Edward Frenkel: The Langlands Proof That Changed Mathematics Forever

Edward Frenkel, a leading mathematician, explains the recent monumental proof in the Langlands program and its impact on modern mathematics. He also revisits earlier work and connects the breakthrough to broader themes in geometry and physics.0:00 Edward's Previous Appearance on TOE1:15 Discoveries in Mathematics4:31 Langland's Program11:02 Counting Problem14:58 Symmetries of the Unit Disc26:55 Part 1 of Edward's Talk30:20 Shimura-Taniyama-Weil Conjecture40:02 Quick Recap42:38 Langlands Dual Group51:50 Rosetta Stone of Math1:00 10 Riemann Surfaces1:10 20 Proof of the Geometric Langlands Conjecture1:21 42 Tribute to Legends1:26 02 Langlands Correspondence for Riemann Surface1:43 30 Galois Groups1:53 33 Other Objects Involved2:10 40 Outro / Support TOESPONSORS:- I personally subscribe to The Economist. SUMMER SALE to Aug 17, 2026: 50% off the annual subscription! No other podcast has this! https://economist.com/TOERESOURCES:- Edward Frenkel's New York Times Bestselling book "Love and Math": https://amzn.to/4gPAVn1- Edward on Linkedin: https://www.linkedin.com/in/edfrenkel/- Edward Frenkel's Twitter: https://x.com/edfrenkel- Edward Frenkel's Official Website: https://edwardfrenkel.com- Edward Frenkel's YouTube: https://youtube.com/@edfrenkel- Edward Frenkel's Instagram: https://www.instagram.com/edfrenkel- Edward Frenkel’s SoundCloud (DJ Moonstein): https://soundcloud.com/moonstein- Edward Frenkel's 1st TOE Episode: https://www.youtube.com/watch?v=n_oPMcvHbAc- Andre Weil’s letter on “Rosetta Stone” of Math: https://www.ams.org/notices/200503/fea-weil.pdf- "Proof of the Geometric Langlands Conjecture" (Papers): https://people.mpim-bonn.mpg.de/gaitsgde/GLC/- Etingof-Frenkel-Kazhdan, “A general framework for the Analytic Langlands Correspondence”: https://arxiv.org/abs/2311.03743- Yuri Manin’s book “Mathematics and Physics”: https://www.amazon.com/Mathematics-Physics-Progress-Mathematical/dp/1489967842- Edward Frenkel’s papers: https://edwardfrenkel.com/frenkel-biblio.pdf- Edward Frenkel’s previous lecture on TOE (Part 1): https://www.youtube.com/watch?v=RX1tZv_Nv4Y- Mathematics and Physics (book): https://www.amazon.com/Mathematics-Physics-Progress-English-Russian/dp/3764330279- Richard Borcherds on TOE: https://www.youtube.com/watch?v=U3pQWkE2KqM- Support TOE on Patreon: https://patreon.com/curtjaimungal- Crypto: https://nowpayments.io/donation/TOE- Listen to TOE on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e- Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join- Join TOE's Newsletter 'TOEmail' at https://www.curtjaimungal.org- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs- iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802- Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything Theories of Everything with Curt Jaimungal features long-form, technically detailed interviews with leading researchers in physics, mathematics, consciousness, and philosophy, exploring topics at the level of active research. For academics, graduate students, and anyone seeking depth beyond popular science. FOLLOW: Substack | Spotify | YouTube | Twitter Learn more about your ad choices. Visit megaphone.fm/adchoices