Theories of Everything with Curt Jaimungal

Math Will Never Be The Same Again... | Yang-Hui He

Jan 3, 2025

In this conversation with Yang-Hui He, a mathematical physicist renowned for his work in string theory and AI, the impact of machine learning on mathematics takes center stage. He explains how AI is uncovering profound discoveries, challenging traditional methods. They delve into string theory's relevance and how collaborative efforts within the community are reshaping mathematical research. From discussing complex topics like the role of computers in problem-solving to examining the future of AI in validating proofs, this chat is a fascinating look at evolving mathematical frontiers.

02:25:09

Episode guests

Yang-Hui He

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Episode notes

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Quick takeaways

AI is transforming mathematical research by identifying patterns and facilitating discoveries that traditional methods may overlook.

Yang-Hui He emphasizes the importance of collaboration across diverse mathematical domains, especially in the context of string theory.

The podcast explores three tiers of mathematical comprehension: bottom-up, top-down, and meta-mathematics, highlighting their unique contributions.

Critical discussions surrounding the roles of AI in mathematics revolve around the balance between pattern recognition and human intuition.

Deep dives

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Intro

2min

Mathematics Meets AI: Insights from String Theory

14min

The Intersection of Mathematics and Computing

4min

Mathematics Meets AI: Breakthroughs and Innovations

8min

The Unparalleled Influence of Terry Tao in Mathematics

3min

AI and Mathematics: The Future of Understanding

22min

Intuition and Conjecture in Mathematics: From Gauss to AI

5min

Mathematics Meets Machine Learning

12min

Bridging AI and Mathematics: A Journey Through Topology

16min

10.

Connecting Mathematics and Physics

23min

11.

Bridging Mathematics and Machine Learning

10min

12.

AI Meets Algebraic Geometry

8min

13.

AI Meets Mathematics: New Insights and Discoveries

10min

14.

Engagement and Community in Podcasting

3min

This episode features Yang-Hui He, a mathematical physicist and professor known for his groundbreaking work in string theory, geometry, and AI-driven approaches to mathematical research, as he explains how machine learning is revolutionizing the field and leading to major discoveries.

As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe

Timestamps:

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

Links Mentioned:

•⁠ ⁠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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#science #physics #ai #artificialintelligence #mathematics

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