The millennium prize problems

Guided by the premise that solving some of the world's most important mathematical problems will advance the field, this book offers a fascinating look at the seven unsolved Millennium Prize problems. This work takes the unprecedented approach of describing these important and difficult problems at the professional level. In announcing the seven problems and a US$7 million prize fund in 2000, the Clay Mathematics Institute emphasized that mathematics still constitutes an open frontier with important unsolved problems. The descriptions in this book serve the Institute's mission to "further the beauty, power and universality of mathematical thinking." Separate chapters are devoted to each of the seven problems: the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, the Navier-Stokes Equation, the P versus NP Problem, the Poincaré Conjecture, the Riemann Hypothesis, and Quantum Yang-Mills Theory. An essay by Jeremy Gray, a well-known expert in the history of mathematics, outlines the history of prize problems in mathematics and shows how some of mathematics' most important discoveries were first revealed in papers submitted for prizes. Numerous photographs of mathematicians who shaped mathematics as it is known today give the text a broad historical appeal. Anyone interested in mathematicians' continued efforts to solve important problems will be fascinated with this text, which places into context the historical dimension of important achievements. A co-publication of the AMS and the Clay Mathematics Institute (Cambridge, MA). "On May 24, 2000, at a meeting at the Collège de France, the Clay Mathematics Institute announced the creation of a US$7 million prize fund for the solution of seven important classic problems that have resisted solution. The prize fund is divided equally among the seven problems. There is no time limit for their solution. The Millennium Prize problems gives the official description of each of the seven problems and the rules governing the prizes"--Information screen History Of Prizes In Mathematics / J. Gray -- Birch And Swinnerton-dyer Conjecture / A. Wiles -- Hodge Conjecture / P. Deligne -- Existence And Smoothness Of The Navier-stokes Equation / C.l. Fefferman -- Poincaré́ Conjecture / J. Milnor -- P Versus Np Problem / S. Cook -- Riemann Hypothesis / E. Bombieri -- Quantum Yang-mills Theory / A. Jaffe, E. Witten. J. Carlson, A. Jaffe, And A. Wiles, Editors. Includes Bibliographical References.