Millennium Prize Problems

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The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. 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.

Quotes[edit]

Solved problem[edit]

Poincaré conjecture[edit]

Main article: Poincaré conjecture

The official statement of the problem was given by John Milnor. A proof of this conjecture was given by Grigori Perelman in 2003.

Unsolved problems[edit]

P versus NP[edit]

Main article: P versus NP problem

The official statement of the problem was given by Stephen Cook.

Hodge conjecture[edit]

Main article: Hodge conjecture

The official statement of the problem was given by Pierre Deligne.

Riemann hypothesis[edit]

Main article: Riemann hypothesis
  • At the beginning of the new millennium the most famous unsolved problem in complex analysis, if not in all of mathematics, is to determine whether the Riemann hypothesis holds.

The official statement of the problem was given by Enrico Bombieri.

Yang–Mills existence and mass gap[edit]

The official statement of the problem was given by Arthur Jaffe and Edward Witten.

Navier–Stokes existence and smoothness[edit]

The official statement of the problem was given by Charles Fefferman.

Birch and Swinnerton-Dyer conjecture[edit]

The official statement of the problem was given by Andrew Wiles.

External links[edit]

Wikipedia
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