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OpenAI Says AI Solved Navier–Stokes and Publishes Lean-Checked Proof

Verification will determine if the machine-produced, Lean-checked demonstration is mathematically sound by examining whether proprietary training data influenced the result.

Overview

  • OpenAI published a formal demonstration and a Lean-checked encoding after announcing that a nonpublic model produced an analytical solution to the Navier–Stokes existence and smoothness question.
  • The company said the result was found using a new internal model and roughly 10,000 autonomous agents in about 88 hours and added it will not claim the Clay Millennium Prize.
  • The Clay Mathematics Institute and independent experts have not accepted or independently verified the proof, so the mathematical community has not endorsed the claim.
  • Mathematicians Tristan Buckmaster and Levent Alpöge say they were working on similar results and allege information about their work reached OpenAI while OpenAI denies direct access to their materials.
  • News outlets estimate the compute effort cost roughly US$10 million, which raises questions about reproducibility and access when a claimed discovery depends on a proprietary, nonpublic model.