Richard Borcherds: Monster Group, String Theory, Moonshine

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00:00:00 Introduction
00:02:35 How Richard began to become interested in math
00:03:42 Unification in mathematics vs. unification in physics
00:04:38 Daily ritual (or non-ritual)
00:05:19 How much time spent working / studying?
00:07:22 Creativity of the old vs young
00:08:30 Greatest strength is obstinance
00:08:58 Working in isolation, with no collaborators (strength or a weakness?)
00:10:48 Starting mathematics in your 20's, 30's, or 40's
00:11:45 Why must you pick a problem you're interested in? What happens when you don't?
00:12:41 What do you during moments of non-creativity / writer's block?
00:15:24 On Richard's IQ and nootropics
00:17:02 Richard's creative process
00:18:33 Does he think more pictorially, algebraically, analytically, verbally, etc.?
00:21:11 Not following "deep work"
00:22:00 Reading non-scientific books
00:22:48 Audience Q: What does Richard think of Jordan Peterson?
00:23:31 Audience Q: Have you experience madness, working in math in isolation?
00:23:56 Audience Q: Does he optimize his diet / fast?
00:24:37 How does he learn new mathematics
00:25:42 Solving problems by ignoring them
00:26:51 Audience Q: Advice for someone in their 20's trying to learn math who's not in the field
00:28:03 Why does Richard not like infinity categories?
00:28:44 Does Richard memorize proofs / theorems?
00:29:53 Happiness and meaning in life (math or relationships / marriage / kids?)
00:30:40 What would Richard do without math?
00:31:32 What was it like to win the Fields medal?
00:33:10 Math discovered vs invented
00:34:35 Why is the Monster Group interesting?
00:37:18 "Quantum Field Theory gives me a headache."
00:39:21 Free will?
00:41:17 God, Simulation Hypothesis, and Many Worlds
00:44:53 On the Hard Problem of Consciousness
00:46:28 Favorite mathematicians (Serre, Witten, Tao, Feynman, Weinberg, etc.)
00:48:22 "Ed Witten is terrifying"
00:49:05 The Monster Group and physics
00:52:55 How to contribute to math if you're an outsider (or a neophyte)?
00:56:15 Is set theory too unwieldy and can we base math off of something different?
01:00:03 Pluralism in the foundations of math or not?
01:02:48 Intuitionist / Finitism / Computational logic?
01:04:29 Can people in their 40's understand advanced math?
01:05:20 Unreasonable effectiveness of mathematics
01:06:19 Does it puzzle him that some people don't understand math?
01:08:09 On Ramanujan
01:10:45 Lectures on Number Theory and the difficulty of QFT
01:14:56 On different learning styles, and philosophy of mathematics
01:17:48 Audience Q: How does one know when they're making progress on a solution?
01:19:11 Langland's program
01:21:45 Audience Q: How does one know what to learn when they don't know what they don't know?
01:24:02 Learning math and physics from YouTube
01:29:46 Audience Q: Goldbach's conjecture
01:31:53 On nervousness, performance anxiety, group theory, and chit-chat
01:38:49 "Secret" math techniques
01:39:56 Why "modular forms" are the most mesmeric of all fields of math
01:41:50 Discovered vs. invented (rebuttal from a famous mathematician)
01:47:17 Biology / Psychology / Philosophy is too confounding
01:49:08 On Grothendieck
01:52:09 How do you choose which topic to pursue in math? (and the ABC conjecture)
01:56:25 No Ghost Theorem, and string theory's connection to the Monster

[dmr]

God I love Richard Borcherds. Man is a certified megagenius and he’s still just charismatic as hell and down to earth

[mehmetxczx]

Thank you for asking the questions of audience. It shows that you care about your viewers questions. I respect that.

[johnimusic]

I am 40 years old, only have experience up to Algebra-1, but I am confident that I will learn calculus, and other advanced mathematics.

I am a professional pianist, been playing/learning since 4 years old. I am at the point where my music is benefiting by applying abstract ideas to my musical improvisation.

One of my reasons for wanting to maximize my mathematical knowledge is so I can apply all of that extra dimensionality into my musical ideas.

[pairadeau]

What a charming and witty fellow. Thank you very much for this interview.

[bernardofitzpatrick]

Riveting discussion! I aspire to be as humble and real as Prof. Richard Borcherds. Thanks Curt - great interviewing skills.

[adamchappell]

Thanks for the interview, 2 hours flew by very quickly.

[lukeneville]

This is really fantastic, the honesty in all the answers is great. I'd love for you to have more people like this on!

[jamesbra]

Was literally just watching his lecture series on complex analysis haha. It was the best one I've ever had honestly, so concise.

[artandculture]

I worked at the Courant Institute for 12 years as an administrator directly for faculty. They are mostly like he is in that they are precise and earnest. It was a great place to enjoy people.

[MrYossell]

Very interesting discussion -- thanks. Thanks to Prof Borcherds for his patience in answering so many with such sincerity and thought. On questions such as free will, to be fair to philosophy, they spend a lot of time discussing different ways of understanding definitions of concepts such as free will (indeed, most criticise them for spending too much time looking at definitions.) I think many of them would agree that the ordinary concept is too ambiguous as it stands for it to get an unequivocal answer.

[QuestionableMathematician]

This channel is fantastic. Looks like the algorithm finally came through for me

[lifetheuniverse]

1:26:00 Being able to pause a lecturing teacher is magic. Stopping to consider my thoughts or just to make an arbitrary comment is the thing I love most about learning from videos.

[danielamorenoarrieta]

Omg, I love this man. He is so humble!

[andresalonsofloresmarin]

I was waiting for this kind of video for years.

[visavou]

Great to hear this! Great questions too!

[erichodge]

What a beautiful interview. Thank you both very much.

[edwardjones]

Wonderful interview! I'm not a mathematician but fascinated by, and envious of, their minds. You interviewed this guy without any awe and even a touch of impudence, and it led to a bunch of personal questions which are precisely those I would want to ask but never dare!

Great questions and thanks to the interviewee for being such a good sport

[mathe]

Watching this podcast was very enjoyable for me...

[genecat]

Borcherd is a treasure and this interview is priceless. Your navigation thru both his comfort and discomfort zones reveals the connection between mathematics and self consciousness itself.

[beback_]

I really admire how he managed to stay polite under a barrage of idiotic questions.