#472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI

About this episode

<p>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 &#38; quantum mechanics, prime numbers &#38; analytics number theory, harmonic analysis, compressed sensing, random matrix theory, combinatorics, and progress on many of the hardest problems in the history of mathematics.<br /> Thank you for listening ❤ Check out our sponsors: <a href="https://lexfridman.com/sponsors/ep472-sc">https://lexfridman.com/sponsors/ep472-sc</a><br /> See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.</p> <p><b>Transcript:</b><br /> <a href="https://lexfridman.com/terence-tao-transcript">https://lexfridman.com/terence-tao-transcript</a></p> <p><b>CONTACT LEX:</b><br /> <b>Feedback</b> &#8211; give feedback to Lex: <a href="https://lexfridman.com/survey">https://lexfridman.com/survey</a><br /> <b>AMA</b> &#8211; submit questions, videos or call-in: <a href="https://lexfridman.com/ama">https://lexfridman.com/ama</a><br /> <b>Hiring</b> &#8211; join our team: <a href="https://lexfridman.com/hiring">https://lexfridman.com/hiring</a><br /> <b>Other</b> &#8211; other ways to get in touch: <a href="https://lexfridman.com/contact">https://lexfridman.com/contact</a></p> <p><b>EPISODE LINKS:</b><br /> Terence&#8217;s Blog: <a href="https://terrytao.wordpress.com/">https://terrytao.wordpress.com/</a><br /> Terence&#8217;s YouTube: <a href="https://www.youtube.com/@TerenceTao27">https://www.youtube.com/@TerenceTao27</a><br /> Terence&#8217;s Books: <a href="https://amzn.to/43H9Aiq">https://amzn.to/43H9Aiq</a></p> <p><b>SPONSORS:</b><br /> To support this podcast, check out our sponsors &#38; get discounts:<br /> <b>Notion:</b> Note-taking and team collaboration.<br /> Go to <a href="https://lexfridman.com/s/notion-ep472-sc">https://notion.com/lex</a><br /> <b>Shopify:</b> Sell stuff online.<br /> Go to <a href="https://lexfridman.com/s/shopify-ep472-sc">https://shopify.com/lex</a><br /> <b>NetSuite:</b> Business management software.<br /> Go to <a href="https://lexfridman.com/s/netsuite-ep472-sc">http://netsuite.com/lex</a><br /> <b>LMNT:</b> Zero-sugar electrolyte drink mix.<br /> Go to <a href="https://lexfridman.com/s/lmnt-ep472-sc">https://drinkLMNT.com/lex</a><br /> <b>AG1:</b> All-in-one daily nutrition drink.<br /> Go to <a href="https://lexfridman.com/s/ag1-ep472-sc">https://drinkag1.com/lex</a></p> <p><b>OUTLINE:</b><br /> (00:00) &#8211; Introduction<br /> (00:36) &#8211; Sponsors, Comments, and Reflections<br /> (09:49) &#8211; First hard problem<br /> (15:16) &#8211; Navier–Stokes singularity<br /> (35:25) &#8211; Game of life<br /> (42:00) &#8211; Infinity<br /> (47:07) &#8211; Math vs Physics<br /> (53:26) &#8211; Nature of reality<br /> (1:16:08) &#8211; Theory of everything<br /> (1:22:09) &#8211; General relativity<br /> (1:25:37) &#8211; Solving difficult problems<br /> (1:29:00) &#8211; AI-assisted theorem proving<br /> (1:41:50) &#8211; Lean programming language<br /> (1:51:50) &#8211; DeepMind&#8217;s AlphaProof<br /> (1:56:45) &#8211; Human mathematicians vs AI<br /> (2:06:37) &#8211; AI winning the Fields Medal<br /> (2:13:47) &#8211; Grigori Perelman<br /> (2:26:29) &#8211; Twin Prime Conjecture<br /> (2:43:04) &#8211; Collatz conjecture<br /> (2:49:50) &#8211; P = NP<br /> (2:52:43) &#8211; Fields Medal<br /> (3:00:18) &#8211; Andrew Wiles and Fermat&#8217;s Last Theorem<br /> (3:04:15) &#8211; Productivity<br /> (3:06:54) &#8211; Advice for young people<br /> (3:15:17) &#8211; The greatest mathematician of all time</p> <p><b>PODCAST LINKS:</b><br /> &#8211; Podcast Website: <a href="https://lexfridman.com/podcast">https://lexfridman.com/podcast</a><br /> &#8211; Apple Podcasts: <a href="https://apple.co/2lwqZIr">https://apple.co/2lwqZIr</a><br /> &#8211; Spotify: <a href="https://spoti.fi/2nEwCF8">https://spoti.fi/2nEwCF8</a><br /> &#8211; RSS: <a href="https://lexfridman.com/feed/podcast/">https://lexfridman.com/feed/podcast/</a><br /> &#8211; Podcast Playlist: <a href="https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4">https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4</a><br /> &#8211; Clips Channel: <a href="https://www.youtube.com/lexclips">https://www.youtube.com/lexclips</a></p>