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

Overview

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 ...

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Overview

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) is likely to play a strong role in determining the course of mathematics in the current century. 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 Keith 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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Editorial Reviews

From Barnes & Noble
Keith Devlin, the Math Guy from NPR's All Things Considered, has composed a challenging, yet accessible book about the seven greatest unsolved mathematical brain-teasers of our time. Each of these problems carries a million-dollar lure, the award offered for its solution by the prestigious Clay Foundation of Cambridge, Massachusetts. Whether viewed as the first step toward that prize or purely as entertainment, The Millennium Problems promises to be a worthwhile investment.
The Los Angeles Times
Devlin, who appears on NPR's Weekend Edition as "the Math Guy" and is the author of numerous books, is a pro. He is savvy about knowing what he might have a chance of explaining and what is likely to get him into trouble. The examples he uses to explain key ideas are often exceptionally well-chosen, and if you want a concise introduction to the Riemann hypothesis, this is your book. — Ben Yandell
Publishers Weekly
The noble idea that advanced mathematics can be made comprehensible to laypeople is tested in this sometimes engaging but ultimately unsatisfying effort. Mathematician and NPR commentator Devlin (The Math Gene) bravely asserts that only "a good high-school knowledge of mathematics" is needed to understand these seven unsolved problems (each with a million-dollar price on its head from the Clay Mathematics Institute), but in truth a Ph.D. would find these thickets of equations daunting. Devlin does a good job with introductory material; his treatment of topology, elementary calculus and simple theorems about prime numbers, for example, are lucid and often fun. But when he works his way up to the eponymous problems he confronts the fact that they are too abstract, too encrusted with jargon, and just too hard. He finally throws in the towel on the Birch and Sinnerton-Dyer Conjecture ("Don't feel bad if you find yourself getting lost... the level of abstraction is simply too great for the nonexpert"), while the chapter on the Hodge Conjecture is so baffling that the second page finds him morosely conceding that "the wise strategy might be to give up." Nor does Devlin make a compelling case for the real-world importance of many of these problems, rarely going beyond vague assurances that solving them "would almost certainly involve new ideas that will... have other uses." Sadly, this quixotic book ends up proving that high-level mathematics is beyond the reach of all but the experts. (Nov.) Copyright 2003 Cahners Business Information.
School Library Journal
Adult/High School-"The Math Guy" from NPR's Weekend Edition makes a case for why theoretical mathematics should matter to the general public. He devotes a chapter to each of the seven problems that the Clay Institute considers the most important mathematical problems of the century-and is, incidently, offering a million dollar prize to anyone who can solve one. Copyright 2004 Reed Business Information.
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Product Details

  • ISBN-13: 9780465017294
  • Publisher: Basic Books
  • Publication date: 11/1/2002
  • Pages: 256
  • Product dimensions: 6.30 (w) x 9.35 (h) x 1.01 (d)

Meet the Author

Keith  Devlin
Keith Devlin
Keith Devlin -- regular National Public Radio commentator and member of the Stanford University staff -- writes about the genetic progression of mathematical thinking and the most head-scratching math problems of the day. And he somehow manages to make it fun for the lay reader.

Biography

Odds are, John Grisham doesn’t get interview questions like this: "If you could meet any mathematician, who would it be?"

But author Keith Devlin does, this time from Discover magazine as part of a January 2001 article coinciding with the publication of his book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. His answer may go a long way toward explaining why he has managed to make the world of numbers not only understandable but also enjoyable to a segment of the population that can’t balance a checkbook without a net -- or backup from MIT.

“Isaac Newton,” Devlin told the inquiring minds at Discover. “He was a quarrelsome, egotistical person, but he also invented calculus. He did it, by the way, when he was a student at Cambridge. The Great Plague was going on, so the university was closed, and young Newton found himself without studies to do. Most 20-year-olds would think, ‘Whoopee! I’ll just have a good time.’ Newton went home and invented calculus.”

It is this same kind of passion for mathematics that has enabled Devlin, now the executive director of the Center for the Study of Language and Information at Stanford University, to persuade readers that arithmetic, geometry and calculus can be a bracing addition to the stack on the bedside table. In The Math Gene, he explains the “innate sense of number” that lives inside the human mind and how the development of mathematical thinking is closely bound to the development of language. In Goodbye, Descartes: The End of Logic and the Search for a New Cosmology of the Mind, he argues against the possibility of artificial intelligence, saying that computers are simply logic machines that cannot replicate the rational thought and communication that are part of human smarts. In his newest book, The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, he explains a historic competition announced by a Cambridge, Massachusetts foundation in 2000: Anyone who could solve any one of seven of the most perplexing math problems of the current age would win $1 million.

In a 1999 review, the Economist noted that “Devlin succeeds both in giving us a glimpse of the internal beauty of the subject and in demonstrating its usefulness in the external world. The Language of Mathematics is lucidly written and richly illustrated, and remains accessible and enthusiastic throughout.”

On NPR’s Weekend Edition, where he has become a regular guest, Devlin is referred to simply as “The Math Guy,” or as host Scott Simon once put it “our white knight of the world of mathematics.”

And, going back to that provocative subtitle in The Math Gene, just how is math like gossip? “Mathematicians deal with a collection of objects -- numbers, triangles, groups, fields -- and ask questions like: ‘What is the relationship between Objects X and Y?. If X does this to Y, what will Y do back to X?’” he told Discover. “It's got plot, it's got characters, it's got relationships between them, and it's got life and emotion and passion and love and hate, a bit of everything you can find in a soap opera. On the other hand, a soap opera isn't going to get you to the moon and back. Mathematics can.”

Just don’t forget to carry the 1.

Good To Know

Devlin was the coauthor of the television special A Mathematical Mystery Tour, broadcast as part of the Nova series in 1984.

He once offered as proof of the human brain’s intuitive math skills the ability to judge speed and distance while driving and the ability to add up bowling scores.

Devlin once managed to explain the mathematical difference between a knot and a tangle to National Public Radio’s listeners.

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    1. Hometown:
      Palo Alto, California
    1. Date of Birth:
      March 16, 1947
    2. Place of Birth:
      Hull, England
    1. Education:
      B.S., King's College, London, 1968; Ph.D., University of Bristol, 1971

Table of Contents

Preface
The Gauntlet is Thrown 1
1 The Music of the Primes: The Riemann Hypothesis 19
2 The Fields We Are Made Of: Yang-Mills Theory and the Mass Gap Hypothesis 63
3 When Computers Fail: The P vs. NP Problem 105
4 Making Waves: The Navier-Stokes Equations 131
5 The Mathematics of Smooth Behavior: The Poincare Conjecture 157
6 Knowing When the Equation Can't Be Solved: The Birch and Swinnerton-Dyer Conjecture 189
7 Geometry Without Pictures: The Hodge Conjecture 213
Further Reading 229
Index 231
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