# Did OpenAI solve the wrong Navier-Stokes problem?

Digest AI · Research · published 2026-09-22T00:24:00Z

Canonical: https://digestai.news/story/did-openai-solve-the-wrong-navier-stokes-problem

## Summary

Two weeks ago OpenAI announced that an internal large language model had produced a proof that satisfies the Navier‑Stokes problem as defined by the Clay Mathematics Institute, a result that would earn the $1‑million prize. The proof relies on a formulation that includes an optional external force, a choice many mathematicians describe as unnatural and disconnected from the core question about blow‑up in force‑free fluids.

Luis Silvestre of the University of Chicago says the original Clay problem remains unsolved, and three mathematicians posted a proof last Thursday showing OpenAI’s approach cannot be extended to the full, force‑free version. Diego Córdoba notes that all known fluids experience some external force, while Luis Martínez‑Zoroa points out that most research focuses on the scenario without one. On September 7 two other mathematicians used AI to generate a blow‑up for a frictionless fluid, and OpenAI produced a similar result less than a day later. Gonzalo Cao‑Labor a says the situation is “really uncertain at this moment” and that the community’s view of OpenAI’s contribution will depend on how the external‑force loophole is judged.

## Key points

- openai’s LLM‑generated proof earned the $1‑million Clay prize but targets a variant with an external force.
- three mathematicians posted a proof last Thursday showing the method cannot extend to the full problem.
- on september 7 two mathematicians used AI to produce a blowup; openai completed a similar result less than a day later.

## Why it matters

The dispute highlights how AI can solve narrowly framed versions of famous math problems, prompting the community to reconsider what counts as genuine progress and how machine‑generated proofs are evaluated.

## Sources

1. [Did OpenAI solve the wrong Navier-Stokes problem?](https://scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem) (scientificamerican.com, 2026-09-22)

Part of the developing story: [OpenAI's Navier-Stokes Claim Sparks Debate](https://digestai.news/thread/openai-reportedly-close-to-solving-hodge-conjecture-its-second-millennium-prize) (2 stories)

## Cite

Digest AI, "Did OpenAI solve the wrong Navier-Stokes problem?", 22 September 2026, https://digestai.news/story/did-openai-solve-the-wrong-navier-stokes-problem

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