Cleared up the notion of ‘proof’ for a mathematician (i.e there are an ‘infinity’ of levels at which mathematics can be done : – Category theory is just one)

Created the machinery that allowed 2nd order logic to be formalised. This lead to P Cohen proof of the undecidablity of continuum hypothesis.

Also to the proof that Mathematics is sound, of course you have to belive in ordinals greater than the continuum.

Finally and not least, A A Markov 1958 proof of the impossiblity of solving the homeomorphy problem for manifolds, dimension 4 and above. A result I believe to be the equivalent of the impossiblity of solving 5 deg poly by radicals. This result in my opinion is the REAL reason why everyone is doing category theory. I must point out that category theory has many enemies in mathematics, who feel that it is only useful for expositionary work, not actual creative stuff (except for Grothendieck)

Essential the Bourbaki spirit now lives in combinatorial group theory and model theory. At the moment these subjects are at the fringe, but I believe that out of these 2 subject will come the mathematics for the 21 century like topology was for the 20th!

an amateur Mathematican

Bourbaki’s heyday was the fifties, part of the same over-emphasis on abstraction that lead to the “new math” disaster. By the 70s, Bourbaki’s influence had started to wane. One reason was that mathematicians had begun to lose interest in overly formalist approaches, another was that Grothendieck showed that very different foundations were needed (i.e. category theory vs. set theory). The influence of physics on mathematics also had an effect.

These days, Bourbaki has little influence in math. Some of their books are actually pretty good, but mostly they are used as technical references, nobody tries to learn anything from them. For a long time now the group has stopped writing more.

Mathematicians still generally do a terrible job of writing readable expository material, but mostly they are no longer doing overly formalistic things. But what they do is inherently different than what physicists do, largely because there is a strong culture of not allowing people to be imprecise, and insisting on absolute clarity of in arguments. Physicists would do well to learn something from this.

One of my best friends was educated in the heyday of “new math”, at Columbia and MIT. In high school of course he was at the top of his class, and in a class by himself technically. He related the following story. He learned calculus from Lang, was doing functional analysis as a high school student etc. etc. Then, he had to teach a course at MIT to engineers. He suddenly realized he couldn’t do a simple surface integral da capo. He stated to me, that he began to consider the entire axiomatic program embodied in Bourbaki to be a total sham, and sought to restructure his knowledge on intuitionist lines (Brouwer, Weyl). Needless to say this was a complete success and now this peson is a world-authority on the math and modeling of turbulence. This was in spite of, not because of, the French program.

I think it can safely be argued that Bourbaki and its intellectual worldview of lofty abstractions and airy-fairy axiomatics has been a disaster for science, has attempted to rip math and physics apart from each other at the sternum, and has created the mental climate in which a ruse like string theory can develop in the first place.

-drl

It’s not so much that prominent French Mathematicians were killed in WWI, but that many of the best math students were killed. Two-thirds of the students at the Ecole Normale Superieure died, this is the place that produced most mathematics teachers and researchers.

For more about this and about Bourbaki, see

http://planetmath.org/encyclopedia/NicolasBourbaki.html

Which French mathematicians were killed in WW I? Also was Bourbaki created to “collect” all known French mathematics?

Thanks,

He did very interesting work on relativistic rotators as a kid.

http://arxiv.org/PS_cache/hep-th/pdf/0303/0303099.pdf

Oops, typo in html. Fixed now. Thanks for pointing this out!

Peter

I think that your link to the “English translation” is missing, at least as of now (10FEb05 @ 14:33:00h) it seems void. (Not that i can’t find the link otherwise… but, just a heads up.

Cheers,