In this episode, mathematical physicist Yang‑Hui He explains how machine learning is reshaping mathematics, from string theory to topology. He discusses the interplay of computation and theory, and highlights new approaches that could change how mathematicians discover proofs.
- 00:00 - String Theory & Mathematics
- 10:54 - How Does One Do Mathematics?
- 16:28 - Computers & Mathematics
- 20:04 - Bottom-Up Mathematics
- 28:44 - Meta-Mathematics
- 46:17 - Top-Down Mathematics
- 55:22 - Pattern Recognition
- 01:01:30 - Platonic Data
- 01:07:15 - A Classic Problem Since 1736
- 01:17:38 - Classical Results for Reimann Surface
- 01:22:29 - Manifolds
- 01:26:52 - Superstring Theory
- 01:30:45 - When Physics Meets Math
- 01:43:01 - Progress in String Theory
- 01:45:45 - Image Processing
- 01:59:33 - Episode Recap
- 02:12:50 - Outro
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RESOURCES:
- The Calibi-Yau Landscape (book): https://amzn.to/41XmUi0
- Machine Learning (book): https://amzn.to/49YQ42t
- Topology and Physics (book): https://amzn.to/4gCcjxr
- Yang-Hui He’s recent physics lecture: https://www.youtube.com/watch?v=AhuZar2C55U
- Roger Penrose on TOE: https://www.youtube.com/watch?v=sGm505TFMbU
- Edward Frenkel’s String Theory discussion on TOE: https://www.youtube.com/watch?v=n_oPMcvHbAc
- Edward Frenkel’s lecture on TOE: https://www.youtube.com/watch?v=RX1tZv_Nv4Y
- Joseph Conlon and Peter Toit on TOE: https://www.youtube.com/watch?v=fAaXk_WoQqQ
- A New Lower Bound For Sphere Packing (article): https://arxiv.org/pdf/2312.10026
- Principia Mathematica (book): https://www.amazon.com/Principia-Mathematica-Alfred-North-Whitehead/dp/1603864377/ref=sr_1_5?crid=2ANIKKX6G8KRK&dib=eyJ2IjoiMSJ9.c62w_u2CfXIK6AaEt-QKx6dp22lbkUr17cSyr3O-rltVBjvb8xCrwLWz8CQ6iWjo8rjmeCsSCwPwM_U0T8_InZfz0vEX9UKDWfSa5Oan86o4YwU6F3GdBPz3J2d_hXbLOc-EULawZ47JksUzndhf5q7ydfCMlK9lYKc2XLZQq-6_dHWQSbjYI82e_dcKw9EWp71DPKIZ9v5qvbyP3CnE7gRpN7uPMZpj-lxlo7Wjsl4.iSUZDFr0n-ZlkiADza8yEePerPoxBJRRCLhO0tQm2wU&dib_tag=se&keywords=principia+mathematica&qid=1735580157&s=books&sprefix=principia+ma%2Cstripbooks%2C122&sr=1-5
- Tshitoyan’s paper on Nature: https://www.nature.com/articles/s41586-019-1335-8
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