On Fri, Sep 19, 2008 at 10:16:31PM -0400, jim stasheff wrote:
John Baez wrote:
I can imagine a new Bourbaki who tries to explain all of mathematics in the language of categories. But I can also imagine a new Bourbaki who tries to explain all of mathematics in the language of infinity-categories.
Is it necessary to have a global point of view to appreciate Bourbaki? I found them quite valuable locally - i.e.. just a few of the chapters by themselves earned my appreciation.
It's easy to appreciate their books locally - but I think they sought a global systematic viewpoint while writing them. It's possible that a "neo-Bourbaki" should take a less systematic approach. Mathematics may be too much in a state of foundational flux for a systematic approach to be successful right now. Maybe the best we can hope for is something a bit more like Wikipedia, where different people contribute different portions of text, and they don't cohere in a polished whole. But presumably anyone calling for a new Bourbaki wants something different from Wikipedia. There's "Scholarpedia": http://www.scholarpedia.org/ but it doesn't seem to be doing anything with math yet, and if it ever does, I bet it'll take a "midde-of-the-road" approach instead of pushing a specific intellectual agenda. I would like to see lots of people try lots of different things. Best, jb