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 Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

SPONSORS: - Go to https://shortform.com/toe for a free trial and an exclusive $50 OFF on your annual subscription - Go to https://vanman.shop/curt to get 15% off your order - Go to https://www.plaud.ai/curt to get a Plaud device today - I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE Janna Levin — Claire Tow Professor of Physics and Astronomy at Barnard College, founding Director of Sciences at Pioneer Works, and co-host of Quanta's The Joy of Why — is working with Brian Greene to explore whether hidden Klein-bottle-shaped dimensions could explain why matter won the war against antimatter after the Big Bang. The geometry does the work — no fudged parameters required. 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 - Universe as Gödel Sentence - 00:05:24 - Unknowable Initial Conditions - 00:10:28 - AI and Non-Computable Consciousness - 00:15:36 - The Hard Problem Paradox - 00:25:25 - Klein Bottle Topology - 00:32:04 - Pin Structures and Chirality - 00:39:56 - Breaking Matter-Antimatter Symmetry - 00:51:26 - Topology and Dark Energy - 00:57:00 - Black Hole Information Paradox - 01:07:04 - ER=EPR and Firewalls - 01:13:37 - Black Holes as Particles - 01:18:42 - Emergent Gravity and Holography - 01:23:43 - Rejecting Physical Infinities - 01:31:41 - Narrative Truth vs. Axioms - 01:41:22 - Insomnia and Mathematical Madness - 01:47:22 - Scientific Mysticism and Honesty - 01:53:34 - Biological Morality and Advice LINKS MENTIONED: - Janna's Substack: jannalevin.substack.com - Janna's Books: amazon.com/stores/author/B001IXTNZQ - Janna's Papers: inspirehep.net/authors/1000438 - Pioneer Works: pioneerworks.org - Whales Don't Want to Go to Mars [Article]: jannalevin.substack.com/p/billions-of-exoplanets-zero-aliens - Black Hole Blues [Book]: amzn.to/4cPOcfr - A Madman Dreams of Turing Machines [Book]: amazon.com/dp/1400032407?tag=toe08-20 - Gödel Incompleteness Theorems: plato.stanford.edu/entries/goedel-incompleteness - Gödel Numbering: en.wikipedia.org/wiki/G%C3%B6del_numbering - Wave Function of the Universe [Paper]: isidore.co/misc/Physics%20papers%20and%20books/Classic%20Papers/Wavefunction%20of%20the%20Universe%20(Hartle%20&%20Hawking).pdf - Janna & Penrose at Oxford: jannalevin.substack.com/p/penrose-and-mein-oxford - Hard Problem of Consciousness [Paper]: consc.net/papers/facing.pdf - Klein Bottle: mathworld.wolfram.com/KleinBottle.html - Klein Bottle Cosmology [Paper]: arxiv.org/abs/2511.23447 - Brane-World Motion in Compact Dimensions [Paper]: arxiv.org/abs/1103.2174 - Dark Energy & Extra Dimensions [Paper]: arxiv.org/abs/0707.1062 - Particle Creation by Black Holes [Paper]: link.springer.com/article/10.1007/BF02345020 - BH Complementarity [Paper]: arxiv.org/abs/hep-th/9306069 - Black Holes: Complementarity or Firewalls? [Paper]: arxiv.org/abs/1207.3123 - Thermodynamics of Spacetime [Paper]: arxiv.org/abs/gr-qc/9504004 - Most Abused Theorem in Math [TOE]: youtu.be/OH-ybecvuEo - Roger Penrose [TOE]: youtu.be/sGm505TFMbU - Roger Penrose [Part 2]: youtu.be/iO03t21xhdk - Neil Turok [TOE]: youtu.be/zNZCa1pVE20 - David Chalmers [TOE]: youtu.be/5r9V1ryksnw - Brian Greene [TOE]: youtu.be/O2EtTE9Czzo - Leonard Susskind [TOE]: youtu.be/2p_Hlm6aCok - Ted Jacobson [TOE]: youtu.be/3mhctWlXyV8 - Juan Maldacena [TOE]: youtu.be/6LbRHMvyrik More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

SPONSORS: - 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 Juan Maldacena wrote the most cited paper in theoretical physics, birthing AdS/CFT and realizing holography — and today, the problem keeping him up at night is wormholes. He suspects space-time isn't fundamental at all, that geometry itself might be what entanglement looks like from the inside. The singularity isn't a place, it's a name for everything we don't yet understand. I hope you enjoy it. 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://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Emergent Space-Time Geometry - 00:05:28 - GR and QM Incompatibility - 00:11:52 - The Singularity Problem - 00:17:00 - Extremal Black Hole Thermodynamics - 00:22:00 - The Island Formula - 00:27:30 - Spacetime and Quantum Information - 00:34:15 - ER equals EPR - 00:41:51 - Traversable Wormhole Physics - 00:47:24 - Simulating Wormholes with Qubits - 00:52:53 - Celestial Holography and Symmetries - 00:58:00 - dS/CFT and Dark Energy - 01:04:24 - Quantum Error Correction Codes - 01:10:00 - The Physicist’s Mindset - 01:15:19 - Inflationary Gravity Wave Predictions - 01:21:03 - Clocks and Emergent Time - 01:26:44 - Is Space-Time Doomed? - 01:32:00 - AI in Theoretical Physics - 01:38:00 - Overcoming Academic Inadequacy LINKS MENTIONED: - Juan Maldacena's Website: https://www.ias.edu/sns/malda - Large N Limit of Superconformal Field Theories [Paper]: https://arxiv.org/abs/hep-th/9711200 - Eternal Black Holes in AdS [Paper]: https://arxiv.org/abs/hep-th/0106112 - Holographic Derivation of Entanglement Entropy [Paper]: https://arxiv.org/abs/hep-th/0603001 - Real Observers Solving Imaginary Problems [Paper]: https://arxiv.org/abs/2412.14014 - Building Spacetime with Quantum Entanglement [Paper]: https://arxiv.org/abs/1005.3035 - Entropy of Bulk Quantum Fields [Paper]: https://arxiv.org/abs/1905.08762 - Entanglement Wedge Reconstruction [Paper]: https://arxiv.org/abs/1905.08255 - Comments on the Double Cone Wormhole [Paper]: https://arxiv.org/abs/2310.11617 - Traversable Wormholes in Four Dimensions [Paper]: https://arxiv.org/abs/1807.04726 - JT Gravity as a Matrix Integral [Paper]: https://arxiv.org/abs/1903.11115 - Single-Minus Gluon Tree Amplitudes [Paper]: https://arxiv.org/abs/2602.12176 - Bulk Locality and Quantum Error Correction [Paper]: https://arxiv.org/abs/1411.7041 - Black Hole Information Paradox: https://en.wikipedia.org/wiki/Black_hole_information_paradox - Chilloquium 2023 [Lecture]: https://youtu.be/Ow81IJyzmUQ - Erik Verlinde [TOE]: https://youtu.be/ilVImMHcr_g - Leonard Susskind [TOE]: https://youtu.be/2p_Hlm6aCok - Edward Frenkel [TOE]: https://youtu.be/RX1tZv_Nv4Y More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science 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

SPONSORS:- Accelerate your efficiency. Sign up for your one-dollar-per-month trial today at http://shopify.com/theories- 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/TOESlavoj Žižek doesn't answer your question — he dismantles it, rebuilds it, and hands you something stranger and more useful than what you started with. Philosopher, provocateur, and self-described pessimist, he's spent decades insisting on something most thinkers shy away from: that freedom isn't the absence of necessity — it's the moment you choose what you fundamentally are. The fall comes first. Paradise was never real to begin with. Reality is the gap, not the thing on either side of it. 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://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS:- 00:00:00 - Socrates and Radical Freedom- 00:05:02 - Quantum Indeterminacy vs. Freedom- 00:10:06 - Ontological Collapse Paradoxes- 00:15:07 - Adorno and Social Antinomies- 00:20:36 - Democritus: Less Than Nothing- 00:25:40 - Sartre and Existential Choice- 00:30:45 - Freudian Death Drive- 00:36:01 - Heidegger and Hysterical Awareness- 00:42:10 - Imp of Perversity- 00:48:07 - Einstein vs. Bohr- 00:53:15 - God’s Ontological Laziness- 00:58:17 - Hegel’s Retroactive Necessity- 01:03:41 - Digital Spirituality and AI- 01:09:18 - Stalin and Failed Projects- 01:14:41 - Hegel in a Wired Brain- 01:20:10 - Religious Convictions and Physics- 01:25:12 - Zen Buddhism and WarLINKS MENTIONED: - Slavoj's Books: https://amazon.com/stores/author/B000APK7P8- Philosophical Investigations into Human Freedom: https://amazon.com/dp/0791468747?tag=toe08-20- Freedom: A Disease Without Cure: https://amazon.com/dp/1350559164?tag=toe08-20- Groundwork of the Metaphysic of Morals: https://www.earlymoderntexts.com/assets/pdfs/kant1785.pdf- Binding, Minds & the Platonic Realm [Lecture]: https://youtu.be/0BVM0UC28nY- Quantum Healing: https://amazon.com/dp/0553348698?tag=toe08-20- Republic of Silence: https://www.theatlantic.com/magazine/archive/1944/12/paris-alive-the-republic-of-silence/656012/- Discourse on the Origin of Inequality: https://amazon.com/dp/0486434141?tag=toe08-20- Beyond the Pleasure Principle: https://www.sas.upenn.edu/~cavitch/pdf-library/Freud_Beyond_P_P.pdf- Philosophy of Spirit: https://www.marxists.org/reference/archive/hegel/jlindex.htm- Hegelian Reading of the New Science of Consciousness: https://www.crisiscritique.org/storage/app/media/2025-08-25/slavoj-zizek.pdf- The Mirror Stage: https://english.hku.hk/staff/kjohnson/PDF/LacanMirrorStageECRITS.pdf- Being and Time: https://amazon.com/dp/0061575593?tag=toe08-20- Less Than Nothing: https://amazon.com/dp/1781681279?tag=toe08-20- The Imp of the Perverse: https://web.english.upenn.edu/~cavitch/pdf-library/Poe_Imp.pdf- Einstein-Bohr Debate: https://www.marxists.org/reference/subject/philosophy/works/dk/bohr.htm- Ages of the World: https://amazon.com/dp/1438474059?tag=toe08-20- Quantum History: https://amazon.com/dp/135056642X?tag=toe08-20- Phenomenology of Spirit: https://amazon.com/dp/0198245971?tag=toe08-20- Philosophy of Right: https://www.marxists.org/reference/archive/hegel/works/pr/preface.htm- White Holes: https://amazon.com/dp/B0BTKZVJJK?tag=toe08-20- Science of Logic: https://amazon.com/dp/1542519918?tag=toe08-20- End of History and the Last Man: https://amazon.com/dp/0743284550?tag=toe08-20More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE Why can't local agreement scale to global truth? At the Mind at Large consciousness conference, hosted by the Center for Process Studies, I make the case using sheaf theory and physics — breaking down consciousness, free will, and the hard problem to show why sincerity beats any polished, totalizing philosophy. 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://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Intellectual Slogan Fatigue - 00:06:11 - The Reverse Elephant Metaphor - 00:11:12 - Local-to-Global Extension Failures - 00:16:13 - Three Senses of Irreducibility - 00:21:16 - Sheaf Theory and Obstructions - 00:26:30 - Hard Problem Formalizations - 00:31:36 - Averted Vision and Consciousness - 00:36:36 - Taxonomy of Everything - 00:41:39 - Pre-articulate Scientific Intimations - 00:46:45 - Speculative Philosophy and Humility - 00:51:47 - Ontological Significance of Vagueness LINKS MENTIONED: - Matthew Segall [TOE]: https://youtu.be/DeTm4fSXpbM - Jenann Ismael [TOE]: https://youtu.be/7kvXihDAOi0 - Aephraim Steinberg [TOE]: https://youtu.be/cOZ3Kto6NIc - The Third Option [TOE]: https://youtu.be/tJsghrZQaYU - Scott Aaronson & David Chalmers [TOE]: https://youtu.be/7PlmOXQ18jk - Curt Debunks "All Possible Paths" [TOE]: https://youtu.be/XcY3ZtgYis0 - Consciousness Iceberg [TOE]: https://youtu.be/65yjqIDghEk - Stephen Wolfram [TOE]: https://youtu.be/FkYer0xP37E - Karl Friston [TOE]: https://youtu.be/uk4NZorRjCo - Michael Levin [TOE]: https://youtu.be/c8iFtaltX-s - Geoffrey Hinton [TOE]: https://youtu.be/b_DUft-BdIE - Noam Chomsky [TOE]: https://www.youtube.com/playlist?list=PLZ7ikzmc6zlORiRfcaQe8ZdxKxF-e2BCY - Anna Ciaunica & Michael Levin [TOE]: https://youtu.be/2aLhkm6QUgA - Mind-at-Large Project: https://ctr4process.org/mind-at-large/ - Process and Reality [Book]: https://amazon.com/dp/0029345707?tag=toe08-20 - The Structure of Science [Book]: https://amazon.com/dp/0915144719?tag=toe08-20 - Sorites Paradox: https://plato.stanford.edu/entries/sorites-paradox/ - The Mathematics of Self [Article]: https://curtjaimungal.substack.com/p/the-mathematics-of-self-why-you-can - Gödel, Escher, Bach [Book]: https://amazon.com/dp/0465026567?tag=toe08-20 - Sheaf (Mathematics): https://en.wikipedia.org/wiki/Sheaf_(mathematics) - Counterexamples in Topology [Book]: https://amazon.com/dp/048668735X?tag=toe08-20 - Process Philosophy: https://plato.stanford.edu/entries/process-philosophy/ - Consciousness Explained [Book]: https://amazon.com/dp/0316180661?tag=toe08-20 - The Conscious Mind [Book]: https://amazon.com/dp/0195117891?tag=toe08-20 - Matter and Memory [Book]: https://amazon.com/dp/1420937804?tag=toe08-20 - Boiling Frog: https://en.wikipedia.org/wiki/Boiling_frog - Peano's Axioms: https://mathworld.wolfram.com/PeanosAxioms.html - Aharonov-Bohm Effect: https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

SPONSORS: - Sign up for Claude today at https://Claude.ai/theoriesofeverything and checkout Claude Pro — which includes access to all of the features mentioned in today's episode - 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 George Ellis is one of those guests who makes you rethink what you thought you understood. Co-author with Stephen Hawking of the singularity theorems, he's spent decades insisting on something most physicists won't touch: that reductionism is simply — patently — false. Physics doesn't decide outcomes. Context does. The thermostat sets the temperature. The algorithm tells the electrons what to do. The physics is the servant, not the master. 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://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Reductionism is Patently False - 00:07:37 - Top-Down Causation Mechanics - 00:13:46 - Modular Hierarchical Structures - 00:21:00 - Causation at Emergent Levels - 00:26:56 - Universal Biological Principles - 00:36:07 - Critiquing Penrose and CCC - 00:42:41 - The Physics of Infinity - 00:48:50 - Agency and Physical Constraints - 00:56:08 - The Open Future - 01:07:23 - Bioelectricity and Goal-Directedness - 01:12:28 - Evolving Block Universe - 01:19:32 - Multiverse as Metaphysics - 01:24:49 - Moral Realism as Data LINKS MENTIONED: - George's Papers: https://inspirehep.net/authors/1010821 - George's Books: https://amazon.com/stores/George-Francis-Rayner-Ellis/author/B00287T2PW - Arrow of Time [Paper]: https://arxiv.org/abs/1302.7291 - Why Reductionism Does Not Work [Paper]: https://link.springer.com/chapter/10.1007/978-3-662-63187-4_6 - Recognizing Top-Down Causation [Paper]: https://arxiv.org/abs/1212.2275 - Top-Down Causation by Information Control [Paper]: https://pmc.ncbi.nlm.nih.gov/articles/PMC3226993/ - Causal Closure of Physics [Paper]: https://arxiv.org/abs/2006.00972 - Issues in Philosophy of Cosmology [Paper]: https://arxiv.org/abs/astro-ph/0602280 - The Music of Life [Book]: https://amazon.com/dp/0199228361?tag=toe08-20 - How Can Physics Underlie the Mind? [Book]: https://amazon.com/dp/3662498073?tag=toe08-20 - Large Scale Structure of Space-Time [Book]: https://amazon.com/dp/0521099064?tag=toe08-20 - The Selfish Gene [Book]: https://amazon.com/dp/0199291152?tag=toe08-20 - World Beyond Physics [Book]: https://amazon.com/dp/0190871334?tag=toe08-20 - Contextual Wavefunction Collapse [Paper]: https://arxiv.org/abs/1807.08171 - A Theory of Biological Relativity [Paper]: https://pubmed.ncbi.nlm.nih.gov/23386960/ - Facing Up to the Problem of Consciousness [Paper]: https://consc.net/papers/facing.pdf - Denis Noble [TOE]: https://youtu.be/K-U-ZB3yHK4 - Michael Levin [TOE]: https://youtu.be/c8iFtaltX-s - Sean Carroll [TOE]: https://youtu.be/9AoRxtYZrZo - Quantum Physics, Digital Computers, and Life [Paper]: https://arxiv.org/abs/2403.06306 - Dynamical Emergence of Biology from Physics [Paper]: https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2018.01966/full - The Whole Truth [Book]: https://amazon.com/dp/0691231354?tag=toe08-20 - Endless Forms Most Beautiful [Book]: https://amazon.com/dp/0393327795?tag=toe08-20 - Topology and Cosmology [Paper]: https://link.springer.com/article/10.1007/BF02450512 More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

SPONSORS: - Go to https://expressvpn.com/theoriesofeverythingyt to find out how you can get up to 4 extra months thanks to our sponsor, ExpressVPN - Accelerate your efficiency. Sign up for your one-dollar-per-month trial today at http://shopify.com/theories - I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE Professor Aephraim Steinberg, winner of Physics World's Breakthrough of the Year in 2011, is an experimentalist who thinks deeply about foundations. For 30 years he's measured aspects of physics others wouldn't touch: Bohmian trajectories, Heisenberg's disturbance bound (he showed it was wrong), even where the photon is inside the double slit. His lab measured negative time, and it keeps reappearing across different experiments. 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://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00:00 - Defining Negative Time - 00:06:50 - Quantum Trajectory Theory - 00:12:44 - The Holland Tunnel Analogy - 00:18:40 - Resonant Atomic Interactions - 00:26:05 - Superluminal Energy Propagation - 00:32:00 - Eight Velocities of Light - 00:38:00 - Causality and Retrocausality - 00:44:00 - Dwell Time vs. Delay - 00:50:24 - Time: Operator or Parameter? - 00:58:21 - Bell's Theorem and Realism - 01:04:55 - Heisenberg's Measurement Disturbance - 01:11:26 - Weak Measurement Formalism - 01:17:37 - Time Symmetry and Entropy - 01:27:07 - Bohmian Trajectories Observed - 01:35:56 - Spin-Statistics and Indistinguishability - 01:42:14 - Quantum Computational Advantage - 01:48:15 - Many Worlds vs. Complexity - 01:54:51 - Psi-Ontic vs. Psi-Epistemic - 02:01:37 - Collapsing Tunneling Particles - 02:08:48 - Larmor vs. Atto Clocks - 02:15:24 - Locality and Information LINKS: - Website: https://www.physics.utoronto.ca/~aephraim/ - Papers: https://scholar.google.com/citations?user=PzUyb6IAAAAJ - Photon Negative Time: https://arxiv.org/pdf/2409.03680 - Photon Time as Excitation: https://arxiv.org/abs/2310.00432 - Atoms in Excited State: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.010314 - Tunneling Atom in Barrier: https://arxiv.org/abs/1907.13523 - Single-Photon Tunneling: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.708 - Traversal Time: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.49.1739 - Gaussian Pulse Propagation: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.1.305 - Pulse in Absorbing Medium: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.48.738 - Eighth Velocity of Light: https://pubs.aip.org/aapt/ajp/article-abstract/45/6/538/1045817/Eighth-velocity-of-light - Attosecond Ionization: https://www.science.org/doi/10.1126/science.1163439 - Tunneling Pulses, Band Gaps: https://attoworld.de/fileadmin/user_upload/tx_attoworld/publications/paper_PhysRevLett_Y1994_M10_D24_V73_P2308.pdf - Evidence of Negative Time: https://www.scientificamerican.com/article/evidence-of-negative-time-found-in-quantum-physics-experiment/ - Light Speed Reduction: https://www.nature.com/articles/17561 - Theory of Light and Colors: https://www.jstor.org/stable/pdf/107113.pdf - Wave Propagation: https://amazon.com/dp/1483253937?tag=toe08-20 - EPR: https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777 - Uncertainty Principle: https://en.wikipedia.org/wiki/Uncertainty_principle - QBism: https://arxiv.org/abs/1003.5209 More: https://curtjaimungal.substack.com Guests do not pay to appear. #science Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

SPONSORS: - 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 The intellectual world is designed to erode your confidence — through rejection rates, delayed feedback, unfair comparisons, and the silence of everyone you've actually helped. In this video I break down why feeling like a fraud is almost a structural inevitability in serious academic and self-directed learning, not a reflection of your actual ability. If you've ever stared at your own work and wondered what's wrong with you, this one's for you. 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://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00 - Intellectual Negativity Bias - 03:22 - Rigor and Intellectual Giants - 05:33 - Invisible Intellectual Impact - 08:43 - Quinean Web of Metrics - 11:01 - Genius Culture Pathologies LINKS MENTIONED: - 7 Signs You're Smarter Than You Think [Substack]: https://curtjaimungal.substack.com/p/7-signs-youre-smarter-than-you-think - Math Proof No One Could Explain [Part 1] [TOE]: https://youtu.be/RX1tZv_Nv4Y - Roger Penrose: Quantum Theory Is Wrong [TOE]: https://youtu.be/sGm505TFMbU - Bernardo Kastrup: Escaping the Illusion [TOE]: https://youtu.be/lAB21FAXCDE - Terence Tao: https://mathstodon.xyz/@tao/113721192051328193 - Curt's Substack: https://curtjaimungal.substack.com - Jacob Barandes: Quantum Theory as Stochastic Process [Wolfram]: https://youtu.be/JsmX3YxiUj0 - The 2,300-Year-Old Math Mistake [TOE]: https://youtu.be/GHGi_XDqKNw - David Bessis: Dual Braid Monoid [Paper]: https://arxiv.org/pdf/math/0101158 - Scott Aaronson: Greatest Unsolved Problem in Math [TOE]: https://youtu.be/1ZpGCQoL2Rk - Scott Aaronson: Truth About Quantum Computing [IAI]: https://youtu.be/KRxC6yzvoys - Beyond Consciousness: Animals, Infants, Petri Brains [TOE]: https://youtu.be/t_YMcEPfqCM - Willard Van Orman Quine [Stanford]: https://plato.stanford.edu/entries/quine/ - Imposter Syndrome Workplace Prevalence: https://www.personneltoday.com/hr/imposter-syndrome-prevalence-uk-research/ - Imposter Syndrome Systematic Review [Paper]: https://pmc.ncbi.nlm.nih.gov/articles/PMC7174434/ - Sabrina @ How the Light Gets In [PhysicsGirl]: https://youtu.be/GrlGdoBGVBs - String Theory & M-Theory, Lecture 1 [Stanford]: https://youtu.be/25haxRuZQUk - Necessity of Complex Numbers [MIT OCW]: https://youtu.be/f079K1f2WQk - Phil Halper: Alternative Universe Theories [IAI]: https://youtu.be/3SpzC6stFhU - Debunking Veritasium: All Possible Paths Myth [TOE]: https://youtu.be/XcY3ZtgYis0 - Gödel's Incompleteness: Most Abused Theorem [TOE]: https://youtu.be/OH-ybecvuEo - Farina vs. Tour: Origin of Life Debate: https://youtu.be/KvGdllx9pJU More links at https://curtjaimungal.substack.com Guests do not pay to appear. #science 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

For much of history, many mathematicians—following thinkers like Aristotle—viewed infinity as a never-ending process rather than a completed object. In the late 19th century, Georg Cantor revolutionized this view by treating infinite sets as mathematical objects that could be compared and studied. His work showed that not all infinities are equal, and that there are infinitely many different sizes of infinity. While his ideas are foundational in modern mathematics, some philosophical schools, such as finitism and ultrafinitism, continue to question whether infinite objects meaningfully exist. I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE 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://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 TIMESTAMPS: - 00:00 - Potential vs. Actual Infinity - 03:12 - Cardinality and Aleph-Null - 06:12 - Diagonalization and Uncountability - 09:21 - ZFC and Logical Independence - 12:23 - Finitism and Ultrafinitism - 15:26 - Continuum Hypothesis Paradoxes - 16:00 - Foundational Mathematical Crisis LINKS MENTIONED: - The Most Abused Theorem in Math [TOE]: https://www.youtube.com/watch?v=OH-ybecvuEo - Dror Bar Natan [TOE]: https://youtu.be/rJz_Badd43c - Hilbert’s Problems: https://mathworld.wolfram.com/HilbertsProblems.html - The Independence of the Continuum Hypothesis [paper]: https://www.pnas.org/doi/pdf/10.1073/pnas.50.6.1143 - Piano arithmetic: https://ncatlab.org/nlab/show/Peano+arithmetic - Cantor’s Diagonal Argument: https://www.researchgate.net/publication/335364685_A_Translation_of_G_Cantor's_Ueber_eine_elementare_Frage_der_Mannigfaltigkeitslehre - Hartog’s Construction: paultaylor.eu/trans/HartogsF-wellord.pdf - Cohen’s Forcing Method: https://timothychow.net/forcing.pdf - Norman Wildberger [TOE]: https://youtu.be/l7LvgvunVCM - Woodin’s lecture: https://youtu.be/nVF4N1Ix5WI In Search of Ultimate-L [paper]: https://www.jstor.org/stable/44164514 - Emily Riehl [TOE]: https://youtu.be/mTwvecBthpQ - Sir Roger Penrose [TOE]: https://youtu.be/sGm505TFMbU - Why Write? [article]: https://curtjaimungal.substack.com/p/why-write ASSETS USED: - Infinity display: https://youtu.be/osa4ptG5lMg - Number counter: https://youtu.be/HRL5uNGXh9U Guests do not pay to appear. #science 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

Emily Riehl, one of the world’s leading category theorists, shares her vision for making infinity category theory something undergrads can actually learn. In this talk, she breaks down how rethinking the foundations of math could change the way it’s taught and understood—and why it might redefine what math even is. I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://tinyurl.com/SpotifyTOE Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join Links: •⁠ ⁠Emily’s profile: https://emilyriehl.github.io/ •⁠ ⁠Emily’s presentation: https://emilyriehl.github.io/files/undergraduates-TOE.pdf •⁠ ⁠A Type Theory For Synthetic ∞-Categories (paper): https://arxiv.org/pdf/1705.07442 •⁠ ⁠Could ∞-Category Theory Be Taught To Undergraduates? (paper): https://arxiv.org/pdf/2302.07855 •⁠ ⁠RZK proof assistant: https://rzk-lang.github.io/rzk/en/latest/ •⁠ ⁠Lean Zulip chat: https://leanprover.zulipchat.com/#recentnews Timestamps: 00:00 A Dream for the Future 01:55 Exploring Infinity Categories 03:54 The Role of Category Theory 10:17 Key Concepts of Category Theory 12:01 The Curry-Howard Correspondence 15:37 Understanding Left Adjoint Functors 24:38 The Innate Lemma Explained 38:29 Proving the Isomorphism 41:50 The Importance of Abstraction 44:04 A Crash Course in Category Theory 44:17 Introduction to Infinity Category Theory 56:27 Fundamental Infinity Groupoids 1:03:34 What Are Infinity Categories? 1:09:12 The Case for Infinity Categories 1:18:12 Transitioning to Homotopy Type Theory 1:22:49 Crash Course in Homotopy Type Theory 1:30:56 Type Constructors Explained 1:34:19 Propositions as Types 1:42:50 Understanding Dependent Types 1:49:01 Identity Types and Their Importance 1:54:03 The Structure of Infinity Groupoids 1:59:33 Hierarchies of Types 2:06:19 The Univalence Axiom 2:08:36 Transitioning to Infinity Category Theory 2:10:04 Simplicial Type Theory Overview 2:14:56 Pre-Infinity Categories Defined 2:24:32 Isomorphisms in Infinity Categories 2:31:48 Computer Formalization in Mathematics 2:40:02 Conclusion and Future Directions Support TOE on Patreon: https://patreon.com/curtjaimungal Twitter: https://twitter.com/TOEwithCurt Discord Invite: https://discord.com/invite/kBcnfNVwqs #science 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