Resolution criteria
This market will resolve to "Yes" if, by December 31, 2031, at least one of the six unsolved Millennium Prize Problems is solved primarily by an artificial intelligence (AI) system. The AI must be credited as the principal solver, not merely as a tool assisting human mathematicians. The solution must be published in a reputable, peer-reviewed mathematical journal and receive general acceptance in the global mathematics community. Official recognition by the Clay Mathematics Institute is not required for resolution. If no such AI-driven solution is achieved by the specified date, the market will resolve to "No."
Background
The Millennium Prize Problems are seven of the most challenging unsolved problems in mathematics, identified by the Clay Mathematics Institute in 2000. Each problem carries a $1 million prize for a correct solution. To date, only the Poincaré Conjecture has been solved, leaving six problems open:
Birch and Swinnerton-Dyer Conjecture: Relates to the number of rational solutions on elliptic curves and their associated L-functions.
Hodge Conjecture: Concerns the relationship between algebraic cycles and cohomology classes in complex projective varieties.
Navier–Stokes Existence and Smoothness: Involves proving the existence and smoothness of solutions to the Navier–Stokes equations governing fluid dynamics.
P vs. NP Problem: Asks whether every problem whose solution can be quickly verified can also be quickly solved.
Riemann Hypothesis: Pertains to the distribution of prime numbers and the zeros of the Riemann zeta function.
Yang–Mills Existence and Mass Gap: Seeks to establish the existence of a quantum field theory that satisfies the Yang–Mills equations and has a positive mass gap.
Considerations
While AI has made significant strides in various fields, its application to solving complex mathematical problems like the Millennium Prize Problems remains an area of active research. The timeline for AI achieving such breakthroughs is uncertain, and the integration of AI in mathematical problem-solving is still evolving.
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