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Theories of Everything with Curt Jaimungal

Edward Frenkel: The Math Proof No One Could Explain Until Now

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6606 Ratings

🗓️ 13 August 2024

⏱️ 138 minutes

🧾️ Download transcript

Summary

Edward Frenkel, a leading mathematician at UC Berkeley, explains the Langlands program, its ties to physics, and the search for a single unifying formula. He also shares his personal journey from representation theory to making math accessible to the public.- 00:00 - Intro- 02:14 - Edward’s Background- 07:04 - Robert Langlands- 15:01 - Physics vs. Mathematics- 34:14 - Unification in Math- 45:48 - What Does Math Actually Describe?- 01:02:57 - Langlands Program- 01:22:08 - Counting Problem- 01:25:55 - Harmonic Analysis- 01:33:58 - “One Formula Rules Them All”- 01:51:58 - The Shimura-Taniyama-Weil Conjecture- 01:55:55 - Original Langlands Program- 02:01:22 - A Twist: Langlands Dual Group- 02:01:55 - Rosetta Stone of Math- 02:11:33 - The Pleasure Comes From The Illusion- 02:14:28 - Support TOESPONSORS:- Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!)- Crypto: https://tinyurl.com/cryptoTOE- PayPal: https://tinyurl.com/paypalTOE- TOE Merch: https://tinyurl.com/TOEmerchRESOURCES:- YouTube Episode Link: https://youtu.be/RX1tZv_Nv4Y- Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join- Join TOEmail at https://www.curtjaimungal.org- Edward Frenke's book "Love & Math": https://amzn.to/4dB1URv- Edward Frenkel's book “Langlands Correspondence for Loop Groups”*: https://amzn.to/3Am99xX- Edward Frenkel's ebook (PDF with hyperlinks)*: https://math.berkeley.edu/~frenkel/loop.pdf- Edward Frenkel's Official Website*: https://edwardfrenkel.com- Edward Frenkel's Twitter*: https://twitter.com/edfrenkel- Edward Frenkel's YouTube*: https://www.youtube.com/edfrenkel- Edward Frenkel's Instagram*: https://www.instagram.com/edfrenkel- Instagram: https://www.instagram.com/theoriesofeverythingpod- TikTok: https://www.tiktok.com/@theoriesofeverything_- 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- Pandora: https://pdora.co/33b9lfP- Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e- 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. SPONSOR: I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE FOLLOW: Substack | Spotify | YouTube | Twitter Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

Transcript

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0:00.0

How are you doing today, Edward?

0:01.6

I'm doing great, Kurt. It's great to see you, and it's great to be back on the Theories of Everything podcast.

0:07.8

Yes, and to give some context for people who are wondering, what is this particular episode about the reason we're here,

0:14.9

is that my good friend, Professor of Physics, Lucas Cardoso, WhatsApp messaged me a web page titled Proof of the Geometric Langlands

0:22.9

Conjecture. And then he asked me if this was legitimate. So I then WhatsApped my other good friend,

0:28.0

namely you, Professor of Mathematics, Edward Frankel, to find out if it was indeed. And you said,

0:33.9

yes. And moreover, we talked about how you're like Forrest Gump. And many mathematical

0:38.7

achievements have you peppered in, either in the foreground or in the background. The Forest Gump on

0:44.2

mathematics. Yes, exactly. So love and math covers some of that. That's your popular book, and the link

0:51.9

to that will be on screen and in the description. And in that book,

0:55.2

you provide an accessible introduction to what's one of the most abstract of all the mathematical topics,

1:01.4

namely the Langland's conjectures. And since this is a recent monumental result, which is decades

1:08.3

in the making, this channel is one of the places where we can go into the technical details in podcast form instead of overviews.

1:15.1

So you brought your trusty iPad and you're going to walk us through what this result means, how it was achieved and what the future looks like.

1:22.3

That's right. Yes. So I'm happy to be back. And I also want to say that from watching your videos of your interviews, of your conversations on this podcast theories of everything, I feel like your audience is more interested, kind of in more in-depth discussion of some fairly sophisticated topics in mathematics, quantum physics, and other areas.

1:47.1

So that's why I was actually happy to accept your invitation to talk about this subject,

1:52.3

which is quite esoteric and quite sophisticated and quite technical, because I know that there

1:58.2

is a sufficient, at least sufficient number of your viewers, of your audience,

2:03.4

who I actually dig this kind of discussions, this kind of discussions, which perhaps go

2:07.8

more, go deeper and into more technical aspects than discussions on other podcasts.

2:13.1

Yes.

2:14.0

So I just want to say from the beginning that this is really a very important achievement indeed.

...

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