David Bessis: What Mathematics Really Is and How to Learn It

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6 • 606 Ratings

🗓️ 23 February 2026

⏱️ 135 minutes

🔗️ Recording | iTunes | RSS

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Summary

What is mathematics, really? Mathematician David Bessis joins me to argue that math isn't about numbers in a Platonic realm or a meaningless game of symbols—it's a cognitive technology for rewiring your brain. We explore why the official definitions of mathematics have been unresolved for 2,300 years, why understanding something means finding it obvious, and how the gap between a beginner and Terence Tao looks less like genetic destiny and more like compound interest on intuition. When asked what mathematics fundamentally is, his answer cuts through millennia of philosophy: it's what happens in your head when you pretend something is true until it feels real. LINKS MENTIONED: Papers, books, websites: - https://davidbessis.substack.com/ - https://scholar.google.com/citations?user=YmJL9KwAAAAJ - https://amazon.com/dp/0300283288?tag=toe08-20 - https://davidbessis.substack.com/p/the-magic-of-mathematical-intuition - https://davidbessis.substack.com/p/weve-been-wrong-about-math-for-2300 - https://arxiv.org/abs/math/9404236 - https://amazon.com/dp/0387900926?tag=toe08-20 - https://davidbessis.substack.com/p/the-curious-case-of-broken-theorems - https://mathworld.wolfram.com/FermatsLastTheorem.html - https://xenaproject.wordpress.com/2024/12/11/fermats-last-theorem-how-its-going/ - https://gwern.net/doc/math/1979-hersh.pdf - https://en.wikipedia.org/wiki/Problem_of_universals - https://plato.stanford.edu/entries/set-theory/zf.html - https://imperialcollegelondon.github.io/FLT/blueprint/ - https://amazon.com/dp/1015393233?tag=toe08-20 - https://annals.math.princeton.edu/2015/181-3/p01 - https://arxiv.org/abs/math/0610778 - https://pi.math.cornell.edu/~bts82/events/homotopyF20/notes/bar-construction-typed.pdf - https://www.edge.org/conversation/reuben_hersh-reuben-hersh-1927-2020 - https://mathshistory.st-andrews.ac.uk/Biographies/Ramanujan/ - https://amazon.com/dp/1107536510?tag=toe08-20 - https://viennot.org/abjc-lectures.html - https://pdf.sciencedirectassets.com/272332/1-s2.0-S0021869306X06555/1-s2.0-S0021869305006150/main.pdf Videos: - https://youtu.be/tYgiVnQubyw - https://youtu.be/RX1tZv_Nv4Y - https://youtu.be/73IdQGgfxas - https://youtu.be/lhpRAWxvY5s - https://youtu.be/rJz_Badd43c - https://youtu.be/c8iFtaltX-s - https://youtu.be/81sPQGIWEfM - https://youtu.be/wbP0KjWm0pw - https://youtu.be/mTwvecBthpQ - https://youtu.be/_sTDSO74D8Q - https://youtu.be/DeTm4fSXpbM SOCIALS: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs Guests do not pay to appear. Theories of Everything receives revenue solely from viewer donations, platform ads, and clearly labelled 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	I'd like us to focus on two questions, both of which you have a provocative response to.
0:05.4	One is inspirational, the second is philosophical. The philosophical one is what is math?
0:11.3	The inspirational one is, why do you believe that IQ, which is traditionally thought of as a necessary
0:16.9	component to doing math well, why do you think that's overstated when it comes to understanding
0:21.9	or contributing to breakthroughs? Let's tackle the conceptual ground first and get into
0:27.7	how fear holds people back and practical steps later. What is math? Hmm. That's a very difficult
0:36.7	question. That's a question that is officially too difficult in the sense that nobody seems to agree on the definition.
0:44.4	And it's, so I have, in one of my substack posts, I have a screenshot of Wikipedia for a couple of months ago.
0:51.7	It's been reshuffled, but the screenshots, the content
0:54.5	stayed the same. The definition of mathematics, according to Wikipedia, says that nobody is
1:00.4	agreeing on the definition of mathematics, which is a big issue. You know, you're teaching something
1:04.9	to millions of, billions of people, and you don't really know what this is. So I think people have been mistaken
1:11.7	because they were trying to define mathematics
1:16.9	without any reference to human beings.
1:20.0	So there are two ways of doing that.
1:22.0	One way is to say that math is about,
1:23.8	you know, it's a science of numbers,
1:25.2	of shapes, of things that exist
1:27.4	in the Platonician
1:28.7	world of ideas.
1:30.5	And there is the other approach that is to say that, you know, math is about logic, about proving
1:34.1	things, about having axioms, theorems, and all that.
	...

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