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 personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. 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 chose to sponsor his final paper — has spent 60 years on one question: can ordinary, finite math be trusted? His theorems show that even concrete statements involving nothing more exotic than rational numbers cannot be proved or refuted within ZFC. The foundations of mathematics, Friedman argues, are not settled bedrock but vertiginous — 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

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