Experts say OpenAI’s final swarm took a different route from the Spanish mathematicians’ program

On October 13, 2026, Scientific American reported that expert groups examining OpenAI’s proposed Navier–Stokes proof increasingly regarded the method used by its final, large agent swarm as distinct from the Spanish mathematicians’ program. Separately, a technical paper identifies a mismatch between a statement in OpenAI’s written paper and the Lean estimate examined by its authors.

The final swarm and the Spanish program

The approaches share a broad strategy: both use a specially constructed, unphysical force of the kind allowed by the Clay Mathematics Institute’s problem formulation. The experts interviewed by Scientific American described the force as being built differently in the final swarm’s approach and the Spanish program. Some experts said a smaller preliminary group may have followed the Spanish program for an intermediate result. They could not determine the model’s exact chain of reasoning, leaving possible influence unresolved. (Scientific American’s October 13 report)

What Lean checks—and what translation adds

Lean is a proof assistant: it checks whether a proof meets the formal statement encoded in its code. Whether that formal statement faithfully represents the mathematics in a natural-language paper is a separate question.

In a paper published October 6, 2026, A. Bastounis, F. Circelli and A. C. Hansen compare OpenAI’s written proof with its Lean formalization. Their clearest example is Lemma 8.6: the natural-language statement uses a bound with four additional input derivatives, while the Lean estimate they examine uses five. (Their technical paper)

The difference is in an intermediate estimate. The authors describe the Lean result as weaker than the natural-language result, but do not conclude that OpenAI’s natural-language proof is false. They also discuss the pressure-flux bound in equation (10.19): the two versions use different terms and assumptions, and the authors say they are difficult to compare directly.

What OpenAI says its result establishes

OpenAI announced its proposed result on September 8, 2026. The company says its proof establishes statements C and D in the Clay Mathematics Institute’s formulation. OpenAI describes a three-dimensional incompressible fluid, initially smooth and at rest, acted on by a smooth external force; it says the fluid develops a finite-time singularity while its energy remains finite. (OpenAI’s announcement)

That is the scope of OpenAI’s announced claim: a blowup result for a forced formulation of the problem.