In short
In short: on May 24, 2000, at the Collège de France in Paris, the Clay Mathematics Institute announced seven Millennium Prize Problems and a $7 million prize fund, $1 million for the solution of each. The problems are: the Birch and Swinnerton-Dyer conjecture, the Hodge conjecture, the Navier-Stokes equation, P vs NP, the Poincaré conjecture, the Riemann hypothesis, and Yang-Mills and the mass gap. Only Poincaré has a confirmed solution, proved by Grigori Perelman.
These aren't riddles for clever people with free time. Each one sits at the base of a whole branch of mathematics or physics. Navier-Stokes describes how fluids flow: water in the tap, air around a wing, blood in a vein. Engineers use the equations every day. For close to a century, though, nobody managed to prove whether their solutions always stay smooth or can break down at some point.
Why we're talking about them now
On September 8, 2026 OpenAI published a text claiming that one of its internal systems reached a solution to the Navier-Stokes problem: a proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity in finite time. The company says it won't claim the prize. The page doesn't cite any check by independent mathematicians or by the Clay institute.
A proof doesn't become true when it's announced. It becomes true when others fail to break it.
How to read a story like this
The measure is the checking. A Lean formalization is a strong signal, because a machine checks every step. Even then, someone has to check that it proves exactly what the problem asks. That's why a solution is accepted when mathematicians outside the team read it and agree, not on the day of the announcement. If you see a headline that AI solved a Millennium problem, look for who besides the author has checked it.
Primary sources
Clay Mathematics Institute: the Millennium ProblemsOpenAI: On the Navier-Stokes Millennium Prize ProblemThe visual is generated code-art, no third-party images.