The millennium problems : the seven greatest unsolved mathematical puzzles of our time

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In 2000, the Clay Foundation of Cambridge, Massachusetts, announced a historic competition: Whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1 million in prize money. There was some precedent for doing this: In 1900 David Hilbert, one of the greatest mathematicians of his day, proposed twenty-three problems, now known as the Hilbert Problems, that set much of the agenda for mathematics in the twentieth century. The Millennium Problems are likely to acquire similar stature, and their solution (or lack of one) will play a strong role in determining the course of mathematics in the current century. They encompass many of the most fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. Keith Devlin, renowned expositor of mathematics, tells here what the seven problems are, how they came about, and what they mean for math and science." "These problems are the brass rings held out to today's mathematicians, glittering and just out of reach. In the hands of Devlin, "the Math Guy" from NPR's Weekend Edition, each Millennium Problem becomes a fascinating window onto the deepest and toughest questions in the field. For mathematicians, physicists, engineers, and everyone else with an interest in mathematics' cutting edge, The Millennium Problems is the definitive account of a subject that will have a very long shelf life.

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In 2000, the Clay Foundation of Cambridge, Massachusetts, announced a historic competition: Whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1 million in prize money. There was some precedent for doing this: In 1900 David Hilbert, one of the greatest mathematicians of his day, proposed twenty-three problems, now known as the Hilbert Problems, that set much of the agenda for mathematics in the twentieth century. The Millennium Problems are likely to acquire similar stature, and their solution (or lack of one) will play a strong role in determining the course of mathematics in the current century. They encompass many of the most fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. Keith Devlin, renowned expositor of mathematics, tells here what the seven problems are, how they came about, and what they mean for math and science." "These problems are the brass rings held out to today's mathematicians, glittering and just out of reach. In the hands of Devlin, "the Math Guy" from NPR's Weekend Edition, each Millennium Problem becomes a fascinating window onto the deepest and toughest questions in the field. For mathematicians, physicists, engineers, and everyone else with an interest in mathematics' cutting edge, The Millennium Problems is the definitive account of a subject that will have a very long shelf life.

Content Note

The gauntlet is thrown -- The music of the primes : the Riemann Hypothesis. Appendix 1. Euclid's proof that there are infinitely many primes ; Appendix 2. How do mathematicians work out infinite sums? ; Appendix 3. How Euler discovered the Zeta Function -- The fields we are made of : Yang-Mills theory and the Mass Gap Hypothesis. Appendix. Group theory : the mathematics of symmetry -- When computers fail : the P vs. NP problem -- Making waves : the Navier-Stokes Equations -- The mathematics of smooth behavior : the Poincaré Conjecture -- Knowing when the equation can't be solved : the Birch and Swinnerton-Dyer Conjecture. Appendix . Notation for infinite sums and products -- Geometry without pictures : the Hodge Conjecture.