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
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1:36:05
4 - Dianna Cowern: Dead or Alive
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/
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1:24:46
3 - Steven Strogatz: In and out of love with math
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Unpublished appendix about Newton's letters to Leibniz: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?
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1:54:07
2 - Sal Khan: Beyond Khan Academy
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.
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44:42
1 - Alex Kontorovich: Improving math
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
Ireland