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.
Next post: Who writes about big questions?
Perhaps, it is worthwhile to find this comment and write more extensively about it.
ReplyDeleteHere is a link to the comment (if I understood this line correctly):
http://golem.ph.utexas.edu/category/2010/06/this_weeks_finds_in_mathematic_60.html#c033480
Thanks. Actually, I had in mind another comment, the one in Tao's blog recommending not to study big theories (like the class field theory - I think the comment was written by a well known number theorist), but mindlessly apply them to small problems. This is the same phenomenon, but on a lower level: there is no need to think about mathematics in the framework of the whole human society; similarly, there is no need to know the framework which allows you to prove your theorems.
DeleteI agree that the terminology "Russian" or "Slavic" is quite misleading...However, your examples of French and European mathematicians date 100 or 50 years back, and you say Thurston is too exceptional to be an example. But even Thurston (correct me if I am wrong)
Deletedid not write a paper on the "larger place of mathematics"; his essays on maths and proofs in maths are not quite that.
On the other hand, everybody mentioned in the original post on the n-cafe is
"Russian-speaking" (and was born in USSR). Could you give any example of a
non-Russian speaking mathematician "speculating about the larger place of mathematics",
and preferably related to his/her mathematical work ?
Well, your question makes very tempting to write a long essay about the current state of mathematics. But this is not really needed.
DeleteStill, I am going to use it as an excuse to write another post, my reply to it (it is again fairly long).
I assume that all recent anonymous comments are written by the same person. I would very much appreciate if you will invent a nickname for yourself and use it to sign them. I just would like to be able to distinguish (or identify) the authors of anonymous comments. If you will use some Google account for this purpose or an OpenID (this will not reveal your real life identity and even relate you to other things on the net), this would be more modern and convenient.
Indeed, all these recent comments were mine; and from now on I shall sign as 'wwwwww'.
Delete(I find OpenID/Google a bit too modern: OpenID does not seem to work well in lynx, text-mode browser...)
I read your reply, and I can see what you mean.. David Corfield and Colin McLarty are philosophers by profession, not mathematicians; Gowers' interests are mostly internal to mathematics. So the question remains: apart from Thurston, are there examples of non-russian "speaking" good mathematicians recently publicly expressing their views wrt "larger place of maths" etc. In the Russian community, Manin, Gromov and, to an extent, Voevodsky come to mind; also Borovik mentioned in the original discussion. Gromov's texts are definitely very interesting ( http://www.ihes.fr/~gromov/PDF/quotationsideas.pdf , http://www.ihes.fr/~gromov/PDF/ergobrain.pdf .
(and I cannot resist giving a link to his "autobiography" http://www.ihes.fr/~gromov/PDF/autobiography-dec20-2010.pdf that has little to do with this discussion..)
wwwwww
Hi, wwwwww would be OK. At least till somebody tries to use 5 or 7 letters w. :-)
DeleteI am still thinking about how to answer to your question. It would be of great help if you would clarify what do you mean by some common words. Say, what do you mean by “recently” (no more than 10, 25, 50 years ago?), “mathematician” (say, somebody not active in the research would qualify?), “Russian community” (I doubt that, for example, Gromov and Manin both belong to any real community smaller than the community of all mathematicians), “larger place of mathematics”, and may be some others.
I think that I need to explain why it is nearly impossible for me to answer your question in the form it is stated now. Namely, by answering it I will implicitly accept some nontrivial assumptions, which I am not inclined to do.
DeleteThe main issue is, probably, the notion of "the Russian community". You list Manin, Gromov, Voevodsky, and Borovik as belonging to it. Gromov left the USSR in 1974, the others around 1990, i.e. more than 20 years ago. Why do you still consider all of them "Russians"? I presume that we are not discussing here their ethnic origin. I fail to see anything specifically Russian in both mathematical works of Gromov and Voevodsky and their opinions. Manin worked on the Mordell conjecture, a topic very popular in Moscow, and that's, probably, all. The mathematical work of Borovik fits the Novosibirsk tastes very nicely, and in this sense he is, probably, Russian. I cannot comment on his books "about mathematics" because I did not read them.
I cannot consider Gowers's interests as internal to mathematics; his main project is elimination of mathematics. Definitely, this goal is not internal to mathematics.
The cited texts of Gromov are very interesting, of course, but do they discuss the "larger place of mathematics" in any substantive way?
Anyhow, I should say that I do not remember any opinion about the "larger place of mathematics", or even, much more narrowly, "larger place of, say, algebraic number theory" which was originally written in Russian (except some remarks by Manin, mostly in his book "A course in the mathematical logic"). Texts which influenced me most were written by French, German, and British mathematicians, plus the famous book of infamous Imre Lakatos (he was a despicable person, but this book, based on his Ph.D. thesis, is great). It was written in English, and I doubt that anybody would be able to discern in this book something Hungarian.
From my point of view, we are trying to argue about a nonexistent phenomenon. If you will be able to make a convincing case for its existence, then, may be, I will be able to say something meaningful about it.