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

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 - DeepMind's AlphaProof 1:47:45 - Human mathematicians vs AI 1:57:37 - AI winning the Fields Medal 2:04:47 - Grigori Perelman 2:17:30 - Twin Prime Conjecture 2:34:04 - Collatz conjecture 2:40:50 - P = NP 2:43:43 - Fields Medal 2:51:18 - Andrew Wiles and Fermat's Last Theorem 2:55:16 - Productivity 2:57:55 - Advice for young people 3:06:17 - The greatest mathematician of all time *PODCAST LINKS:* - Podcast Website: https://lexfridman.com/podcast - Apple Podcasts: https://apple.co/2lwqZIr - Spotify: https://spoti.fi/2nEwCF8 - RSS: https://lexfridman.com/feed/podcast/ - Podcast Playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4 - Clips Channel: https://www.youtube.com/lexclips *SOCIAL LINKS:* - X: https://x.com/lexfridman - Instagram: https://instagram.com/lexfridman - TikTok: https://tiktok.com/@lexfridman - LinkedIn: https://linkedin.com/in/lexfridman - Facebook: https://facebook.com/lexfridman - Patreon: https://patreon.com/lexfridman - Telegram: https://t.me/lexfridman - Reddit: https://reddit.com/r/lexfridman