There’s a genuine surge of AI-assisted activity across the remaining Millennium Problems right now, most concentrated in the last few weeks of August–September 2026.

Here’s where each stands.
Riemann Hypothesis
The biggest concrete movement is here. An unreleased research version of Anthropic’s Claude improved the long-standing lower bound on the fraction of non-trivial zeta zeros lying on the critical line from 41.6% to 67.2%, by creatively combining prior results from Aryan, Baluyot–Goldston–Suriajaya–Turnage-Butterbaugh, and Bombieri after running roughly 60 subagents for a day and a half on 31 million output tokens. Mathematicians Levent Alpöge and Ralph Furman at Anthropic validated the result but found it genuinely hard to follow, and within weeks independent human mathematician Youness Lamzouri published a simpler, non-AI proof of the same bound, while others pushed a related prime-gap bound down from 246 to 240 and then to 212 using a system called Axiom Math. Despite this, most working number theorists remain pessimistic about the core hypothesis itself — Rutgers’s Alex Kontorovich says “nothing is happening, and I don’t really expect anything to happen,” and Oxford’s James Maynard (co-author of the biggest recent human breakthrough tightening the zero-free region) says he doesn’t see his own work as the right direction for actually proving RH.

P vs NP
This remains the least touched by the current AI wave — expert consensus still leans toward P ≠ NP, but there is “very little progress toward a proof,” and it was highlighted in Harvard’s ongoing Millennium lecture series (Madhu Sudan spoke on it in December 2025) as an active but stalled research area. No major AI-driven breakthrough has been reported here as of September 2026.

Yang–Mills Existence and Mass Gap
Quiet but steady non-AI progress: rigorous constructions already exist in lower dimensions, and probabilistic/stochastic-analysis techniques are slowly being extended toward the full four-dimensional case, which some observers rank alongside Navier–Stokes as the “most likely candidate” for the next problem to fall within a decade. Sourav Chatterjee (Stanford) presented on this exact topic in Harvard’s lecture series in October 2025.

Birch and Swinnerton-Dyer, and the Hodge Conjecture
These two have seen the least visible reinvigoration in the current AI-driven wave — no major 2026 breakthroughs surfaced in current reporting, and they continue to be characterized simply as unsolved, alongside P vs NP and Yang-Mills, in the general roundups of Millennium Problem status.

The Bigger Pattern: AI Labs Racing on Open Problems
Beyond Riemann specifically, OpenAI has said its new model “GPT-6 Astra” generated new results or “substantial progress” on multiple decades-old open math and theoretical CS problems, and a broader benchmarking study found that of ten selected hard open problems, AI systems produced essentially flawless or near-flawless solutions on seven of them, at compute costs of only tens to hundreds of dollars per problem. This context is exactly why the Navier–Stokes claim landed the way it did — it’s part of a visible pattern of frontier labs (OpenAI, Anthropic, and startups like Axiom Math) explicitly aiming AI systems at the Clay Institute’s problem list, though as with Navier–Stokes, most of these results (aside from the well-vetted incremental Riemann bound) still await independent mathematical community verification before they count as settled.