Background

The Millennium Prize Problems are seven legendary open questions in mathematics announced by the Clay Mathematics Institute (CMI) in year 2000, each carrying a US $1 million reward for the first correct solution. Grigori Perelman’s 2003 proof of the Poincaré Conjecture settled one of them, leaving six unsolved challenges:

• Birch and Swinnerton-Dyer Conjecture

• Hodge Conjecture

• Navier–Stokes Existence and Smoothness

• P vs NP

• Riemann Hypothesis

• Yang–Mills Existence and Mass Gap

A single AI system producing a formally accepted proof for any one of these six problems would represent a historic milestone for both mathematics and artificial-intelligence research.

Resolution Criteria

1. Evidence required

   • A peer‑reviewed paper in a recognised scientific journal or an officially accepted CMI submission must demonstrate that the proof was generated by an AI system and that it fully resolves one of the six unsolved Millennium Prize Problems.

2. AI autonomy

   • Humans may design, train, fine‑tune or prompt the model, but the complete logical argument must be produced autonomously by the AI.

   • Human assistance is limited to setting up the architecture, curating publicly available training data and verifying formatting; no new mathematical insights may be added by people.

3. Timing of Resolution

   • The market resolves YES if at any time before Jan 1, 2040 a qualifying proof that satisfies Criteria 1 (Evidence required) and Criteria 2 (AI autonomy) becomes publicly available.