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Unpublished appendix about Newton's letters to Leibniz: 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/

Learn more about this episode's sponsor, Brilliant: https://brilliant.org/3b1b

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