Founder of the Secret Society of Mathematicians 103
Anti-Globalism suggests an article at Science News on the passing of Henri Cartan, one of the founding members of a strange and influential group of French mathematicians in the twentieth century. "In the 1930s, a group of young French mathematicians led an uprising that revolutionized mathematics. France had lost most of a generation in the First World War, so the emerging hotshots in mathematics had few elders to look up to. And when these radicals did look up, they didn't like what they saw. The practice of mathematics at the time was dry, scattered and muddled, they believed, in need of reinvention and invigoration... Using the nom de plume Nicolas Bourbaki (after a dead Napoleonic general), they wrote a series of textbooks laying out mathematics the right way. Though the young mathematicians started out only intending to write a good textbook for analysis..., they ended up creating dozens of volumes which formed a manifesto for a new philosophy of mathematics. The last of the founders of Bourbaki, Henri Cartan, died August 13 at age 104... Two of his students won the Fields medal..., one won the Nobel Prize in physics and another won the economics Nobel."
Not so secret... (Score:4, Informative)
This was common knowledge when I was taking advanced Math classes in mid 1970's.
Re:You meant the wrong way (Score:4, Informative)
Bourbaki books are the most boring books you can buy. Avoid them at all costs.
This is a bit extreme. While they're certainly not the best books to begin learning a subject, they're great reference books. They're well written, (generally) correct, and what's more, they've got some seriously elegant proofs. And from what I recall, they do have some diagrams (e.g., their commutative algebra book).
Re:Why are we celebrating these books? (Score:4, Informative)
Bourbaki was writing for a graduate student or professional level mathematician, not a public audience. The writing is dry by today's standards - indeed, many texts today use more prose and include diagrams. However, Bourbaki was very good at getting the mathematics itself clearly defined.
Re:You meant the wrong way (Score:5, Informative)
Umm. I have a few texts from the late 1800s, and they are absolutly completely worse. Bourbaki's is the abstraction. ( I have their volume on abstract algebra, that I referred to while I was taking that graduate level course. Theirs is a terse work, much more accurate, and well though out. ) A few Springer-Verlag texts are worse also.
Re:You meant the wrong way (Score:1, Informative)
Better books:
Walter Rudin: Complex and Real Analysis (splendid book for students, great explanation of measure theory),
functional analysis from same author is good too.
Kato: Perturbation theory (very good book but quite hard, wait till graduate).
Brezis: functional analysis (french): a little abstract but short. Some early chapters are a little boring.
Yosida: functional analysis (haven't had time to finish it, so my opinion on it is not set).
Hormander: Series on linear operators are a reference. Very long.
Adams: Sobolev Spaces: very useful to know the theorems in non standard situations, the proofs are instructive even though you might not need know them.
Kallenberg: probability. I'm no probabilist but the first chapters are very well organized and written in a consitent manner.
The worst of these books is infintely better than any book by Bourbaki. Stop your idolatry of these mathematicians. Bourbaki is just a group cult writing awful books.
Re:Why are we celebrating these books? (Score:2, Informative)
Many people blame Bourbaki for the horrendous "new math" which infected mathematics teaching in the 1960's. And there is some validity to that accusation. A scathing indictment of Bourbaki was given by the renowned mathematician V.I. Arnold, author of famous books on classical mechanics and differential equations. Arnold tears apart the dry, lifeless and phony "rigor" and "purity" of Bourbaki and others who divorce mathematics from reality, which he describes as "sectarianism and isolationism which destroy the image of mathematics as a useful human activity in the eyes of all sensible people." Here's a link to his full comments:
http://pauli.uni-muenster.de/~munsteg/arnold.html [uni-muenster.de]
As a mathematician, I have to agree with the critics of Bourbaki. It put mathematics on the wrong path, in my opinion, and much of that influence continues on today. Mathematicians would do well to heed Arnold's advice on the direction mathematics needs to take. "Pure mathematicians" and other people who still think that Bourbaki was "doing mathematics the right way" are simply misguided.
About the Bourbaki crowd... (Score:1, Informative)
1. Bourbaki was not a "secret society", although it didn't publish a membership list because membership wasn't particularly official. Even some non-French mathematicians participated occasionally.
2. They did not publish "text" books, they published carefully written reference books.
3. The reputation was they they met once a year or so in a nice French resort with a reputation for good wine, to enjoy themselves and argue about the best wording for proofs in the next volumes.
4. While in principle, you might read Bourbaki without a previous grounding -- indeed, substantial preparation -- in practice, it is not likely.
A handful of people who read slashdot may have read some Bourbaki, but it's hard to imagine cultures more different than the slapdash opinions here, and the carefully crafted logic and style which underlies the Bourbaki compendia.
(D. Erbach writing as AC)