Millennium Prize Problems

On October 6, 2026, OpenAI put 722 manuscripts from an unreleased internal model on GitHub, including a zero-free region for the Riemann zeta function and the rational Hodge conjecture for CM abelian varieties. None is independently confirmed, Lean documentation covers only 235 of 372 result families, and some mathematicians are asking for proof.

Among the 722 manuscripts in 372 result families is a claimed proof of the full Birch–Swinnerton-Dyer leading-term formula for elliptic curves over the rationals, under conditions on the corank of a q-power Selmer group. This is narrower than the full conjecture, and specialists have yet to check it independently.

Rongchang Liu, Kening Lu and Lin Shi prove a local Hartman–Grobman theorem at zero for the unforced 3D Navier–Stokes equation on the torus, conjugating its flow to the heat semigroup in H^s for s>7/2. It is a local result near zero and does not address the regularity or blow-up question itself.