When axioms clash with intuition

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 sponsors; no guest or associated entity has ever given compensation, directly or through intermediaries.

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