A Lean-verified proof can still prove the wrong theorem: scrutinizing OpenAI's Navier-Stokes claim
MasterWitcher69 · reddit · 2026-09-19
A Reddit breakdown of why "Lean checked it" doesn't mean OpenAI's Navier-Stokes result settles the Clay Millennium Problem. OpenAI claims its system constructed a smooth 3D fluid, starting at rest under a smooth external force, that develops a singularity in finite time, with a Lean-formalized proof. But Lean only verifies that a conclusion follows from the encoded definitions — someone must still confirm those definitions match the original Clay problem.
The author fed OpenAI's write-up and the Clay problem statement to a tool called Apodex to map each official requirement (initial conditions, forcing, energy bounds, singularity) to the result. Both extremes look wrong: "officially solved" overclaims, but "external forcing disqualifies it" may too, since the official formulation permits smooth forcing under specified conditions.
Clay's prize rules require publication in a qualifying outlet, a two-year waiting period, and general acceptance by the math community. The open question: how do formal-proof practitioners verify the Lean theorem is the theorem humans intended?
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