In September, OpenAI announced that AI-assisted work had produced a result concerning finite-time singularity formation for the Navier–Stokes equations, which model fluid motion. A crucial detail for interpreting the claim is that the construction uses an external force.
Forced and unforced questions
The Clay Mathematics Institute’s official problem statement includes an option that allows external forcing. OpenAI’s announced construction addresses that kind of case. Whether a singularity can form from smooth initial data without an external force remains a separate question. A claimed proof for one formulation does not automatically resolve the other.
In a subsequent preprint, Peter Constantin, Mihaela Ignatova and Vlad Vicol analyze specific properties of the OpenAI construction. Under their stated assumptions, they find that the force cannot vanish near the singular point. The authors explicitly say they have not verified the correctness of the original construction.
Review and the prize
The preprint does not rule out every possible path to an unforced result; it concerns a particular class of constructions. Both the original result and subsequent analysis remain matters for mathematical scrutiny. Without a verified official decision, neither prize award nor final acceptance should be assumed.
