Background

The Millennium Prize Problems are seven illustrious open problems in mathematics designated by the Clay Mathematics Institute (CMI) in year 2000, each carrying a $1 million dollar prize for the first correct solution. The Poincaré Conjecture has already been solved; only six remain:

• Birch and Swinnerton‑Dyer Conjecture

• Hodge Conjecture

• Navier–Stokes Existence and Smoothness

• P vs NP

• Riemann Hypothesis

• Yang–Mills Existence and Mass Gap

An AI system producing a formally accepted proof for any one of these six problems would constitute a historic milestone for both mathematics and artificial‑intelligence research.

Resolution criteria

1. Evidence required – A peer‑reviewed paper in a recognized scientific journal or an officially accepted Clay Institute submission must show that the proof was generated by an AI system and fully resolves one of the six unsolved Millennium Prize Problems.

2. AI autonomy – Humans may design, train, or fine‑tune the model, but the final mathematical proof must be produced autonomously by the AI. Human assistance is limited to setting up the AI architecture and verifying/verbatim formatting; humans may not add new logical steps or insights.

3. Earliest‑year rule – The market resolves to the bracket containing the calendar year in which the qualifying paper (pre‑print or journal) is first made public. If multiple problems are solved by AI, the earliest qualifying publication date counts.

4. Fail‑safe – If no qualifying solution is by before January 1, 2051 the market resolves to Not applicable.