Millennium Prize Problems

Seven mathematical problems designated by the Clay Mathematics Institute in 2000, each carrying a million-dollar prize for a correct solution. The Riemann Hypothesis is one of them.

Riemann Hypothesis: A conjecture that every nontrivial zero of the Riemann zeta function has real part one-half. One of the seven problems, linking prime-number patterns to the zeros of a complex function.
Clay Mathematics Institute: A private foundation that supports mathematical research and established the Millennium Prize Problems. It created the prizes and oversees their award rules.
Grigori Perelman: A Russian mathematician who proved the Poincaré conjecture and declined major mathematical honors. His proof resolved one prize problem, while he declined its million-dollar award.
Clay Mathematics Institute Prize Rules: The Clay Mathematics Institute’s conditions for eligibility, review, and payment of its Millennium Prize awards. A proposed solution must satisfy these rules before its prize can be awarded.
P versus NP: The open problem of whether every problem whose solution can be checked quickly can also be solved quickly. This prize problem asks whether efficient verification implies efficient computation.
Landmark Papers in Mathematics: A collection of influential papers that shaped the development of mathematics. The institute commissioned essays on the historical background of each problem.
Poincaré Conjecture: The theorem that every simply connected, closed three-dimensional manifold is homeomorphic to the three-sphere. This was the sole Millennium Prize Problem solved and awarded.
Peer Review: Evaluation of scholarly work by experts in the relevant field. The institute requires a solution to receive broad acceptance in the mathematics community.
Navier–Stokes existence and smoothness: The problem of proving global existence and smoothness, or finding a breakdown, for three-dimensional Navier–Stokes fluid equations. It asks whether a core model of fluid motion remains mathematically well-behaved.
International Congress of Mathematicians: A quadrennial international mathematics conference organized by the International Mathematical Union. The prize problems were announced at its 2000 meeting in Paris.

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