Yang-Hui He: How AI Is Reshaping Pure Mathematics Right Now

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6 • 606 Ratings

🗓️ 23 May 2025

⏱️ 115 minutes

🔗️ Recording | iTunes | RSS

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Summary

Yang-Hui He explores how AI is reshaping pure mathematics, from the murmuration conjecture to Riemann Hypothesis. We examine the changing research landscape, the role of intuition, and what a future where machines generate discoveries faster than humans might look like.0:00 Introduction1:34 Changing Landscape3:30 ML Categories6:53 Researchers: Birds vs Hedgehogs9:36 Personal Experiences11:44 Future Role of Academics14:08 AI Mathematician Presentation16:14 Intuition in Discovery18:00 AI Assistance in Vague Problems18:48 Newton and AI20:59 Literature Processing24:34 Acknowledging Modern Mathematicians26:54 Data Influence30:22 Riemann Hypothesis Implications31:55 BST Conjecture and Data33:29 Collaborations and Limits36:04 Future of Math and AI38:31 Image Processing and Intuition41:57 Visual Thinking49:24 AI‑Assisted Discovery51:34 Murmuration Conjecture Interaction57:05 Hierarchies of Difficulty58:43 Memoration Breakthrough1:00:28 Understanding BSD Conjecture1:01:45 Diophantine Equations1:03:39 Cubic Complexity1:19:03 Neural Networks Predictions1:21:36 Breaking the Birch Test1:24:44 BSD Conjecture Clarified1:26:21 AI Role in Discovery1:30:29 Memoration Phenomenon1:32:59 PCA Analysis1:35:50 Emergence of Memoration1:38:35 Conjectures and AI1:41:29 Generalizing Biases1:44:55 Future of AI in Math1:49:28 Brave New World of DiscoveryRESOURCES:- Topology and Physics (book): https://amzn.to/3ZoneEn- Machine Learning in Pure Mathematics and Theoretical Physics (book): https://amzn.to/4k8SXC6- The Calabi‑Yau Landscape (book): https://amzn.to/43DO7H0- Yang‑Hui’s bio and published papers: https://www.researchgate.net/profile/Yang-Hui-He- A Triumvirate of AI‑Driven Theoretical Discovery (paper): https://arxiv.org/abs/2405.19973- Edward Frenkel explains the Geometric Langlands Correspondence on TOE: https://www.youtube.com/watch?v=RX1tZv_Nv4Y- Stone Duality (Wiki): https://en.wikipedia.org/wiki/Stone_duality- Summer of Math Exposition: https://some.3b1b.co/- Machine Learning meets Number Theory: The Data Science of Birch–Swinnerton‑Dyer (paper): https://arxiv.org/pdf/1911.02008- The L‑functions and modular forms database: https://www.lmfdb.org/- Epoch AI FrontierMath: https://epoch.ai/frontiermath/the-benchmark- Mathematical Beauty (article): https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/- https://cell.ver.so/TOE- I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE- Join My New Substack (Personal Writings): https://curtjaimungal.substack.com- Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e- Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join- Patreon: https://patreon.com/curtjaimungal- Crypto: https://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9- PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs 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

Transcript

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0:00.0	What the hell? This is bizarre that this pattern exists. It went from zero to almost 100% immediately.
0:05.7	I was amazed.
0:08.8	I'm extremely excited. Today we're going to be talking about a new paradigm of science,
0:13.5	AI research in particular for math and physics, as well as do a deep dive into Professor
0:18.2	Yang Hui He's murmuration conjecture.
0:22.1	Professor, what am I leaving out?
0:24.8	I think, well, thank you very much for having you again.
0:26.7	I had so much fun talking to you last time.
0:29.3	And it's great fun. So I got so excited about this new field of AI-assisted theoretical discovery,
0:35.9	you know, in pure mathematics and theoretical physics,
0:38.2	that we're really entering a new era of discovery.
0:43.2	And it's amazing. It's happening every week, you know, there's something new that could
0:48.2	potentially be transformative in the way we do science.
0:52.6	Yes, you said it shocked the math world, maybe even the physics world and the science world in general.
0:58.0	Yeah, absolutely.
0:59.0	So I'm going to talk about a little bit more details about this, but just private companies like DeepMind, you know, the fact that they're getting Nobel Prizes and, you know,
1:12.9	and all these various AI companies, Open AI, Epic AI, they're actually doing fundamental research
1:20.2	with their models and that are beginning to solve problems in real research, at the real research level.
1:31.5	So this is quite exciting, quite exciting times.
1:35.6	Why don't you talk about how the landscape of research has changed with the advent of these new AI models?
1:40.8	Now, there's a large class, like there's LLMs, but then there's also new machine learning
1:44.3	techniques in general that you have uncovered and other people have uncovered. So why don't
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