Get ready to witness a turning point in mathematical history: in this episode, we dive into the AI breakthroughs that stunned number theorists worldwide. Join us as Professor Yang-Hue Hi discusses the murmuration conjecture, shows how DeepMind, OpenAI, and EpochAI are rewriting the rules of pure math, and reveals what happens when machines start making research-level discoveries faster than any human could. AI is taking us beyond proof straight into the future of discovery.

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Timestamps:

00:00 Introduction to a New Paradigm

01:34 The Changing Landscape of Research

03:30 Categories of Machine Learning in Mathematics

06:53 Researchers: Birds vs. Hedgehogs

09:36 Personal Experiences with AI in Research

11:44 The Future Role of Academics

14:08 Presentation on the AI Mathematician

16:14 The Role of Intuition in Discovery

18:00 AI's Assistance in Vague Problem Solving

18:48 Newton and AI: A Historical Perspective

20:59 Literature Processing with AI

24:34 Acknowledging Modern Mathematicians

26:54 The Influence of Data on Mathematical Discovery

30:22 The Riemann Hypothesis and Its Implications

31:55 The BST Conjecture and Data Evolution

33:29 Collaborations and AI Limitations

36:04 The Future of Mathematics and AI

38:31 Image Processing and Mathematical Intuition

41:57 Visual Thinking in Mathematics

49:24 AI-Assisted Discovery in Mathematics

51:34 The Murmuration Conjecture and AI Interaction

57:05 Hierarchies of Difficulty

58:43 The Memoration Breakthrough

1:00:28 Understanding the BSD Conjecture

1:01:45 Diophantine Equations Explained

1:03:39 The Cubic Complexity

1:19:03 Neural Networks and Predictions

1:21:36 Breaking the Birch Test

1:24:44 The BSD Conjecture Clarified

1:26:21 The Role of AI in Discovery

1:30:29 The Memoration Phenomenon

1:32:59 PCA Analysis Insights

1:35:50 The Emergence of Memoration

1:38:35 Conjectures and AI's Role

1:41:29 Generalizing Biases in Mathematics

1:44:55 The Future of AI in Mathematics

1:49:28 The Brave New World of Discovery

Links Mentioned:

- 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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