1 - Alex Kontorovich: Improving math

Steven Strogatz, a mathematician at Cornell and author of The Joy of x, Infinite Powers, and most recently Big Math (with Alex Townsend), returns to the podcast for a conversation about what AI means for the field of mathematics. Steven believes that the field is anything but dead. In fact, this might be the best time to go into math.They discuss whether human understanding still matters when machines can find the answers, why we may come to value our own imperfections more, and what the job of a mathematician could look like in the years ahead. The conversation also covers a paper-folding puzzle that turns students who hate math into students who get it, a passage from Ecclesiastes, and why, for Steven, math has always been about people.Join the Patreon at https://www.patreon.com/c/3blue1brown/Discover exciting roles for the mathematically curious at https://www.3blue1brown.com/talent00:00 Relaunching the 3b1b Podcast01:58 AI is the conversation among mathematicians03:21 What do you tell a student considering math?04:06 AI as the great equalizer06:20 Mathematical "rizz"09:17 What if AI becomes a superhuman explainer?12:34 Will "mathematician" still be a profession?13:37 Finding humanity more precious16:58 What's left for those who want to be pioneers?21:39 Is solving the problem the point?28:01 Two cultures of mathematics, and pure vs. applied29:14 How Maxwell's math revealed the nature of light33:55 Is understanding overrated?43:50 Fermat vs. Goldbach: math that generates more math47:43 Will human mathematicians exist?54:44 Why learn math when AI can do it?1:01:28 What should earn academic status?1:05:21 Ecclesiastes: "Everything is beautiful in its time"1:07:40 Does mathematical beauty depend on problem solving?1:12:44 Math Explorations and the one-cut triangle puzzle1:18:57 Should we still grade homework?1:24:29 Research in the service of teaching1:28:23 What should a math PhD look like now?1:33:30 Poincaré, Lorenz and the birth of chaos theory1:37:39 What's next for Steve

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