rationale:

Overall Progress and Baseline The pace of AI mathematical capability has been extraordinary, advancing from almost zero to solving 90% of a leading research-problem benchmark and producing a wave of partial results on major conjectures in just 18 months. However, under the strict definitions of complete, expert-accepted resolution, no listed problem has yet been solved. Every Millennium-level output so far is partial, unrefereed, or withheld. With about 13 years left until the 2040 cutoff, it is highly likely that at least one resolution occurs, but verification bottlenecks, potential theoretical limits (such as statements being independent of standard axioms), and the stark qualitative gaps between partial and full statements warrant a 10% probability that none of these specific problems is completely resolved first. This balances those obstacles against the related timeline forecast , with Unforced 3D Navier–Stokes and Yang–Mills the strongest beneficiaries of the high probability of a resolution before 2040.

The Front-Runner: Unforced 3D Navier–Stokes Unforced 3D Navier–Stokes (29%) is the leading candidate because computational blowup searches fit agentic capabilities extremely well. Massive parallel search efforts—like the one that deployed 10,000 agents to find finite-time blowup for the forced equations (Clay statements C and D)—are already operational. The unforced statements A and B remain open, and forcing is a structural ingredient in the existing construction rather than a cosmetic assumption to delete https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf. Nonetheless, existing human-led Euler-blowup programs https://anima-ai.org/2026/09/07/stable-singularity-of-the-euler-equations-on-r3-without-forcing/ https://cims.nyu.edu/~tristanb/statement.pdf and the consensus that unforced blowup is now "very feasible" Finite time blowup with smooth forcing term for ... - Terence Tao make this the most natural target for an outright AI resolution.

The Second Tier: Riemann Hypothesis and Yang–Mills The Riemann Hypothesis (15%) and the Yang–Mills mass gap (15%) follow closely, buoyed by recent partial breakthroughs that open new attack vectors. For RH, AI systems have achieved fast progress on zero-free regions and zero proportions, but number theorists warn against extrapolating quasi-Riemann results directly to the full hypothesis due to a steep conceptual barrier at the 1/2 line https://www.anthropic.com/research/riemann-zeta AI Proved the Quasi-Riemann Hypothesis. What Happens ... AI Proved the Quasi-Riemann Hypothesis. What Happens .... Similarly, the announced existence proofs for 4D Yang–Mills and QCD suggest a major opening OpenAI Says Its Models Produced Three Proofs in Math ... Working with academic communities to build scientific ... Yang–Mills existence and mass gap OpenAI said AI cracked major math, computing and ... - Quartz Yang–Mills existence and mass gap. However, these proofs are currently withheld and explicitly omit the mass gap, which mathematical physicists regard as the deeper difficulty of the full Clay problem Working with academic communities to build scientific ....

Trailing Conjectures and Persistent Barriers The remaining problems share the rest of the probability mass, largely penalized for steep conceptual barriers or a lack of clear AI inroads. Birch–Swinnerton-Dyer (6%) and Hodge (6%) have seen partial AI claims—Selmer corank at most 1 and CM abelian varieties, respectively Sharing AI progress in mathematics https://www.claymath.org/wp-content/uploads/2022/05/birchswin.pdf https://www.claymath.org/wp-content/uploads/2022/06/hodge.pdf—but generalizing to all ranks and smooth projective varieties is an enormous leap. (Hodge receives marginal credit because a disproof would count). Twin primes (6%) is hindered by the parity barrier, which blocks a straightforward extrapolation of sieve improvements A human set a new mathematical record. Then AI came for it Open question: The parity problem in sieve theory - Terence Tao. Finally, the Exponential Time Hypothesis refutation explicitly leaves P vs NP (5%) open https://github.com/anthropics/formal-math/tree/main/eth The P Versus NP Problem, while the abc conjecture (5%) and Collatz conjecture (3%) continue to face profound theoretical obstacles with no meaningful AI progress reported to date Why abc is still a conjecture [1909.03562] Almost all orbits of the Collatz map attain ....