Resolution criteria

This market will resolve to YES if, before January 1, 2030, all seven Millennium Prize Problems are officially solved or widely recognized by the global mathematical community as solved. Otherwise, this market will resolve to NO.

The seven Millennium Prize Problems are:

1. Poincaré Conjecture (Solved)

2. Birch and Swinnerton-Dyer Conjecture

3. Hodge Conjecture

4. Navier–Stokes Existence and Smoothness

5. P versus NP Problem

6. Riemann Hypothesis

7. Yang–Mills Existence and Mass Gap

A remaining problem will be considered "solved" if either of the following conditions is met before January 1, 2030:

• The Clay Mathematics Institute (CMI) officially announces that the problem has been solved, or awards/offers the Millennium Prize for its solution.

• There is an overwhelming consensus within the global mathematics community that a correct proof or disproof has been published and verified, as reported by major scientific and mathematical bodies or outlets (e.g., the International Mathematical Union, the American Mathematical Society, Nature, Science, or Quanta Magazine).

If any of the remaining six problems lack a verified solution meeting these criteria by January 1, 2030, the market will resolve to NO.

Background

The Millennium Prize Problems are seven of the most difficult challenges in mathematics, established by the Clay Mathematics Institute in 2000 with a $1 million prize designated for each solution.

Only one problem has been officially resolved: the Poincaré Conjecture, solved by Grigori Perelman in 2003 (with the prize formally awarded, and subsequently declined, in 2010). On September 8, 2026, OpenAI published a paper claiming to have solved the Navier–Stokes existence and smoothness problem using an advanced internal AI system, presenting a proof formalized in Lean. However, this proposed proof has not yet undergone the extensive peer-review process required by the mathematical community. Per the official CMI rules, a proposed solution must survive rigorous examination for a minimum of two years post-publication before it can be considered for the prize.

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