Millennium Prize Problems

The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. As of November 2012, 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. The Poincaré conjecture, the only Millennium Prize Problem to be solved so far, was solved by Grigori Perelman, but he declined the award in 2010.

The seven problems are:

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

Read more about Millennium Prize Problems:  P Versus NP, The Hodge Conjecture, The Poincaré Conjecture (proven), The Riemann Hypothesis, Yang–Mills Existence and Mass Gap, Navier–Stokes Existence and Smoothness, The Birch and Swinnerton-Dyer Conjecture, Works

Famous quotes containing the words millennium, prize and/or problems:

    “At the end of one millennium and nine centuries of Christianity, it remains an unshakable assumption of the law in all Christian countries and of the moral judgment of Christians everywhere that if a man and a woman, entering a room together, close the door behind them, the man will come out sadder and the woman wiser.”
    —H.L. (Henry Lewis)

    “Then, though I prize my friends, I cannot afford to talk with them and study their visions, lest I lose my own. It would indeed give me a certain household joy to quit this lofty seeking, this spiritual astronomy, or search of stars, and come down to warm sympathies with you; but then I know well I shall mourn always the vanishing of my mighty gods.”
    —Ralph Waldo Emerson (1803–1882)

    “Sustained unemployment not only denies parents the opportunity to meet the food, clothing, and shelter needs of their children but also denies them the sense of adequacy, belonging, and worth which being able to do so provides. This increases the likelihood of family problems and decreases the chances of many children to be adequately prepared for school.”
    —James P. Comer (20th century)