The mathematician and author sees mathematical patterns everywhere — from DNA to fireflies to social connections.

After graduating from high school, without a clear plan for what to do next, Laura Andrews started asking herself a lot of questions. A spiral of big philosophical thoughts that led her to sit down and write to us with a question that was… oddly mathematical.  What is the most average size thing, if you take into account everything in the universe. So, along with mathematician Steven Strogatz, we decided to see if we could sit down and, in a friendly throwdown of guesstimates and quick calculations, rough out an answer.  Special thanks to all the listeners who sent in their responses to this question. Episode Credits:Reported by - Soren Wheeler and Alex NeasonProduced by - Annie McEwenwith mixing help from - Arianne WackFact-checking by - Natalie A. Middletonand Edited by  - Alex Neason Citations: BooksYou can find links to many books by Steven Strogatz here: https://www.stevenstrogatz.com/all-books MediaAnd the podcast he does for Quanta Magazine, The Joy of Why, here: https://www.quantamagazine.org/tag/the-joy-of-why/ Our newsletter comes out every Wednesday. It includes short essays, recommendations, and details about other ways to interact with the show. Sign up (https://radiolab.org/newsletter)!Radiolab is supported by listeners like you. Support Radiolab by becoming a member of The Lab (https://members.radiolab.org/) today.Follow our show on Instagram, Twitter and Facebook @radiolab, and share your thoughts with us by emailing radiolab@wnyc.org.   Leadership support for Radiolab’s science programming is provided by the Gordon and Betty Moore Foundation, Science Sandbox, a Simons Foundation Initiative, and the John Templeton Foundation. Foundational support for Radiolab was provided by the Alfred P. Sloan Foundation.

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which we discussed --- Chaos and Nonlinear dynamics https://amzn.to/3lFQjrU Infinite powers https://amzn.to/3AnvXIg Unpublished appendix about Newton's letters to Leibniz: 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