The 3b1b podcast 3 - Steven Strogatz: In and out of love with math
High School Problem Spark
- Stephen Strogatz became emotionally invested in a tough high school geometry problem about angle bisectors.
- This first genuine mathematical experience sparked his love for problem solving and persistence.
Motivate Abstract Definitions
- Motivating definitions through intuitive, relatable questions helps students grasp abstract concepts better.
- Presenting the notion of metric spaces via "distance" between functions makes the material engaging and understandable.
Engage With Varied Approaches
- Try multiple approaches to engage students because math appeals differently to everyone.
- For some, beauty inspires, for others, applications or competition spark passion.
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Unpublished appendix about Newton's letters to Leibniz: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?