Will AI produce a proof of finite-time blow-up for the unforced Navier–Stokes equations before 2027?
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Atrasado9/09/26, 19:42 UTC31/12/26, 23:59 UTC
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Title: Will AI produce a proof of finite-time blow-up for the unforced Navier–Stokes equations before 2027?
- Description:
- On September 8, 2026, OpenAI announced an AI-generated, Lean-verified proof that the 3D incompressible Navier–Stokes equations can develop a finite-time singularity from smooth initial data under a smooth external force.
- That construction addresses options C and D of the Clay Institute's official problem statement, which permit a smooth forcing term satisfying specified decay conditions; Clay has said the problem is "apparently settled" pending its review.
- This market is about a different and still-open question: the unforced equations (f ≡ 0).
- No external force is available to drive the singularity, and mathematicians have identified concrete obstacles to removing the force from the current construction.
