Richard Borcherds: The Monster Group and Monstrous Moonshine

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6 • 606 Ratings

🗓️ 17 March 2021

⏱️ 96 minutes

🔗️ Recording | iTunes | RSS

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Summary

I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE Richard Borcherds, a Fields Medalist, talks about the Monster Group, its links to string theory, and his self‑study path in mathematics. He also dives into creativity, learning strategies, free will, consciousness, and the simulation hypothesis.0:00 Introduction2:35 How Richard got interested in math3:42 Math vs physics unification4:38 Daily ritual (or non‑ritual)5:19 Time spent working / studying7:22 Creativity old vs young8:30 Greatest strength: obstinacy8:58 Working in isolation: strength or weakness?10:48 Starting math in 20s, 30s, 40s11:45 Choosing a problem you care about12:41 Dealing with non‑creativity / writer’s block14:40 Depression as a scientist15:24 IQ and nootropics17:02 Creative process18:33 Thinking style: pictorial, algebraic, etc.21:11 Not following “deep work”22:00 Reading non‑scientific books22:48 Audience: view on Jordan Peterson23:31 Audience: experience of madness in isolation23:56 Audience: diet / fasting24:37 Learning new mathematics25:42 Solving problems by ignoring them26:51 Advice for 20s learning math outside field28:03 Dislike of infinity categories28:44 Memorizing proofs/theorems?29:53 Happiness and meaning: math vs life30:40 Life without math31:32 Winning the Fields Medal32:19 What makes math meaningful?33:10 Discovered vs invented34:35 Why the Monster Group matters37:18 “Quantum Field Theory gives me a headache.”39:21 Free will?41:17 God, simulation hypothesis, many worlds44:53 Hard problem of consciousness46:28 Favorite mathematicians48:22 “Ed Witten is terrifying”49:05 Monster Group and physics52:55 Contributing to math as outsider55:44 Many Worlds again56:15 Is set theory too unwieldy?1:00:03 Pluralism in math foundations1:02:48 Intuitionist / finitisim / computational logic?1:04:29 Can 40‑year‑olds learn advanced math?1:05:20 Unreasonable effectiveness of math1:06:19 Why some don’t understand math?1:08:09 On Ramanujan1:10:45 Number theory lectures & QFT difficulty1:14:56 Learning styles & philosophy of math1:17:48 Knowing progress on a solution1:19:11 Langlands program1:21:45 Knowing what to learn when unaware1:24:02 Learning math & physics from YouTube1:29:46 Goldbach's conjecture1:31:53 Nervousness, anxiety, group theory, chit‑chat1:38:49 “Secret” math techniques1:39:56 Why modular forms are mesmeric1:41:50 Rebuttal: discovered vs inventedSPONSORS:- Patreon: https://patreon.com/curtjaimungal- PayPal: https://bit.ly/2EOR0M4- Twitter: https://twitter.com/TOEwithCurt- iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802- Pandora: https://pdora.co/33b9lfPRESOURCES:- YouTube link: https://youtu.be/xu15ZbxxnUQ- Richard Borcherd's YouTube: https://www.youtube.com/channel/UCIyDqfi_cbkp-RU20aBF-MQ 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 Learn more about your ad choices. Visit megaphone.fm/adchoices

Transcript

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0:00.0	Theoretic, it's absolutely wonderful. It's this wonderfully consistent theory with all sorts of
0:04.9	surprising coincidences that all just happen to work out. It's behaving as if it were the ultimate
0:10.9	theory of life, the universe and everything. Unfortunately, it just doesn't tie up with experiment yet.
0:18.2	Today we cover E8, Quantum Field Theory and Ed Witten, with today's guest Richard Bortchards,
0:24.5	a professor of mathematics at the University of Berkeley and a Fields Medalist.
0:28.4	Just so you know, a Fields Medal is the mathematical equivalent of the Nobel Prize.
0:32.7	This is part two of our conversation, the first part you can find by clicking the link in the description.
0:38.9	And it covers string theory, the monstrous moonshine conjecture, Richard's work schedule slash habits.
0:44.5	And in this podcast, we delve even deeper into those topics. But if you like an introduction,
0:49.3	then visit that part one. In mathematics, there was a conjecture by John Conway, suggesting
0:53.5	that there's more than a superficial
0:55.0	connection between the monster group and the J function. This is what's called the monstrous moonshine
1:00.3	conjecture, and this is in part what Richard Bortchers won the Fields Medal for. In fact, there are two
1:05.0	highly cited papers, one called the monstrous moonshine and monstrous Lee superalgebras, and the
1:10.6	second is called vertex algebras, cac- Lee Super Algebras, and the second is called Vertex Algebras,
1:12.6	Kakmoudi Algebras, and the Monster.
1:14.6	At some point in the next few months, I would love to tackle these papers and do an explanation video in the same vein as the Crash Course on Physics,
1:21.6	which you can see here there's a thumbnail somewhere and you can click the link in the description to see.
1:26.6	If you have a vote for which paper in particular, that is the Lee Super Algebra paper or the vertex operator algebra paper,
1:33.5	then let me know in the comment section. My name's Kurt Jymungle. I have a background in mathematical
1:37.4	physics. This podcast is called Theories of Everything is dedicated to the exploration of theories
1:42.7	of everything from a theoretical physics perspective,
	...

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