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The Millennium Problems 1 Hardcover – October 15, 2002

ISBN-13: 978-0465017294 ISBN-10: 0465017290 Edition: First Edition
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Editorial Reviews

From 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.
Copyright 2002 Reed Business Information, Inc.

From School Library Journal

Adult/High School-In May, 2000, the Clay Mathematics Institute posted a million-dollar prize to anyone able to solve any of what it considered the seven most important mathematical problems of the 21st century. They were chosen not for theoretical beauty alone, but because many of them deal with concepts in fields like physics, computer science, and engineering, and exist because practitioners in those fields are already using theoretical or practical design solutions that have not been mathematically proven. Devlin, "The Math Guy" from NPR's Weekend Edition, does a good job explaining the background of the problems and why theoretical mathematics as a discipline should matter to a general audience. Each problem has a chapter of its own and is given a treatment that, where applicable, extends back to the ancient Greeks. A passing knowledge of mathematics is important for taking in Devlin's work but a major in the subject is not, and this book should satisfy anyone looking for a layman's guide to modern theoretical mathematics. Or hoping to win a million dollars.
Sheryl Fowler, Chantilly Regional Library, VA
Copyright 2003 Reed Business Information, Inc.

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Product Details

  • Hardcover: 256 pages
  • Publisher: Basic Books; First Edition edition (October 16, 2002)
  • Language: English
  • ISBN-10: 0465017290
  • ISBN-13: 978-0465017294
  • Product Dimensions: 9.4 x 6.3 x 1 inches
  • Shipping Weight: 1.1 pounds
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (33 customer reviews)
  • Amazon Best Sellers Rank: #1,161,447 in Books (See Top 100 in Books)

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More About the Author

Dr. Keith Devlin is a mathematician at Stanford University in California. He is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He has written 31 books and over 80 published research articles. His books have been awarded the Pythagoras Prize and the Peano Prize, and his writing has earned him the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. (Archived at http://www.stanford.edu/~kdevlin/MathGuy.html.)

He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition.

He writes a monthly column for the Mathematical Association of America, "Devlin's Angle": http://www.maa.org/devlin/devangle.html

Customer Reviews

4.1 out of 5 stars

Most Helpful Customer Reviews

59 of 60 people found the following review helpful By Royce E. Buehler on January 17, 2003
Format: Hardcover
... but keep it in mind for that teenage nerd in your life.
To help you evaluate my evaluation, let me note up front that I have three long-ago years of graduate math courses under my belt, which made me familiar with four of the seven problems discussed here. I got bored with much of the account of those four, had fun with the discussion of the sixth problem (the Birch and Swinnerton-Dyer Conjecture, which has to do with rational points on elliptic curves), and obtained a vague picture of the remaining two.
My three-star rating is bound to be misleading. Keith Devlin has an enormous gift for mathematical explanation, but as he himself recognizes, in attempting to explain to the proverbial man on the street the seven Millenium Problems (for solving each of which the Clay Mathematical Institute, hoping to spur mathematical research in the 21st century somewhat as David Hilbert did with his famous set of 23 problems in the century just past, has put up a cool million American dollars), he has bitten off more than anyone could possibly chew. I don't mean to suggest it could have been done any better.
If you hanker to tackle the problems and win one of those millions for yourself, start hankering for some other pipe dream. These problems are tough. If you want to thoroughly understand what they consist of, you will need to go to the official technical description of the problems in the book jointly prepared by the Clay institute and the American Mathematical Society. If you want a light overview of them, there's no such thing, but this book is as good a compromise between ease and clarity as you will get.
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56 of 63 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on April 20, 2003
Format: Hardcover Verified Purchase
In this book the author makes a sincere attempt to describe to a popular audience the content behind seven mathematical problems that were chosen by a private foundation called "The Clay Institute" as being deep enough to warrant a prize of $1,000,000 for their solution. The goal is realized in some parts of the book, but falls short in others, but it still is of value to those who are curious about the history and content behind these problems. The author is aware of the difficulty in describing the content of the problems to readers without substantial mathematical preparation, and he does a good job in general.
One can of course think of many other problems that fit the stature of the millennium problems, such as the invariant subspace conjecture, or developing a complete mathematical model of the cell, but these seven will no doubt spark the curiosity of a few young persons as they further their studies in mathematics. Some of the millennium problems, such as the Riemann hypothesis, the NP problem, the Poincare conjecture, and the Navier-Stokes equations, require only an undergraduate education. The others definitely require more background, just to understand even the statement of the problem. All of the them are fascinating, and will no doubt stimulate some incredibly interesting mathematical constructions.
Personal note for anyone interested (from someone who has worked on one of these problems for several years): For those readers who are thinking about attacking one of these problems, it is important to be really interested in solving it, for your own satisfaction, and not to be concerned about the financial reward or what the solution will bring you in terms of professional advancement.
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17 of 17 people found the following review helpful By "50cent-haircut" on October 23, 2002
Format: Hardcover
If you solve any of the seven problems proposed by the Clay Mathematics Institute, you win one million dollars and a piece of history with your name on it. Let's face it; you and I aren't going to solve these problems. But this book makes a lot of what's relevant in contemporary mathematics and physics a public information and knowledge, and that's an honorable feat. Each of the seven problems are incredibly difficult to understand on their own. Keith Devlin does an excellent job of providing a historical and mathematical background for each of these problems for the laymen, and in process, reveals how the solutions to these problems would bring an exponential leap for the human knowledge as a whole. (Devlin does an exceptional job chronicling the history of math and physics that led to Yang-Mills Theory and Mass Gap, as well as Poincare Conjecture and P vs NP) For more detailed exposition of these problems, you are better off reading the official CMI book, or checking the official website of CMI, [url]. But if you are interested in the importance of these problems and the implications the solutions to these problems can have on our lives, this book will more than suffice.
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17 of 18 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on January 28, 2003
Format: Hardcover
Is the solution of any mathematics problem worth one million dollars? Yes, in fact there are seven such problems. In 1999, Landon Clay established the Clay Mathematical Foundation and in 2000, the Clay Foundation announced seven separate prizes of one million U. S. dollars for the solution of each of seven mathematics problems. In keeping with the famous list of unsolved problems enunciated by David Hilbert at the turn of the previous century, this list can be considered the problems for the new century, which also happens to be a new millennium.
Make no mistake, these problems are very hard. Even with all his mathematical expertise. Devlin readily admits that he really does not understand them all and had a very difficult time writing about them at a level so that a general audience could understand the basics of the problems. The seven problems are
· The Riemann hypothesis
· Yang-Mills Theory and the Mass Gap Hypothesis
· The P vs. NP Problem
· The Navier-Stokes Equations
· The Poincare Conjecture
· The Birch and Swinnerton-Dyer Conjecture
· The Hodge Conjecture
and the Riemann hypothesis is distinguished in that it is the only one that was also on Hilbert's list at the turn of the previous century. In his descriptions of the last two problems, it is clear that Devlin is struggling to understand the fundamentals of the problems.
Nevertheless, he does manage to inform the reader about what the problems are about, as well as a taste of how difficult they are. Like the problems David Hilbert stated in 1900, this collection of problems forms a marker by which the mathematical progress of this century will be measured. For that reason, all mathematicians should learn something about them, and this book is an ideal initial step.
Published in Recreational Mathematics e-mail newsletter, reprinted with permission.
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