The Millennium Prize ProblemsJames A. Carlson, Arthur Jaffe, Andrew Wiles, Clay Mathematics Institute, American Mathematical Society American Mathematical Soc., 2006 - 165 Seiten 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 openfrontier 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, theNavier-Stokes Equation, the P versus NP Problem, the Poincare 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. Information for our distributors: A co-publication of the AMS and the Clay Mathematics Institute(Cambridge, MA). |
Inhalt
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STEPHEN COOK | 87 |
ENRICO BOMBIERI | 107 |
ARTHUR JAFFE AND EDWARD WITTEN | 129 |
Rules for the Millennium Prizes | 153 |
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Häufige Begriffe und Wortgruppen
3-manifolds Academy algebraic cycles algebraic varieties analytic Andrew Wiles arithmetic Arthur Jaffe Atiyah awarded axioms Berlin Boolean Cambridge century checking relation classical Clay Mathematics Institute cohomology complexity theory computation construction counterexample Courtesy curvature defined Deligne dimensions Dirichlet divisor Edward Witten elliptic curves essay Euclidean Euler example existence Fermat's Last Theorem finite fields formula four-dimensional gauge theory genus Geom geometry Hilbert Hodge conjecture homeomorphic input integral interaction known L-functions language linear lower bounds manifold mass gap Math mathematicians methods Millennium Prize Problems modular Navier-Stokes equations NP problem NP-complete number theory Paris Photo Phys physics Pierre Deligne Poincaré Conjecture polynomial polynomial-time algorithm prime numbers Princeton proof properties prove quantum field theory question rational points renormalization Riemann hypothesis satisfies Sciences Smale smooth solved space space-time Springer-Verlag Tate three-dimensional topic Topology Turing machine University variable vector weak solution Wightman Yang-Mills theory York zeros
Beliebte Passagen
Seite 25 - The whole of my remaining realizable estate shall be dealt with in the following way: The capital shall be invested by my executors in safe securities and shall constitute a fund, the interest on which shall be annually distributed in the form of prizes to those who. during the preceding year, shall have conferred the greatest benefit on mankind.
Seite 22 - Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries?
Seite 24 - This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us. Moreover a mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful...
Seite 153 - Institute] will decide whether a solution merits detailed consideration ... The SAB will pay special attention to the question of whether a prize solution depends crucially on insights published prior to the solution under consideration. The SAB may (but need not) recommend recognition of such prior work in the prize citation, and it may (but need not) recommend the inclusion of the author of prior work in the award. Thus far there is only one serious contender for a Clay Prize, and that is Grisha...
Seite 24 - ... demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us. "Moreover a mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock our efforts. It should be to us a guidepost on the tortuous paths to hidden truths, ultimately rewarding us by the pleasure in the successful solution.
Seite 82 - Otal, J.-P.: The hyperbolization theorem for fibered 3-manifolds. Translated from the 1996 French original by Leslie D. Kay. SMF/AMS Texts and Monographs, 7. American Mathematical Society, Providence, RI; Societe Mathematique de France, Paris (2001) 102.