About a fortnight ago, I had to make a sudden trip and, as reading material, brought with me some print-outs that had been lying on my desk for a long time. One of those was An Interview with Vladimir Arnold, which appeared in the Notices of the AMS in 1997. Vladimir Arnold is regarded as one of the great living mathematicians and the number of disciplines in which he has worked is truly astounding. (The areas are Dynamical Systems, Differential Equations, Hydrodynamics, Magnetohydrodynamics, Classical and Celestial Mechanics, Geometry, Topology, Algebraic Geometry, Symplectic Geometry, and Singularity Theory.) What I found out by reading the above-mentioned interview is that he is certainly a man with strong opinions and that he has no qualms about airing them.
One answer of his that really got me thinking was this one:
Lui: Do you notice any differences in the way people from different cultures do mathematics?
Arnold: I was unaware of these differences for many years, but they do exist. A few years ago,
I was participating in an International Science Foundation (ISF) meeting in Washington, DC.
This organization distributes grants to Russian scientists. One American participant suggested
support for some Russian mathematician because “he is working in a good American style.”
I was puzzled and asked for an explanation. “Well,” the American answered, “it means that he is traveling a lot to present all his latest results at all our conferences and is personally known to all experts in the field.” My opinion is that ISF should better support those who are working in the good Russian style, which is to sit at home working hard to prove fundamental theorems which will remain the cornerstones of mathematics forever!
It is certainly true that travel and networking are fundamental parts of our daily life at work. What Arnold seems to be saying, however, is that we may be pushing this part of our work too far, and that this might be detrimental to the purely scientific part of our work. Of course, each of us has different work pattern, but there seems to be a tendency these days to shun good old scholarship for the modern gods of networking, leadership and what not.
Arnold also paints a picture of his days as a student at Mechmat (Moscow State University Mechanics and Mathematics Faculty) in the fifties. He says:
"The constellation of great mathematicians in the same department when I was studying at the
Mechmat was really exceptional, and I have never seen anything like it at any other place. Kolmogorov, Gelfand, Petrovskii, Pontriagin, P. Novikov, Markov, Gelfond, Lusternik, Khinchin,
and P. S. Alexandrov were teaching students like Manin, Sinai, S. Novikov, V. M. Alexeev, Anosov, A. A. Kirillov, and me."
I guess that it is hard to argue against his opinion. I looked up some of these names on the web, and this is really a most impressive collection.
Finally, to add a little more to the debate, Arnold seems to indicate that in 1997 it was still possible for a Western mathematician to build a good career rediscovering weaker versions of results known earlier to Russian mathematicians. And I have not mentioned his opinions on Bourbaki and the French mathematical establishment :-)
There are definitely worse ways to spend a few minutes during a flight than reading that interview.