The AI Math That Left Number Theorists Speechless

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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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Exploring theoretical physics, consciousness, Ai, and God in a technically rigorous manner. If you'd like to support this endeavor, then please visit the Patreon ( https://patreon.com/curtjaimungal ). Thank you for your charitable and kindhearted support. My name's Curt Jaimungal, a Torontonian with a degree in mathematical physics from the University of Toronto and I analyze various Theories of Everything from this analytic perspective, though more and more opening up to alternative approaches. The separating factor of TOE from other podcasts is its focus on depth even at the risk of limiting the audience due to how much detail we delve into subjects. Paralleling the intensity found in academic discourse, we're increasingly embracing a spectrum of unconventional ideas to conduct research during this podcast, rather than merely conveying existing information. Contact toe [at] indiefilmTO [dot] com for business inquiries / sponsorship.

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