Great conversation! Finding balance between how much you think for yourself vs how much you learn thought resonated a lot with me, I've been thinking a lot about that recently. Also, re popularizing mathematics: I think that 3B1B (Grant Sanderson) will have a greater impact on mathematics, via spurring the mathematical interest in youth, than many great mathematicians did. Indirectly of course as it's hard to quantify it but nonetheless.

00:00 ceremonies 01:35 Bourguignon (IHES) on Gromov, Gromov's working methods, interest in biology, medicine 05:25 interview proper commences: early years 06:24 Rademacher & Toeplitz's book 06:40 high school interest in chemistry, Russian problem books, mathematical circle 07:55 Leningrad University, environment 08:30 high intensity, devotion to science, Kolmogorov and Gelfan'd's belief in universality of math. 09:30 talent, "I don't think I'm exceptional" 10:05 why leave the country? if something is prohibited you do it! 10:48 Russian style, schools, education 11:30 Moscow vs Leningrad; Gelfan'd seminar, other seminars (Piatetski-Shapiro) 12:53 Russian vs Western mathematics 13:37 prize for Geometry, highlights in geometry, problem with axiomatics 16:46 novel and original idea in Riemannian geometry 17:30 softening of geometry: inequalities, asymptotics 18:18 can get deep results with this novel approach; influence of Nash, Cheeger, "things are quite simple, right before your eyes if you just ... properly" 19:15 Nash, have read all of Nash's papers (the only one to have done so?), Nash's power (analytic, geometric), intuition, originality, "thinking in a most unusual way", his deep thinking on manifolds, influence of Nash and Smale 21:50 symplectic geometry, pseudo-holomorphic curves, Gromov-Witten invariant, Pogorelov on convex surfaces, quasi-analytic functions (Bers, Lipman?), "I don't understand a word" 23:20 result most proud of ? (pseudo-holomorphic curve structure) 23:45 math. and applications, math. biology (hyperbolic groups and cell division) 25:35 believes there's a still unknown mathematical framework yet to be discovered 26:00 explain PCR (Polymerase Chain Reaction) 27:45 recognition by biologists? we ask them questions, sometimes we make them think 28:30 chemical kinetics (of Guldberg, Waage) as example of close collaboration between mathematicians and scientists 29:30 computer graphics, Gromov-Hausdorff distance 32:00 can the mediation between science and mathematics be improved? 32:38 Taddei's educational initiative (biology for non-biologists) 33:55 computers in mathematics; computers as a tool 35:19 underlying philosophy on how to do mathematics; there's no recipe; retain balance between how much you think for yourself and how much you learn from others 36:10 problem-solver vs theory-builder? 36:36 think about math. all the time? 37:00 how many hours per day on math. 37:28 age vs experience 38:00 important things done before age 30 (von Neumann)? had already thought of the ideas I have now, forty years ago 39:32 prizes esp. the Abel Prize; 40:44 thoughts on Abel 41:10 posthumous paper of Abel's - insurmountable problems just need new perspective 42:34 the future of mathematics - how much of the mathematical tree can we know? new schemes of computation 44:52 the Earth as we know it on finite time? pessimistic? 47:14 education - minds of gifted youth not developed well enough; education destroys potential geniuses; education has to be tailored to each individual 49:16 the way we learn is not how we think it works 51:15 not seeing the teacher, a person of authority (experiments) 52:26 how to show that mathematics needs continuing support (students drop mathematics once they leave school) 54:47 Numbers and Figures (Rademacher, Toeplitz), Courant's What is Mathematics? books on mathematics; writing books is honourable; few can write for general audiences; role of political figures in encouraging math.

For those who are looking for the book by Toeplitz and Rademacher, it is titled 'The Enjoyment of Mathematics' which is actually an English translation of the German original Von Zahlen und Figuren (Numbers and Figures).

GROMOV A MASTER

He looks like Perelman with beard!

I went to a seminar with Gromov where he looked at a simple problem in group theory where there were too many basis words or something. He then said, "Let this be the fundamental group of a manifold, M and let R be the curvature". I'm very impressed at his ability to use geometry to solve a seemingly unrelated problem.

Because I can watch how nodal-vibrational sounds decay from string to string on the inside frame of a piano, it doesn't mean I can read and play orchestral music, but now I understand the harmonic measures that make good music, in a more integrated way, by probabilistic correlations in temporal potential quantization. Not quite Mathematics, but interesting. Stating the obvious is the self-defining difference of Calculus when you "spell out" Euler's pure-math e-Pi-i function-> prime-cofactor function.., 1-0-infinity log-antilog nodal-vibrational interference positioning.., resonance bonding measures of harmonic i-inflation spin-spiral distribution, in i-reflection Absolute Zero-infinity reference-framing stasis.. ONE-INFINITY Singularity is a Fractal scaling composition of "decay" bigger and older than the Piano.., but the orientation to the principle is identical. "Nuclear Energy"

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