Background

The Millennium Prize Problems are seven of the most challenging unsolved problems in mathematics, established by the Clay Mathematics Institute in 2000. Only one problem, the Poincaré Conjecture, has been solved to date (by Grigori Perelman in 2003). The remaining problems are the Riemann Hypothesis, P versus NP, Yang-Mills and Mass Gap, Navier-Stokes Existence and Smoothness, Birch and Swinnerton-Dyer Conjecture, and Hodge Conjecture.

Resolution Criteria

• Resolves YES if a human mathematician or team of mathematicians solves one of the remaining Millennium Prize Problems without significant AI assistance

• Resolves NO if an AI system generates the accepted solution

• Partial resolutions are possible for cases where AI played a supporting but not primary role:

  • Minor AI assistance (e.g., computation verification) would resolve mostly YES

  • Substantial AI contribution to key insights would resolve mostly NO

  • The exact percentage will be determined by the market creator based on the specifics of the solution

Considerations

• Current AI systems excel at structured problems but struggle with the creative, intuitive reasoning often required for breakthrough mathematical proofs

• The definition of "AI assistance" may evolve as technology advances

• Resolution will be based on the official acceptance of a solution by the Clay Mathematics Institute and detailed analysis of the solution process