Episode 74 · The Machine's Theorems
Chasing the Singularity: Computers, Swirls and Forcing
Farah and Augustin follow the race to a singularity: Luo–Hou's boundary blowup and Chen–Hou's computer-assisted proof, the 2025 'Discovery of Unstable Singularities', Ganeshram–Duruisseaux–Anandkumar, then amplification across scales and the Alpöge–Buckmaster forced blowups for IPM, Boussinesq and Euler (Lean-formalised, not peer-reviewed). Euler is not a Clay problem. Keywords: Navier-Stokes, Euler, blowup, singularity, Luo-Hou, Chen-Hou, PINNs, computer-assisted proof, Córdoba, Martínez-Zoroa, Alpöge, Buckmaster, Beale-Kato-Majda, Lean
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Inside this episode
- Cold open: two papers in one weekend
- What a singularity would look like
- Road one: the shape that repeats as it shrinks
- Turning a photograph into a proof
- Neural networks go hunting
- The seventh of September: a candidate in open space
- Road two: the builders and the smooth push
- Alpöge and Buckmaster: Euler with a perfectly smooth push
- How it was made, and what Buckmaster said
- Tao's reading: remarkable, and not the point
- Why it matters, and the ledger
Production credits & AI disclosure
Scripts generated with Claude Opus. Synthetic narration generated with Edge TTS. Reviewed, listened to, and approved by Sankalp Thakur.