The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time

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Basic Books, 2002 - Mathematics - 237 pages
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In 2000, the Clay Foundation 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 the mathematician David Hilbert proposed twenty-three problems that set much of the agenda for mathematics in the twentieth century. The Millennium Problems--chosen by a committee of the leading mathematicians in the world--are likely to acquire similar stature, and their solution (or lack of it) is likely to play a strong role in determining the course of mathematics in the twenty-first century. Keith Devlin, renowned expositor of mathematics and one of the authors of the Clay Institute's official description of the problems, here provides the definitive account for the mathematically interested reader.
 

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Contents

The Gauntlet is Thrown
1
The Music of the Primes The Riemann Hypothesis
19
Appendix 1 Euclids Proof That There Are Infinitely Many Primes
53
How Do Mathematicians Work Out Infinite Sums?
55
How Euler Discovered the Zeta Function
59
The Fields We Are Made Of YangMills Theory and the Mass Gap Hypothesis
63
Group Theory The Mathematics of Symmetry
97
When Computers Fail The P vs NP Problem
105
Making Waves The NavierStokes Equations
131
The Mathematics of Smooth Behavior The Poincare Conjecture
159
Knowing When the Equation Cant Be Solved The Birch and SwinnertonDyer Conjecture
191
Natation for Infinite Sums and Products
211
Geometry Without Pictures The Hodge Conjecture
215
Further Reading
231
Index
233
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About the author (2002)

Keith Devlin is the Dean of the School of Social Science at St. Mary's College, Moraga, California, and a Senior Researcher at the Center for the Study of Language and Information at Stanford University. He is the author of 22 books, one interactive CD-ROM, and over 65 technical research papers in mathematics. His voice is heard regularly on National Public Radio, on such programs as "Weekend Edition," "Talk of the Nation," "Science Friday," "Sounds Like Science," and "To the Best of Our Knowledge." His previous books include Life by the Numbers, the companion to a PBS series that aired in April and May, 1998; Goodbye Descartes: The End of Logic; and The Language of Mathematics: Making the Invisible Visible.

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