Yang-Hui He: Why AI Will Permanently Transform How Math Is Done

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6 • 606 Ratings

🗓️ 3 January 2025

⏱️ 137 minutes

🔗️ Recording | iTunes | RSS

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Summary

Yang-Hui He explains how machine learning is reshaping mathematics from string theory to topology. He discusses the interplay of computation and theory, and highlights new approaches that could change how mathematicians discover proofs.- 00:00 - String Theory & Mathematics- 10:54 - How Does One Do Mathematics?- 16:28 - Computers & Mathematics- 20:04 - Bottom-Up Mathematics- 28:44 - Meta-Mathematics- 46:17 - Top-Down Mathematics- 55:22 - Pattern Recognition- 01:01:30 - Platonic Data- 01:07:15 - A Classic Problem Since 1736- 01:17:38 - Classical Results for Reimann Surface- 01:22:29 - Manifolds- 01:26:52 - Superstring Theory- 01:30:45 - When Physics Meets Math- 01:43:01 - Progress in String Theory- 01:45:45 - Image Processing- 01:59:33 - Episode Recap- 02:12:50 - OutroSPONSORS:- I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOERESOURCES:- The Calibi-Yau Landscape (book): https://amzn.to/41XmUi0- Machine Learning (book): https://amzn.to/49YQ42t- Topology and Physics (book): https://amzn.to/4gCcjxr- Yang-Hui He’s recent physics lecture: https://www.youtube.com/watch?v=AhuZar2C55U- Roger Penrose on TOE: https://www.youtube.com/watch?v=sGm505TFMbU- Edward Frenkel’s String Theory discussion on TOE: https://www.youtube.com/watch?v=n_oPMcvHbAc- Edward Frenkel’s lecture on TOE: https://www.youtube.com/watch?v=RX1tZv_Nv4Y- Joseph Conlon and Peter Toit on TOE: https://www.youtube.com/watch?v=fAaXk_WoQqQ- A New Lower Bound For Sphere Packing (article): https://arxiv.org/pdf/2312.10026- Principia Mathematica (book): https://www.amazon.com/Principia-Mathematica-Alfred-North-Whitehead/dp/1603864377/ref=sr_1_5?crid=2ANIKKX6G8KRK&dib=eyJ2IjoiMSJ9.c62w_u2CfXIK6AaEt-QKx6dp22lbkUr17cSyr3O-rltVBjvb8xCrwLWz8CQ6iWjo8rjmeCsSCwPwM_U0T8_InZfz0vEX9UKDWfSa5Oan86o4YwU6F3GdBPz3J2d_hXbLOc-EULawZ47JksUzndhf5q7ydfCMlK9lYKc2XLZQq-6_dHWQSbjYI82e_dcKw9EWp71DPKIZ9v5qvbyP3CnE7gRpN7uPMZpj-lxlo7Wjsl4.iSUZDFr0n-ZlkiADza8yEePerPoxBJRRCLhO0tQm2wU&dib_tag=se&keywords=principia+mathematica&qid=1735580157&s=books&sprefix=principia+ma%2Cstripbooks%2C122&sr=1-5- Tshitoyan’s paper on Nature: https://www.nature.com/articles/s41586-019-1335-8- New Substack! Follow my personal writings and EARLY ACCESS episodes here: https://curtjaimungal.substack.com- Enjoy TOE on Spotify!: https://tinyurl.com/SpotifyTOE- Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join- Support TOE on Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!)- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs- Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything Theories of Everything with Curt Jaimungal features long-form, technically detailed interviews with leading researchers in physics, mathematics, consciousness, and philosophy, exploring topics at the level of active research. For academics, graduate students, and anyone seeking depth beyond popular science. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

Transcript

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0:30.1	Yang Hui, hey, welcome to the podcast. I'm so excited to speak with you. You have an energetic
0:35.5	humility and your expertise and your passion comes
0:38.5	across whenever I watch any of your lectures. So it's an honor. It's a great pleasure and great
0:44.4	honor to be here. In fact, I'm a great admirer of yours. We've interviewed several of my very
0:49.2	distinguished colleagues like, you know, Roger Penrose and Edick Franco. I actually watched some of them.
0:54.8	It's actually really nice. Wonderful. Wonderful. Well, it's humbling to hear. So firstly,
1:00.1	people should know that we're going to talk about or you're going to give a presentation on AI
1:04.0	and machine learning mathematics and the relationship between them, as well as the three
1:08.7	different levels of what math is in terms of
1:12.1	production and understanding, bottom up, top down, and then the meta. But prior to that,
1:17.3	what specific math and physics disciplines initially sparked your interest? And how did the
1:22.0	collaboration with Roger come about? So my, you know, my bread and butter was mathematical physics, especially, you know,
	...

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