Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472

Description

Terence Tao is widely considered to be one of the greatest mathematicians in history. He won the Fields Medal and the Breakthrough Prize in Mathematics, and has contributed to a wide range of fields from fluid dynamics with Navier-Stokes equations to mathematical physics & quantum mechanics, prime numbers & analytics number theory, harmonic analysis, compressed sensing, random matrix theory, combinatorics, and progress on many of the hardest problems in the history of mathematics. Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep472-sb See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. *Transcript:* https://lexfridman.com/terence-tao-transcript *CONTACT LEX:* *Feedback* - give feedback to Lex: https://lexfridman.com/survey *AMA* - submit questions, videos or call-in: https://lexfridman.com/ama *Hiring* - join our team: https://lexfridman.com/hiring *Other* - other ways to get in touch: https://lexfridman.com/contact *EPISODE LINKS:* Terence's Blog: https://terrytao.wordpress.com/ Terence's YouTube: https://www.youtube.com/@TerenceTao27 Terence's Books: https://amzn.to/43H9Aiq *SPONSORS:* To support this podcast, check out our sponsors & get discounts: *Notion:* Note-taking and team collaboration. Go to https://lexfridman.com/s/notion-ep472-sb *Shopify:* Sell stuff online. Go to https://lexfridman.com/s/shopify-ep472-sb *NetSuite:* Business management software. Go to https://lexfridman.com/s/netsuite-ep472-sb *LMNT:* Zero-sugar electrolyte drink mix. Go to https://lexfridman.com/s/lmnt-ep472-sb *AG1:* All-in-one daily nutrition drink. Go to https://lexfridman.com/s/ag1-ep472-sb *OUTLINE:* 0:00 - Introduction 0:49 - First hard problem 6:16 - Navier–Stokes singularity 26:26 - Game of life 33:01 - Infinity 38:07 - Math vs Physics 44:26 - Nature of reality 1:07:09 - Theory of everything 1:13:10 - General relativity 1:16:37 - Solving difficult problems 1:20:01 - AI-assisted theorem proving 1:32:51 - Lean programming language 1:42:51 -