Jump to navigation Jump to search This article is about the math prizes. For the technology prize, see Millennium Technology Prize. This article needs additional citations for verification. The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute on May 24, 2000. To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved by the Russian mathematician Grigori Perelman in 2003.
In dimension 2, a sphere is characterized by the fact that it is the only closed and simply-connected surface. The Poincaré conjecture states that this is also true in dimension 3. It is central to the more general problem of classifying all 3-manifolds. Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. August 2006, and Perelman was selected to receive the Fields Medal for his solution, but he declined the award. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are also in P. The official statement of the problem was given by Stephen Cook. The Hodge conjecture is that for projective algebraic varieties, Hodge cycles are rational linear combinations of algebraic cycles.
The official statement of the problem was given by Pierre Deligne. The official statement of the problem was given by Enrico Bombieri. Mills theory is a generalization of the Maxwell theory of electromagnetism where the chromo-electromagnetic field itself carries charges. The official statement of the problem was given by Arthur Jaffe and Edward Witten. Stokes equations describe the motion of fluids, and are one of the pillars of fluid mechanics. However, theoretical understanding of their solutions is incomplete. For the three-dimensional system of equations, and given some initial conditions, mathematicians have not yet proved that smooth solutions always exist, or that if they do exist, they have bounded energy per unit mass. The problem is to make progress towards a mathematical theory that will give insight into these equations, by proving either that smooth, globally defined solutions exist that meet certain conditions, or that they do not always exist and the equations break down. The official statement of the problem was given by Charles Fefferman.
The Birch and Swinnerton-Dyer conjecture deals with certain types of equations: those defining elliptic curves over the rational numbers. The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. The official statement of the problem was given by Andrew Wiles. Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture. Russian mathematician rejects million prize – Boston. Why Philosophers Should Care About Computational Complexity”. Arthur Jaffe and Edward Witten “Quantum Yang-Mills theory. The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time. We are your best resource for getting an XBOX One for free!
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