Clay Mathematics Institute - Millennium Prize Problems

Millennium Prize Problems

The institute is best known for establishing the Millennium Prize Problems on May 24, 2000. These seven problems are considered by CMI to be "important classic questions that have resisted solution over the years". For each problem, the first person to solve it will be awarded $1,000,000 by the CMI. In announcing the prize, CMI drew a parallel to Hilbert's problems, which were proposed in 1900, and had a substantial impact on 20th century mathematics. Of the initial twenty-three Hilbert problems, most of which have been solved, only the Riemann hypothesis (formulated in 1859) is included in the seven Millennium Prize Problems.

For each problem, the Institute had a professional mathematician write up an official statement of the problem, which will be the main standard by which a given solution will be measured against. The seven problems are:

• P versus NP
• The Hodge conjecture
• The Poincaré conjecture - solved, by Grigori Perelman
• The Riemann hypothesis
• Yang–Mills existence and mass gap
• Navier–Stokes existence and smoothness
• The Birch and Swinnerton-Dyer conjecture.

Some of the mathematicians who were involved in the selection and presentation of the seven problems were Atiyah, Bombieri, Connes, Deligne, Fefferman, Milnor, Mumford, Wiles, and Witten.