Theories of Everything with Curt Jaimungal

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This is a podcast about quantum field theory as a mathematician sees it, and about mathematics after AI. Dan Freed, a Harvard mathematician who directs its Center of Mathematical Sciences and Applications, joins to explain why, with quantum field theory, “you never see the whole elephant.” We discuss why quantum mechanics is projective, when an anomaly is a feature rather than a bug, and how Witten’s Chern-Simons talk reportedly took shape overnight after a pub dinner with Atiyah and Segal. The conversation also covers what makes dimension four so strange, the 475 AI-written math papers, whether mathematicians should mourn the old way of working, and what Isadore Singer taught Dan about the freedom to err. I hope you enjoy.

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TIMESTAMPS:
- 00:00 - Living With Confusion
- 07:37 - Can AI Crack Yang-Mills?
- 16:49 - Mourning the Mathematician
- 21:52 - What Is QFT, Really?
- 29:46 - Quantum Mechanics Is Projective
- 36:51 - Determinant Line Bundles
- 46:52 - Anomalies: Feature, Not Bug
- 52:00 - Non-Invertible Symmetries: An Oxymoron?
- 1:01:07 - Classical vs Quantum Theories
- 1:07:31 - Witten's Chern-Simons Breakthrough
- 1:15:52 - Exotic R4 and Spacetime
- 1:21:11 - Why Chalkboards Beat Slides
- 1:29:05 - Can Quantization Be a Functor?
- 1:35:30 - Witten vs Reshetikhin-Turaev
- 1:45:25 - The Freedom to Err
- 1:52:32 - Instantons, Defects, New Research
- 1:58:26 - Hopeful and Scared of AI

LINKS:
- Dan Freed's Home Page [Website]: https://people.math.harvard.edu/~dafr/
- Dan Freed's Papers (Google Scholar): https://scholar.google.com/citations?user=8xW9d5IAAAAJ
- Dan Freed's Papers on arXiv: https://arxiv.org/search/?searchtype=author&query=Freed%2C+Daniel+S
- Instantons and Four-Manifolds [Book]: https://amazon.com/dp/038797377X?tag=toe08-20
- On Determinant Line Bundles [Paper]: https://web.ma.utexas.edu/users/dafr/detsur.pdf
- The Analysis of Elliptic Families I: Determinant Bundles [Paper]: https://projecteuclid.org/euclid.cmp/1104115586
- Remarks on Chern-Simons Theory [Paper]: https://arxiv.org/abs/0808.2507
- What Is an Anomaly? [Paper]: https://arxiv.org/abs/2307.08147
- Anomalies and Invertible Field Theories [Paper]: https://arxiv.org/abs/1404.7224
- Reflection Positivity and Invertible Topological Phases [Paper]: https://arxiv.org/abs/1604.06527
- Topological Symmetry in Quantum Field Theory [Paper]: https://arxiv.org/abs/2209.07471
- Fully Local Reshetikhin-Turaev Theories [Paper]: https://arxiv.org/abs/2601.05518
- Higher Algebraic Structures and Quantization [Paper]: https://arxiv.org/abs/hep-th/9212115
- Hirosi Ooguri [TOE]: https://youtu.be/jCutz701TGo
- Jacob Tsimerman [TOE]: https://youtu.be/6uIJdXmB4vE
- Olaf Dreyer [TOE]: https://youtu.be/FNTUNsmXuLI

Full reading list for this episode (all 87 sources): https://curtjaimungal.com

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This episode is about mathematics in the age of AI. Richard Borcherds, a Fields Medalist and professor of mathematics at UC Berkeley, and Eric Weinstein, who earned his PhD in mathematics at Harvard, join to take up three questions. What is mathematics about, what is the future for math students, and what is at stake? We discuss whether AI can build theories or only solve problems, why pure mathematics is worth funding, and what is left for human mathematicians. The conversation also covers the sporadic groups, whether math will go the way of chess, and who deserves credit if a stranger with an AI proves the Riemann hypothesis.

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TIMESTAMPS:
- 00:00 - Has AI Conquered Math?
- 07:14 - Six-Sphere and Exotic Spheres
- 12:49 - Secrecy, Credit, and Purity
- 19:46 - Why Fund Pure Math?
- 31:45 - Octonions and Exceptional Lie Groups
- 42:00 - Calculation Without Understanding?
- 48:24 - "AI Is Better Than Me"
- 54:03 - The Chess Precedent
- 1:02:08 - "You Do Not Know Your Value"
- 1:09:39 - Math as a Public Good
- 1:15:15 - What Is Math About?
- 1:23:33 - The Human Moat
- 1:30:01 - Feynman's Hidden Calculations
- 1:39:19 - What's Truly at Stake?
- 1:50:07 - Who Gets Credit Now?
- 1:54:15 - What Is a Spinor?

LINKS:
- Richard Borcherds' Papers: https://scholar.google.com/citations?user=k8VB8MYAAAAJ
- Geometric Unity: A First Look [Lecture]: https://youtu.be/Z7rd04KzLcg
- Extension of Self-Dual Yang-Mills Equations Across the Eighth Dimension [Thesis]: https://www.proquest.com/docview/303973536
- Monstrous Moonshine and Monstrous Lie Superalgebras [Paper]: https://link.springer.com/article/10.1007/BF01232032
- Generalized Kac-Moody Algebras [Paper]: https://math.berkeley.edu/~reb/papers/gkma/gkma.pdf
- What Is the Monster? [Paper]: https://arxiv.org/abs/math/0209328
- Renormalization and Quantum Field Theory [Paper]: https://arxiv.org/abs/1008.0129
- Eric Weinstein [X]: https://x.com/EricRWeinstein
- The Edge of Everything [Book]: https://substack.com/@curtjaimungal/note/c-206576916
- Sharing AI Progress in Mathematics [Article]: https://openai.com/index/sharing-ai-progress-in-mathematics/
- AI Solves 79-Year-Old Six-Dimensional Sphere Mystery [Article]: https://www.scientificamerican.com/article/ai-solves-79-year-old-math-mystery-of-six-dimensional-spheres/
- Scott Aaronson [TOE]: https://youtu.be/3yXtXTwz4J4
- Mikhail Gromov [TOE]: coming soon
- Dan Freed [TOE]: https://youtu.be/3jntzMm_SBs

Full reading list for this episode (all 88 sources): https://curtjaimungal.com

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This episode is about where consciousness begins. Mark Solms, neuropsychologist and psychoanalyst at the University of Cape Town, joins to explain why he thinks it begins not in the cortex but in raw feeling from the upper brainstem. We discuss patients who lost REM sleep but kept dreaming, what that means for Freud’s wish theory, and children born without a cortex who still giggle and startle. He argues the hard problem was tackled from the wrong end, starting with visual perception instead of feeling. The conversation also covers dual-aspect monism, Markov blankets and the free energy principle, his attempt to engineer an artificial agent that feels, and why he thinks that at death the second law wins.

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TIMESTAMPS:
- 00:00 - What Is Consciousness?
- 07:00 - Why Would We Self-Sacrifice?
- 15:37 - The Beggar: Care vs Rage
- 22:33 - What Is Neuropsychoanalysis?
- 31:15 - Why Do We Dream?
- 45:42 - Affect, Sentience, Consciousness
- 51:57 - Can You Betray Your Feelings?
- 56:58 - Hidden Motives and Willpower
- 01:04:28 - Hard Problem: Wrong Starting Point
- 01:14:44 - Children Born Without Cortex
- 01:21:21 - Dual-Aspect Monism
- 01:34:22 - Against Corticocentrism
- 01:39:58 - Death and the Second Law

LINKS:
- Mark's Papers: https://scholar.google.com/citations?user=vD4p8rQAAAAJ
- Mark's Books: https://www.amazon.com/stores/author/B001K8A6FA/allbooks?_encoding=UTF8&pd_rd_w=ci3uq&content-id=amzn1.sym.7e190e19-9f6f-4df8-807a-5a7608594741&pf_rd_p=7e190e19-9f6f-4df8-807a-5a7608594741&pf_rd_r=134-0336993-4380237&pd_rd_wg=QOJv5&pd_rd_r=9aa4ed5b-7598-43aa-ab31-3a27213a55fe
- Mark's Twitter: https://x.com/Mark_Solms
- The Hidden Spring [Book]: https://amazon.com/dp/1324021918?tag=toe08-20
- The Only Cure [Book]: https://amazon.com/dp/B0FWZXMHF1?tag=toe08-20
- The Brain and the Inner World [Book]: https://amazon.com/dp/1855759829?tag=toe08-20
- The Neuropsychology of Dreams [Book]: https://amazon.com/dp/1138989584?tag=toe08-20
- The Hard Problem of Consciousness and the Free Energy Principle [Paper]: https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2018.02714/full
- Inferring Affective Consciousness in an Artificial Agent [Paper]: https://arxiv.org/abs/2609.03883
- How and Why Consciousness Arises [Paper]: https://discovery.ucl.ac.uk/id/eprint/10057681/
- Dreaming and REM Sleep Are Controlled by Different Brain Mechanisms [Paper]: https://pubmed.ncbi.nlm.nih.gov/11515144/
- Mark Solms [Bio]: https://neubauercollegium.uchicago.edu/people/mark-solms
- Mark Solms, University of Cape Town [Website]: https://humanities.uct.ac.za/department-psychology/contacts/mark-solms
- A Neuropsychoanalytic Perspective on the Hard Problem [Lecture]: https://youtu.be/r6J8pFHY2Fc
- Why and How Consciousness Arises [Lecture]: https://youtu.be/F7WF5gzPG1k

Full reading list for this episode (all 72 sources): https://curtjaimungal.com

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This episode is about math after AI started solving its open problems. Scott Aaronson, director of the Quantum Information Center at UT Austin, joins to explain why there is no making this go away. We discuss who gets credit for AI proofs, what is left for PhD students, and OpenAI’s apparent proof of the unique games conjecture. His wife, the complexity theorist Dana Moshkovitz, has worked on that conjecture since they met. The conversation also covers whether a lab that proved P equals NP should release it, and how AI overturned a conjecture he and Greg Kuperberg posed, with consequences for black hole firewalls. We end with Maxwell’s demon and why he thinks integrated information theory is wrong.

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TIMESTAMPS:
- 00:00 - AI Solved the Unique Games Conjecture
- 06:01 - Is Math About Understanding?
- 14:26 - OpenAI vs. Anthropic Disclosure
- 21:21 - Who Gets Credit for AI Proofs?
- 26:46 - Mourning the Mathematician
- 35:39 - The AI Denialism Problem
- 41:31 - Association for Human Mathematics
- 47:24 - If AI Proves P = NP
- 52:53 - Is Physics Next?
- 58:51 - Unitary Synthesis Problem Solved
- 01:04:30 - Black Hole Firewalls & P vs PSPACE
- 01:15:41 - Maxwell's Demon & Pseudo-Entropy
- 01:22:32 - Why IIT Is Wrong

LINKS:
- The Mathocalypse [Article]: https://scottaaronson.blog/?p=10169
- The Mathocalypse, Comment #115 [Article]: https://scottaaronson.blog/?p=10169#comment-2041220
- P =? NP [Paper]: https://www.scottaaronson.com/papers/pnp.pdf
- Quantum Versus Classical Proofs and Advice [Paper]: https://arxiv.org/abs/quant-ph/0604056
- Quantum Computation vs. Firewalls [Paper]: https://arxiv.org/abs/1301.4504
- Limits on Efficient Computation in the Physical World [Paper]: https://arxiv.org/abs/quant-ph/0412143
- Talk at Columbia University [Article]: https://scottaaronson.blog/?p=9243
- Computational Complexity and Explanations in Physics [Lecture]: https://youtu.be/GcbLL4C3VwY
- Why I Am Not an Integrated Information Theorist [Article]: https://scottaaronson.blog/?p=1799
- Giulio Tononi and Me: A Phi-nal Exchange [Article]: https://scottaaronson.blog/?p=1823
- Dispatches From the Possibly Last Days of Human Relevance [Article]: https://scottaaronson.blog/?p=9782
- The Age of Wonders and Terrors [Article]: https://scottaaronson.blog/?p=10062
- Ten Signs a Claimed Mathematical Breakthrough Is Wrong [Article]: https://scottaaronson.blog/?p=304
- AI Alignment Theory Course at UT Austin [Article]: https://scottaaronson.blog/?p=10125
- Dana Moshkovitz [Website]: https://www.cs.utexas.edu/~danama/
- The Unique Games Theorem [Paper]: https://github.com/openai/math/blob/main/preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf
- Dan Freed [TOE]: https://youtu.be/3jntzMm_SBs

Full reading list for this episode (all 58 sources): https://curtjaimungal.com

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This is a podcast about whether AI could discover the laws of physics before we do. Hirosi Ooguri, chair of Caltech’s Division of Physics, Mathematics and Astronomy, joins for his first English podcast to explain why AI has moved faster in mathematics than in physics. He fears it could solve physics in a way we cannot understand. We discuss why quantum field theory lacks a firm mathematical foundation, quantum gravity as the “final boss,” the swampland distance conjecture he proposed with Cumrun Vafa, and his estimate that, left to humans, verifying string theory could take 2,250 years. The conversation also covers the PhD thesis numbers that turned up in a Mathieu group table twenty years later. What an honor.

FOLLOW:
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TIMESTAMPS:
- 00:00 - Measuring Earth in Fifth Grade
- 06:58 - Why Physics, Not Platonic Math?
- 12:34 - Nothing Below the Planck Length?
- 23:15 - Why AI Can't Verify Physics
- 30:47 - Yang-Mills: Hardest Millennium Problem
- 36:31 - Why QFT Resists Rigor
- 46:19 - What If Yang-Mills Fails?
- 52:35 - Are LLMs Just Grad Students?
- 01:01:09 - Swampland and AdS/CFT
- 01:12:57 - Gravity Breaks Wilson's Paradigm
- 01:21:45 - Will AI Surpass Physicists?
- 01:26:58 - 2,250 Years to Verify Strings?
- 01:34:03 - Is String Theory Disappointing?
- 01:40:27 - Distance Conjecture and Inflation
- 01:46:24 - Mathieu Moonshine Discovery
- 01:52:59 - What Would Make Him Quit Strings?
- 02:02:28 - Days of Blank Paper

LINKS:
- Hirosi Ooguri [Caltech PMA]: https://www.pma.caltech.edu/people/hiroshi-hirosi-ooguri-oguri
- On the Geometry of the String Landscape and the Swampland, Ooguri & Vafa [Paper]: https://arxiv.org/abs/hep-th/0605264
- Non-Supersymmetric AdS and the Swampland, Ooguri & Vafa [Paper]: https://arxiv.org/abs/1610.01533
- Constraints on Symmetry From Holography, Harlow & Ooguri [Paper]: https://arxiv.org/abs/1810.05337
- Continuous Family of CFTs and Exactly Marginal Operators, Komatsu et al. [Paper]: https://arxiv.org/abs/2512.11045
- Universal Bounds on CFT Distance Conjecture, Ooguri & Wang [Paper]: https://arxiv.org/abs/2405.00674
- Notes on the K3 Surface and the Mathieu Group M24, Eguchi, Ooguri & Tachikawa [Paper]: https://arxiv.org/abs/1004.0956
- Exploring the Holographic Entropy Cone via Reinforcement Learning, He, Lee & Ooguri [Paper]: https://arxiv.org/abs/2601.19979
- The Holographic Entropy Cone, Bao et al. [Paper]: https://arxiv.org/abs/1505.07839
- De Sitter Space and the Swampland, Obied et al. [Paper]: https://arxiv.org/abs/1806.08362
- Knot Invariants and Topological Strings, Ooguri & Vafa [Paper]: https://arxiv.org/abs/hep-th/9912123
- Topological Lattice Models in Four Dimensions, Ooguri [Paper]: https://arxiv.org/abs/hep-th/9205090
- Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes [Paper]: https://arxiv.org/abs/hep-th/9309140

Full reading list for this episode (all 103 sources): https://curtjaimungal.com

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