Millenium Prize Problems: Problems Worth $1M Each

On May 24, 2000, the Clay Mathematics Institute established seven Prize Problems. These problems are called the Millenium Prize Problems.  A solution to each unsolved problem is worth $1 000 000 dollars. These problems are

  1. P versus NP
  2. Hodge conjecture
  3. Poincaré conjecture
  4. Riemann hypothesis
  5. Yang–Mills existence and mass gap
  6. Navier–Stokes existence and smoothness
  7. Birch and Swinnerton-Dyer conjecture

As of this writing (12 years later), six problems are still unsolved.  The Poincare Conjecture was solved by Grigori Perelman in 2006. Dr. Perelman was awarded the Millenium Prize in 2010, but he declined the award.