Yang-Hui He: How AI Is Reshaping Pure Mathematics Right Now
1 tim 59 min•23 maj 2025
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 Introduction
1:34 Changing Landscape
3:30 ML Categories
6:53 Researchers: Birds vs Hedgehogs
9:36 Personal Experiences
11:44 Future Role of Academics
14:08 AI Mathematician Presentation
16:14 Intuition in Discovery
18:00 AI Assistance in Vague Problems
18:48 Newton and AI
20:59 Literature Processing
24:34 Acknowledging Modern Mathematicians
26:54 Data Influence
30:22 Riemann Hypothesis Implications
31:55 BST Conjecture and Data
33:29 Collaborations and Limits
36:04 Future of Math and AI
38:31 Image Processing and Intuition
41:57 Visual Thinking
49:24 AI‑Assisted Discovery
51:34 Murmuration Conjecture Interaction
57:05 Hierarchies of Difficulty
58:43 Memoration Breakthrough
1:00:28 Understanding BSD Conjecture
1:01:45 Diophantine Equations
1:03:39 Cubic Complexity
1:19:03 Neural Networks Predictions
1:21:36 Breaking the Birch Test
1:24:44 BSD Conjecture Clarified
1:26:21 AI Role in Discovery
1:30:29 Memoration Phenomenon
1:32:59 PCA Analysis
1:35:50 Emergence of Memoration
1:38:35 Conjectures and AI
1:41:29 Generalizing Biases
1:44:55 Future of AI in Math
1:49:28 Brave New World of Discovery
RESOURCES:
- 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
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- Twitter: https://twitter.com/TOEwithCurt
- Discord Invite: https://discord.com/invite/kBcnfNVwqs
0:00 Introduction
1:34 Changing Landscape
3:30 ML Categories
6:53 Researchers: Birds vs Hedgehogs
9:36 Personal Experiences
11:44 Future Role of Academics
14:08 AI Mathematician Presentation
16:14 Intuition in Discovery
18:00 AI Assistance in Vague Problems
18:48 Newton and AI
20:59 Literature Processing
24:34 Acknowledging Modern Mathematicians
26:54 Data Influence
30:22 Riemann Hypothesis Implications
31:55 BST Conjecture and Data
33:29 Collaborations and Limits
36:04 Future of Math and AI
38:31 Image Processing and Intuition
41:57 Visual Thinking
49:24 AI‑Assisted Discovery
51:34 Murmuration Conjecture Interaction
57:05 Hierarchies of Difficulty
58:43 Memoration Breakthrough
1:00:28 Understanding BSD Conjecture
1:01:45 Diophantine Equations
1:03:39 Cubic Complexity
1:19:03 Neural Networks Predictions
1:21:36 Breaking the Birch Test
1:24:44 BSD Conjecture Clarified
1:26:21 AI Role in Discovery
1:30:29 Memoration Phenomenon
1:32:59 PCA Analysis
1:35:50 Emergence of Memoration
1:38:35 Conjectures and AI
1:41:29 Generalizing Biases
1:44:55 Future of AI in Math
1:49:28 Brave New World of Discovery
RESOURCES:
- 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.
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