"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?
$15m in tokens; but what about labor?
What about compressible fluids?
"Blowup for the Boussinesq equations with smooth forcing" (2026) 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
"Finite Time Blowup for the Euler equation" (2026) https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194e...
Lean proof: openai/NavierStokesAndEuler: https://github.com/openai/NavierStokesAndEuler
How to tree shake Lean4? (Edit: `lake shake`,)
[1] https://github.com/openai/NavierStokesAndEuler/tree/main/Nav...
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...
"Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases" (2025) https://arxiv.org/html/2501.15701v2
...
From https://news.ycombinator.com/item?id=49389524#49404787:
> "I/Q Sampling for Signal Phase" (2026-08) 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 :
> 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