Inside the Secret Math Society Known Simply as Nicolas Bourbaki

https://www.quantamagazine.org/inside-the-secret-math-society-known-as-nicolas-bourbaki-20201109/

by pykello • 4 days ago

20 7 4 days ago

rramadass3• 4 days ago

Nice.

Another interesting article; The Mathematical Pranksters behind Nicolas Bourbaki - https://daily.jstor.org/the-mathematical-pranksters-behind-n...

And of course wikipedia; Nicolas Bourbaki - https://en.wikipedia.org/wiki/Nicolas_Bourbaki

Anybody here actually browsed/read/studied the Bourbaki books? How approachable are they and what is the easiest one to start with?

Any expository/explanatory/commentary/annotation of the texts for the mathematically inclined layman?

saghm2• 3 days ago

I feel like the Wikipedia article does not explain the backstory well:

Bourbaki was founded in response to the effects of the First World War which caused the death of a generation of French mathematicians; as a result, young university instructors were forced to use dated texts

Why would there not be textbooks after people died? Were they bringing the textbooks to the schools or something? Or were they saying that new textbooks weren't written because of the lack of French authors available? I hadn't thought that having textbooks maybe 15 years old would be a huge deal given the pace that math moves, but maybe that's only because the concepts for an undergraduate math course when I was in school were a lot further behind where the research is happening nowadays compared to back then.

adrian_b2• 3 days ago

Before the second WW, mathematics was moving at much faster paces than after WWII, when many theories became more or less settled and only their practical applications continued to develop at a fast pace.

The modern variants of some branches of mathematics like topology or the theory of tensors have appeared during the first WW (e.g. the book of Felix Hausdorff, "Grundzüge der Mengenlehre"). Especially topology had a great influence on almost all other branches of mathematics, prompting them to reformulate many things in more general frameworks.

Therefore, by the end of WWI, it was true that many older mathematics manuals were considered obsolete, so they felt the need to write new manuals, brought up-to-date.

adrian_b2• 3 days ago

When I was young, I have read more than half of them.

They should better be read in order, starting with the theory of sets.

I do not believe that they are useful for learning for the first time some part of mathematics, but they are useful to revisit already known parts, to think about them while examining a more rigorous or alternative exposition of the concepts.

Some of the books also contain interesting facts about the history of mathematics.

See the Wikipedia descriptions, e.g.:

https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_math%C3%...

Especially if you can read French, you can find many of the books on archive.org.

rramadass3• 2 days ago

Some additional resources that i dug up;

1) Wayne Aitken from California State University has a 52-page Bourbaki, Theory of Sets, Chapter I, Description of Formal Mathematics: Summary and Commentary - https://public.csusm.edu/aitken_html/

This is a commentary in the sense that I sometimes give explicit comments, but also more subtly by my choices in changing terminology, phrasing, notation, or proof in an eﬀort to clarify Bourbaki for myself and a modern reader. So to get the full Bourbaki experience, the reader should read this document alongside Bourbaki’s original. But if the reader just wants a good sense of what is in Bourbaki this document is reasonably complete. So this document can potentially be of service to two classes of readers: (1) readers of Bourbaki’s original first chapter who want to benefit from extra commentary and some indication on how the approach looks from a more modern point of view, and (2) readers who, without necessarily reading Bourbaki’s chapter, want to get a feel for Bourbaki’s approach, but from a more modern point of view.

2) The Ignorance of Bourbaki by A.R.D.Mathias - https://www.researchgate.net/publication/226448759_The_ignor...

3) Further Remarks on Bourbaki by A.R.D.Mathias - https://www.scribd.com/document/645181972/A-R-D-MATHIAS-Furt...

Inside the Secret Math Society Known Simply as Nicolas Bourbaki

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