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/
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Dianna Cowern is the host of Physics Girl: https://www.youtube.com/c/physicsgirl
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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Unpublished appendix about Newton's letters to Leibniz: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