7 Millennium Prize Problems:
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. As of September 2011, six of the problems remain unsolved. A correct solution to any of the problems results in a US$1,000,000 prize (sometimes called a Millennium Prize) being awarded by the institute. Only the Poincaré conjecture has been solved, by Grigori Perelman, who declined the award.
The seven problems are:
1.P versus NP problem
3.Poincaré conjecture (solved, see solution of the Poincaré conjecture)
5.Yang–Mills existence and mass gap
6.Navier–Stokes existence and smoothness
7.Birch and Swinnerton-Dyer conjecture