A set of seven classic unsolved problems, which carry a prize of 1 million US dollars each. They were published by the Clay Mathematics Institute on 24 May 2000. They are: P versus NP; the Hodge conjecture; the Riemann hypothesis; Yang–Mills existence and mass gap; Navier–Stokes existence and smoothness; the Birch and Swinnerton-Dyer conjecture. The Poincaré conjecture was solved in 2006 by Grigori Perelman. For further details, see appendix 22.

http://www.claymath.org/millennium-problems The Millennium Prize problems home page.