Episode Details

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Math has a proof checker. Can physics get one? Jonathan Gorard, an applied mathematician and the cofounder and CEO of Lanyon AI, joins to explain why AI took off in math and coding but not yet in physics. We discuss an AI finishing the formal check of a Fields Medal proof and why it scared him, why he thinks “I detected a particle” rests on 20 to 50 levels of theory, and what Alan Turing’s PhD student Robin Gandy tried to build for physics. The conversation also covers his push to make physics executable, why he thinks mysteries are artifacts of description languages, and whether there is still a place for the physicist.

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TIMESTAMPS:
- 00:00 - The Sphere Packing Shock
- 05:53 - Science as Product vs Process
- 11:20 - Is Science Just Hedonism?
- 20:56 - Why Academics Ignored AI
- 31:54 - Why Leave Princeton?
- 39:56 - Turing's Student and Physics Formalization
- 44:56 - Theory-Ladenness of Observation
- 50:22 - Why Math Isn't Enough
- 58:19 - Sapir-Whorf for AI
- 01:05:49 - Filtering the Paper Deluge
- 01:12:07 - Can AI Transmit Understanding?
- 01:19:38 - Human-Readable AI Reasoning
- 01:25:59 - Must AI Be Embodied?
- 01:31:50 - Mysteries Are Description Language Artifacts
- 01:41:54 - Grieving Physics
- 01:49:59 - What's Left for Physicists?
- 01:55:18 - The Next Description Language
- 02:02:26 - Spacetime Discreteness and Beacons

LINKS:
- Jonathan Gorard [Wolfram Physics Project]: https://www.wolframphysics.org/pages/people/jonathan-gorard/
- Lanyon AI: https://www.lanyon.ai/
- Lanyon AI Founding Team: https://www.lanyon.ai/company/
- Shock with Confidence: Formal Proofs of Correctness for Hyperbolic PDE Solvers [Paper]: https://arxiv.org/abs/2503.13877
- BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for PDEs [Paper]: https://arxiv.org/pdf/2602.14853
- General Relativistic Hydrodynamics in Discrete Spacetime [Paper]: https://arxiv.org/pdf/2402.02331
- The Empirical Metamathematics of Euclid and Beyond [Paper]: https://arxiv.org/pdf/2107.07337v1
- Math Inc. Sphere Packing Announcement: https://www.math.inc/sphere-packing
- The Sphere Packing Problem in Dimension 8 [Paper]: https://arxiv.org/pdf/1603.04246
- Progress in Formalizing Sphere Packing in Dimension 8 [Paper]: https://arxiv.org/pdf/2604.23468
- On Axiomatic Systems in Mathematics and Theories in Physics [Paper]: https://www.cs.ox.ac.uk/people/ohad.kammar/scans/gandy-thesis-ocr.pdf
- Hilbert's Sixth Problem: Axioms of Physics [Paper]: https://people.reed.edu/~davidp/341/resources/hilbert.pdf
- Hilbert's Program [SEP]: https://plato.stanford.edu/entries/hilbert-program/
- On Computable Numbers [Paper]: https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
- Lean Proof Assistant [Wikipedia]: https://en.wikipedia.org/wiki/Lean_(proof_assistant)
- The Lean Mathematical Library [Paper]: https://leanprover-community.github.io/papers/mathlib-paper.pdf

Full reading list for this episode (all 114 sources): https://curtjaimungal.com

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