The interest in big questions about mathematics in different communities

Previous post: William Thurston about the humanity and mathematics


Reply to the (first) comment to the pervious post.

Even if there is such a phenomenon as a tendency of some ethnic groups to speculate about the larger place of mathematics, it is unlikely to be either Russian or Slavic phenomenon. The word "Russian" usually used in the USA to designate anybody or anything coming from Russia or the (former) USSR. Most of "Russians" in the USA and other Western countries are, in fact, of Jewish extraction (usually not practicing any religion, including Judaism), and therefore are neither "Russians" in the USSR sense (this one is purely ethnical), nor Slavic. May be “European” would be more correct, but this would eliminate the very appealing reference to “the mysterious Russian (or Slavic) soul”.

Some of the most important writings about mathematics and its role for the humanity due to H. Poincaré (French), F. Klein (German), N. Bourbaki (French, or French-Jewish if we turn to the ethnicity), A. Weil (French, ethnically Jewish, and deeply influenced by Bhagavad Gita and related philosophy), just to give the most prominent examples. I quoted A. Weil a lot in the first posts in this blog. I believe that these examples alone are sufficient to dispel any myths about “the mysterious Russian/Slavic soul” at least in this question.

It seems to me that the opposition of the American and the European cultures is more relevant. Americans are much more focused on “practical” things of immediate importance. I mean very immediate: say, having a grant is more important than proving good theorems. This is not specific for mathematics and shows up everywhere, from arts to Hollywood to highways repairs. Naturally, “Russian” mathematicians transplanted to the US soil stand out. So would be French mathematicians, but there is virtually none of them in the US.

The late William Thurston was an example of an American mathematician paying attention to the larger issues. But he was too exceptional (even his education was rather unusual; one can read in Wiki about the undergraduate school he attended) to serve as an example.

Much more typical is a comment I once come across in T. Tao’s blog. This was an advice to young mathematicians: do not try to understand big general theories; use them as black boxes to solve specific narrow problems (and then soon you will have publications, grants, etc. – Owl). This was a big shock for me despite I knew personally people working in this manner. This approach, in particular, makes American mathematical literature less reliable than, say, the French one. The Soviet/Russian mathematical literature is also not very reliable sometimes, but by different reasons: some people write for their close friends only (but expect and usually get a universal recognition).

Perhaps, it is worthwhile to find this comment and write more extensively about it.

Another manifestation of the American attitude is the fact that general (especially partially philosophical) questions are regularly closed at Mathoverflow.

I agree that the n-categories are one of the most interesting things happening in mathematics now, perhaps the most interesting. But with the current pace of the development, they are still decades away from recognition by the whole mathematical community (if it will survive).


P.S. The title and the tags are slightly modified on March 13, 2013 in order to avoid at least some spam.


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