The 3b1b podcast

Tai-Danae Bradley does research applying tools from physics to understanding language models, all under the broader umbrella of category theory. She is also the brilliant mind behind the blog https://www.math3ma.com/ Try out the episode sponsor: http://brilliant.org/3b1b

Dianna Cowern is the host of Physics Girl: https://www.youtube.com/c/physicsgirl Try out the episode sponsor: http://brilliant.org/3b1b Contents: 0:00 - Intro 0:47 - Ad, Brilliant 2:03 - Relationship with math growing up 9:05 - Thoughts on teaching 16:36 - When students are genuinely curious 22:02 - Physics at MIT 27:53 - Alternate value systems 35:01 - Starting Physics Girl 40:20 - Taking down videos 48:49 - Authenticity on YouTube 53:17 - Advice on documenting learning 59:13 - Giving talks 1:07:51 - Dead or Alive  1:12:37 - Storytelling in explainer videos Edited by Ralph Crewe https://www.youtube.com/c/IsntThatSomething/

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. --- 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which we discussed --- Chaos and Nonlinear dynamics https://amzn.to/3lFQjrU Infinite powers https://amzn.to/3AnvXIg Unpublished appendix about Newton's letters to Leibniz: 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://youtu.be/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?

In this conversation with Sal Khan, we discuss his new project (Schoolhouse.world) as well as the Khan Lab School that he started in 2014. Sal's new tutoring platform: https://schoolhouse.world/ The Khan Lab School: https://www.khanlabschool.org/ Learn more about this episode's sponsor, Brilliant: https://brilliant.org/3b1b Visit that link to get 20% off an annual subscription, and to let them know you came from here.

Alex Kontorovich is a research mathematician at Rutgers University, a distinguished visiting professor at the MoMath Museum, and Editor-in-Chief of Experimental Mathematics, among other things.  The tweet referenced at the end: https://twitter.com/AlexKontorovich/status/1172715174786228224