Did OpenAI solve the wrong Navier-Stokes problem?

OpenAI announced a claimed proof of a million‑dollar Navier‑Stokes blowup by generating a construction that produces finite‑time singularities, but the construction crucially uses an external forcing term permitted by one option in Charles Fefferman’s original Clay Institute formulation. The strategy builds on recent work by Diego Córdoba and Luis Martínez‑Zoroa, who developed a programmatic method to design a very specific force that triggers blowup; two other mathematicians then used that program plus AI to exhibit a blowup for a frictionless fluid and OpenAI completed a related construction within a day. Subsequent work by three mathematicians, however, proves that OpenAI’s approach fundamentally depends on that contrived external force and can never be extended to the unforced Navier‑Stokes equations that most fluid dynamicists consider the physically and mathematically meaningful case.

As a result, the Clay problem’s official wording may be satisfied while the central Navier‑Stokes question - whether intrinsic fluid dynamics alone can produce singularities - remains open. The episode exposes a “loophole” in problem formulation, sparks debate over whether external forcing should have been allowed, and highlights a shift in mathematical work: large language models are powerful at constructing explicit counterexamples but currently weaker at proving impossibility results. Mathematicians are rethinking problem statements and research tactics in light of AI’s ability to find exotic, nonphysical constructions.