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"OpenAI has solved the Navier-Stokes Millennium problem using $15m of AI effort" https://www.newscientist.com/article/2588063-openai-has-solved-the-navier-stoke

"OpenAI has solved the Navier-Stokes Millennium problem using $15m of AI effort" https://www.newscientist.com/article/2588063-openai-has-solved-the-navier-stokes-millennium-problem-using-15m-of-ai-effort/ https://www.newscientist.com/article/2588063-openai-has-solv... $15m in tokens; but what about labor? What about compressible fluids?

westurner 7d ago
"Blowup for the Euler equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/euler.pdf https://cims.nyu.edu/~tristanb/euler.pdf "Blowup for the Boussinesq equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/boussinesq.pdf https://cims.nyu.edu/~tristanb/boussinesq.pdf "Extending the Córdoba–Martínez-Zoroa IPM Blow-Up to Uniformly Spacetime Smooth Forcing" (2026) https://cims.nyu.edu/~tristanb/ipm.pdf https://cims.nyu.edu/~tristanb/ipm.pdf "Finite Time Blowup for the Euler equation" (2026) https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194ece1/euler.pdf https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194e... Lean proof: openai/NavierStokesAndEuler: https://github.com/openai/NavierStokesAndEuler https://github.com/openai/NavierStokesAndEuler
- westurner 7d ago
  Is everything in NavierStokesAndEuler/NavierStokes [1] precedent to the derivations? How to tree shake Lean4? (Edit: `lake shake`,) [1] https://github.com/openai/NavierStokesAndEuler/tree/main/NavierStokes https://github.com/openai/NavierStokesAndEuler/tree/main/Nav...
  - westurner 7d ago
    (I am again posting this comment, which was certainly censored in error: https://news.ycombinator.com/item?id=49605915#49633297 https://news.ycombinator.com/item?id=49605915#49633297 ) What about compressible fluids? Existing Navier-Stokes models for compressible fluids: "On the implosion of a compressible fluid II: Singularity formation" (2022) https://projecteuclid.org/journals/annals-of-mathematics/vol https://projecteuclid.org/journals/annals-of-mathematics/vol... "Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases" (2025) https://arxiv.org/html/2501.15701v2 https://arxiv.org/html/2501.15701v2 ... From https://news.ycombinator.com/item?id=49389524#49404787 https://news.ycombinator.com/item?id=49389524#49404787: > "I/Q Sampling for Signal Phase" (2026-08) https://share.gemini.google/rDVcVwDnWPTc https://share.gemini.google/rDVcVwDnWPTc : >> It's a Twistor-Grassmanian mapping? From "Navier-Stokes Breakthrough, FTLE, and SQG" (2026-09) https://share.gemini.google/sq2XmhphMFWE https://share.gemini.google/sq2XmhphMFWE : > The Mathematical Formulation: Because SQS is explicitly a superfluid Bose–Einstein condensate, treating it purely as a classical Navier–Stokes fluid misses quantized vorticity. The full formulation maps to the Gross–Pitaevskii (Euler–Korteweg) equations via the Madelung transformation ... > To adapt the Córdoba–Martínez-Zoroa (CMZ) / Buckmaster / OpenAI Lean cascade to Euler–Korteweg, three core structural adjustments must be made: > - Irrotationality Constraint > - Third-Order Dispersion > - Hydrodynamic Energy Functional
westurner 7d ago
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westurner 7d ago

"Blowup for the Euler equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/euler.pdf https://cims.nyu.edu/~tristanb/euler.pdf "Blowup for the Boussinesq equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/boussinesq.pdf https://cims.nyu.edu/~tristanb/boussinesq.pdf "Extending the Córdoba–Martínez-Zoroa IPM Blow-Up to Uniformly Spacetime Smooth Forcing" (2026) https://cims.nyu.edu/~tristanb/ipm.pdf https://cims.nyu.edu/~tristanb/ipm.pdf "Finite Time Blowup for the Euler equation" (2026) https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194ece1/euler.pdf https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194e... Lean proof: openai/NavierStokesAndEuler: https://github.com/openai/NavierStokesAndEuler https://github.com/openai/NavierStokesAndEuler

westurner 7d ago
Is everything in NavierStokesAndEuler/NavierStokes [1] precedent to the derivations? How to tree shake Lean4? (Edit: `lake shake`,) [1] https://github.com/openai/NavierStokesAndEuler/tree/main/NavierStokes https://github.com/openai/NavierStokesAndEuler/tree/main/Nav...
- westurner 7d ago
  (I am again posting this comment, which was certainly censored in error: https://news.ycombinator.com/item?id=49605915#49633297 https://news.ycombinator.com/item?id=49605915#49633297 ) What about compressible fluids? Existing Navier-Stokes models for compressible fluids: "On the implosion of a compressible fluid II: Singularity formation" (2022) https://projecteuclid.org/journals/annals-of-mathematics/vol https://projecteuclid.org/journals/annals-of-mathematics/vol... "Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases" (2025) https://arxiv.org/html/2501.15701v2 https://arxiv.org/html/2501.15701v2 ... From https://news.ycombinator.com/item?id=49389524#49404787 https://news.ycombinator.com/item?id=49389524#49404787: > "I/Q Sampling for Signal Phase" (2026-08) https://share.gemini.google/rDVcVwDnWPTc https://share.gemini.google/rDVcVwDnWPTc : >> It's a Twistor-Grassmanian mapping? From "Navier-Stokes Breakthrough, FTLE, and SQG" (2026-09) https://share.gemini.google/sq2XmhphMFWE https://share.gemini.google/sq2XmhphMFWE : > The Mathematical Formulation: Because SQS is explicitly a superfluid Bose–Einstein condensate, treating it purely as a classical Navier–Stokes fluid misses quantized vorticity. The full formulation maps to the Gross–Pitaevskii (Euler–Korteweg) equations via the Madelung transformation ... > To adapt the Córdoba–Martínez-Zoroa (CMZ) / Buckmaster / OpenAI Lean cascade to Euler–Korteweg, three core structural adjustments must be made: > - Irrotationality Constraint > - Third-Order Dispersion > - Hydrodynamic Energy Functional

westurner 7d ago

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