Steven Strogatz, an applied mathematician at Cornell, is a prominent figure in the field of nonlinear dynamics and chaos, and a widely beloved popularizer of math. Episode sponsor: https://brilliant.org/3b1b Brilliant is a great site/app for being more active in learning math. Note from Strogatz's high school geometry: https://twitter.com/stevenstrogatz/status/1562812593596956674?s=20&t=cAePOusuX3vlwg0NzTjRhQ -- Books by Strogatz which we discussed -- Chaos and Nonlinear dynamics https://amzn.to/3lFQjrU Infinite powers https://amzn.to/3AnvXIg Unpublished appendix about Newton's letters to Leibniz: https://static1.squarespace.com/static/5436e695e4b07f1e91b30155/t/5dd434fb9d105d031ded69de/1574188283323/Appendix+2+-+Newton+on+infinite+series+and+the+Epistola+Posterior+v4.pdf -- Other things which came up -- Strogatz's senior thesis: https://static1.squarespace.com/static/5436e695e4b07f1e91b30155/t/5dca1c993141bb5946c54b45/1573526688118/The-mathematics-of-supercoiled-DNA.pdf His first published paper: https://www.pnas.org/content/pnas/78/3/1461.full.pdf Crick’s paper about linking numbers and nucleosomes with the memorable comment that inspired his experiment with the ribbon: https://www.pnas.org/content/pnas/73/8/2639.full.pdf The 4-dog chase problem and its solution. https://www.theguardian.com/science/2019/jun/03/can-you-solve-it-dogs-in-pursuit https://www.theguardian.com/science/2019/jun/03/did-you-solve-it-dogs-in-pursuit For a full solution with calculus, see Strogatz's book "The Calculus of Friendship" https://amzn.to/3CyVe48 Survey for kids on their desired occupation: https://www.prnewswire.com/news-releases/lego-group-kicks-off-global-program-to-inspire-the-next-generation-of-space-explorers-as-nasa-celebrates-50-years-of-moon-landing-300885423.html A radical approach to real analysis https://amzn.to/2VwtgF3 Twitter thread on what, morally, a normal subgroup is. https://mobile.twitter.com/sbagley/status/1296211024534622208 Leibniz formula via patterns from primes https://www.youtube.com/watch?v=NaL_Cb42WyY -- Table of contents -- 0:00 - Intro 1:15 - Ad 1:59 - The perfect problem for a high school student 12:43 - Starting the Princeton undergrad 22:52 - The most beautiful proof 26:58 - What makes someone love a problem? 36:05 - Putting lessons online 41:57 - In and out of pre-med 47:05 - The geometry of DNA 58:53 - Using teaching as a means to learn 1:09:47 - Do students like history? 1:18:39 - The truth of Newton and Leibniz 1:23:29 - Archimedes, a true great 1:28:32 - Pitfalls of pure math exposition 1:39:03 - "Morality" in math 1:43:20 - An under-motivated culture 1:51:48 - What's next?