Loved to listen and learn. The Mathematicians who ask d questions need to learn a lot that they should ask more queations to the awardee in which s/he pronounces less clearly. Regards
@33:00 English is also unreasonably effective in the sciences. The real question is why mathematics is _universally_ "unreasonably effective" in the sciences (English language is not). One decent response is to say there is no mathematical notion of "effective reasonability" so there is no scientific answer. Another is to point out numbers are basic in any measurement, and to use numbers imprecisely is going to be a bit useless. So you need to use numbers precisely to get effectiveness. And then you are by definition doing mathematics (by design and by choice). In which case the qualifier "unreasonable" goes away and you only have "effectiveness".
00:15 beginnings, family influences
00:55 no Olympiad success
02:00 mathematical talent
02:30 schooling (WWII, USSR)
04:20 teachers
05:35 Moscow State University (Mekh mat)
07:40 mathematics vs. mechanics
08:52 Dynkin
10:13 Kolmogorov
10:35 Gel'fand
12:31 Rokhlin, Abramov
17:25 Dynamical systems
18:03 Ergodic systems
19:25 Chaos vs. Probability
22:52 Entropy
24:47 Billiards
26:45 Ornstein's Isomorphism Thm
28:10 Billiards in higher dimensions
28:52 Markov partitions, Sinai-Bowen-Ruelle
31:28 Wigner's Unreasonable Effectiveness
33:50 Math. + Phys. = Cats & Dogs
36:06 Gel'fand
36:52 anti-Semitism in USSR
43:49 Arnol'd
46:40 good results can't be stolen
48:35 the move to Princeton
50:12 comparing education regimes
50:50 what's not liked about USA system
52:30 teaching; prefers teaching undergrads
54:10 working in later years
55:05 Kolmogorov
59:15 style of problem-solving
1:00:02 Poincare-style insights
1:00:55 other interests
Loved to listen and learn. The Mathematicians who ask d questions need to learn a lot that they should ask more queations to the awardee in which s/he pronounces less clearly.
Regards
Thank you for that list.
To the interviewers: please ask similar questions about internal politics to the able laureates from USA.
@33:00 English is also unreasonably effective in the sciences. The real question is why mathematics is _universally_ "unreasonably effective" in the sciences (English language is not). One decent response is to say there is no mathematical notion of "effective reasonability" so there is no scientific answer. Another is to point out numbers are basic in any measurement, and to use numbers imprecisely is going to be a bit useless. So you need to use numbers precisely to get effectiveness. And then you are by definition doing mathematics (by design and by choice). In which case the qualifier "unreasonable" goes away and you only have "effectiveness".