all the original members were as the accounts of the early days vary, all the founding members were connected to École Normale Supérieure in Paris and included Henri Cartan, Claude Chevalley, Jean Coulomb, Jean Delsarte, Jean Dieudonné, Charles Ehresmann, René de Possel, Szolem Mandelbrojt and André Weil. Other mathematicians, for example Hyman Bass and Alexander Grothendieck, joined later.

Hope you enjoyed this introduction on the Bourbaki group. Let me know if you want me to write a blog post that focuses more on the mathematics they established. M x

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