OpenAI submits AI-generated counterexample for a Navier–Stokes singularity

OpenAI has submitted a proof built around a specific counterexample to the Navier–Stokes equations: a physically meaningful initial flow that evolves toward a point with infinite velocity. The proof still requires expert review, which could take years, and may prove incorrect or require substantial revision.

If validated, the result would place a mathematical limit on the equations’ applicability. It could also become an additional diagnostic check when a computational fluid-dynamics simulation fails to converge, although its practical relevance to real-world flows is currently considered limited.

The submitted PDF was described as entirely AI-generated and as lacking an elegant, human-style construction. The assessment distinguishes obtaining a potentially correct proof from understanding it, suggesting that AI could produce valid mathematical results before humans understand how they work.