The Genius Who Invented Reverse Mathematics

SPONSORS: - Go to https://www.plaud.ai/curt to get a Plaud device today - Go to https://shortform.com/toe for a free trial and an exclusive $50 OFF on your annual subscription - I subscribe to The Economist for their science and tech coverage. As a TOE listener, get 35% off! No other podcast has this: https://economist.com/TOE Harvey Friedman — the youngest professor in Stanford's history, founder of reverse mathematics, and the mathematician Kurt Gödel personally chose to sponsor his final paper — has spent 60 years on a single, audacious question: can ordinary, finite math be trusted? His theorems suggest otherwise, showing that even the most concrete and natural mathematical statements — involving nothing more exotic than rational numbers — cannot be proved or refuted within the gold standard of mathematical foundations, ZFC. The foundations of mathematics, Friedman argues, are not settled bedrock but something far more vertiginous: totally up in the air, and made more mysterious, not less, by his own work. FOLLOW: - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Substack: https://curtjaimungal.substack.com/subscribe - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - Crypto: https://nowpayments.io/donation/TOE - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Gödel’s Incompleteness Misinterpretations - 00:09:48 - Woodin vs. Friedman Foundations - 00:17:28 - Category Theory vs. Logic - 00:24:30 - Borel Determinacy Paradoxes - 00:31:23 - Embedded Maximality Principles - 00:41:18 - Tree(3) and Kruskal’s Theorem - 00:47:40 - Finitism and Large Cardinals - 00:53:11 - Divine Consistency and Angels - 01:03:25 - Reverse Mathematics Origins - 01:11:14 - Constructive Logic and Intuitionism - 01:21:17 - Theology and AI Immortality LINKS MENTIONED: - Harvey Friedman Papers: https://u.osu.edu/friedman.8/foundational-adventures/publications/ - Harvey Friedman YouTube: https://www.youtube.com/@harveyfriedman4465/videos - Harvey Friedman Chess Club: https://cclchess.com/ - This Man Is About to Blow Up Mathematics [Article]: https://nautil.us/this-man-is-about-to-blow-up-mathematics-236446 - Harvey Lecture at OSU: https://youtu.be/NAGQD-bSXok - Most Abused Theorem in Math [TOE]: https://youtu.be/OH-ybecvuEo - John Norton [TOE]: https://youtu.be/Tghl6aS5A3M - Emily Riehl [TOE]: https://youtu.be/mTwvecBthpQ - What Is Infinity? [TOE]: https://youtu.be/rHtqGrtcB1w - Norman Wildberger [TOE]: https://youtu.be/l7LvgvunVCM - Wolfgang Smith [TOE]: https://youtu.be/lF4S_P_o-g0 - Scott Aaronson [TOE]: https://youtu.be/1ZpGCQoL2Rk - Consciousness Iceberg [TOE]: https://youtu.be/65yjqIDghEk - Edward Frenkel [TOE]: https://youtu.be/n_oPMcvHbAc - Elan Barenholtz [TOE]: https://youtu.be/A36OumnSrWY - Michael Levin [TOE]: https://youtu.be/c8iFtaltX-s - Godel Incompleteness Theorems: https://plato.stanford.edu/entries/goedel-incompleteness/ - Consistency of Axiom of Choice [Book]: https://archive.org/details/dli.ernet.469796/page/18/mode/2up - Independence of Continuum Hypothesis [Paper]: https://www.jstor.org/stable/71858 - Borel Determinacy [Paper]: https://www.jstor.org/stable/1971035 - Paris-Harrington Theorem: https://mathworld.wolfram.com/Paris-HarringtonTheorem.html - The God Letter: https://uncertaintist.wordpress.com/wp-content/uploads/2012/10/einstein-letter-gutkind-excerpts.pdf - Undecidable Propositions of Principia Mathematica [Book]: https://amazon.com/dp/0486669807?tag=toe08-20 - Categories for the Working Mathematician [Book]: https://amazon.com/dp/1441931236?tag=toe08-20 - On Necessary Use of Abstract Set Theory [Paper]: https://www.sciencedirect.com/science/article/pii/0001870881900219 - Borel Set: https://en.wikipedia.org/wiki/Borel_set More links: https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices