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.
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.
What you're saying make sense, but it doesn't help me understand the connection between people dying in WWI and the lack of recent textbooks. The two people the article describes as having the initial conversation were 30 and 28 years old (give or take a year each) in 1934, which is fairly young for a professor by modern standards, but this means they also presumably had been doing mathematics for around a decade each at this point. Did they not have any older colleagues at all who could have written textbooks? Why didn't they write textbooks in that time period when there would have been ones published in other languages outside of France? I'm not doubting the accuracy of the history being given here or in the Wikipedia article; like I said in my initial comment, I just don't think it's being explained very well, because there's still a gap for me between "lots of people died in the war" and "15 years later there are no textbooks".
I just put in your query (i.e. "Bourbaki was founded ..., young university instructors were forced to use dated texts") into Google AI Mode to explain with references/links/citations which it did reasonably well. The main points are;
1) It was in late 19th century/early 20th century that the german (and other european) mathematicians (Hilbert et al.) revolutionized rigour in the teaching of mathematics with the establishment of definition/theorem/proof (DTP) "new math" style which we understand today as the norm.
2) WWI (1914-1918) wiped out over half the french mathematicians from the various top french mathematical training academies. This was the "lost generation" creating a demographic gap of mathematicians who were trained in the new style above.
3) Thus in mid-1930s you had only a small group of young french mathematicians (Cartan, Weil etc.) who were exposed to the rigorous style now pushed into professorship positions. However their previous generation being lost in the war meant most books were from 19th century written using the "old style math" (i.e. less rigorous). Eg. Standard french university textbooks on Calculus/Analysis were by Edouard Goursat rooted in old 19th century concepts. Hence they are frustrated and start writing books under the Bourbaki name to reestablish french mathematics rigorously.
So a generational crisis (i.e. loss in war) happens when mathematics undergoes a fundamental shift. This leads to books becoming outdated. Young french mathematicians inspired by german abstract school set about unifying all of mathematics using the new rigorous style in terms of various abstract mathematical structures.
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.
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.
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?
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.
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.
What you're saying make sense, but it doesn't help me understand the connection between people dying in WWI and the lack of recent textbooks. The two people the article describes as having the initial conversation were 30 and 28 years old (give or take a year each) in 1934, which is fairly young for a professor by modern standards, but this means they also presumably had been doing mathematics for around a decade each at this point. Did they not have any older colleagues at all who could have written textbooks? Why didn't they write textbooks in that time period when there would have been ones published in other languages outside of France? I'm not doubting the accuracy of the history being given here or in the Wikipedia article; like I said in my initial comment, I just don't think it's being explained very well, because there's still a gap for me between "lots of people died in the war" and "15 years later there are no textbooks".
I just put in your query (i.e. "Bourbaki was founded ..., young university instructors were forced to use dated texts") into Google AI Mode to explain with references/links/citations which it did reasonably well. The main points are;
1) It was in late 19th century/early 20th century that the german (and other european) mathematicians (Hilbert et al.) revolutionized rigour in the teaching of mathematics with the establishment of definition/theorem/proof (DTP) "new math" style which we understand today as the norm.
2) WWI (1914-1918) wiped out over half the french mathematicians from the various top french mathematical training academies. This was the "lost generation" creating a demographic gap of mathematicians who were trained in the new style above.
3) Thus in mid-1930s you had only a small group of young french mathematicians (Cartan, Weil etc.) who were exposed to the rigorous style now pushed into professorship positions. However their previous generation being lost in the war meant most books were from 19th century written using the "old style math" (i.e. less rigorous). Eg. Standard french university textbooks on Calculus/Analysis were by Edouard Goursat rooted in old 19th century concepts. Hence they are frustrated and start writing books under the Bourbaki name to reestablish french mathematics rigorously.
So a generational crisis (i.e. loss in war) happens when mathematics undergoes a fundamental shift. This leads to books becoming outdated. Young french mathematicians inspired by german abstract school set about unifying all of mathematics using the new rigorous style in terms of various abstract mathematical structures.
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.
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...