In this episode Professor Yang‑Hue Hi explores how AI is reshaping pure mathematics, from the murmuration conjecture to breakthroughs on the 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.
- 00:00 - Introduction
- 01:34 - Changing Landscape
- 03:30 - ML Categories
- 06:53 - Researchers: Birds vs Hedgehogs
- 09:36 - 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/
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- https://www.economist.com/toe
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