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Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers Paperback – May 9, 2006

3.2 out of 5 stars 20 customer reviews

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Editorial Reviews

From Publishers Weekly

Now that Fermat's famous last theorem has been solved, the greatest unsolved math problem is the Riemann hypothesis, which concerns the distribution of prime numbers. After the announcement of a $1-million prize for its solution in 2000, three popular books on the hypothesis appeared in 2003, of which the best is John Derbyshire's Prime Obsession (because, contrary to conventional publishing wisdom, it gives the mathematics necessary to understanding the problem). Unfortunately, unlike Fermat's last theorem, the Riemann hypothesis is complicated; indeed, it's all but unfathomable to those without a grasp of such difficult concepts as using imaginary numbers as exponents. Dartmouth math professor Rockmore writes elegantly and makes ample use of analogy, but because he avoids equations, including the zeta function that's an essential component of the hypothesis, he can really talk only around the subject. Compared to his predecessors, Rockmore moves quickly through the history and focuses on more recent approaches to tackling the problem. Still, for all the author's earnest efforts to explain such terms as eigenvalues and Hermitian matrices, most lay readers will be left scratching their heads.
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. --This text refers to an out of print or unavailable edition of this title.

From Booklist

The Riemann hypothesis, posed in 1859 in connection with Riemann's investigation of the distribution of prime numbers among integers, is the most important unsolved problem in mathematics today: it impinges not merely on almost every area of modern mathematics but on fundamental questions in quantum physics as well. Rockmore's book provides an engaging introduction to the problem and its history up to the present day, eschewing equations in favor of narrative and metaphor. While some of the resulting flights of fancy bog down in verbiage, others are clever and helpful. Rockmore explains linear transformations as views of the world's colors through the lenses of sunglasses, and he connects the Riemann hypothesis to the physics of balls and bumpers in an imagined billiard hall, "the Chaotic Cue, tucked away on a small side street in our mythical village of Quantum Chaos." Thumbnail biographies of the dramatis personae provide diversion and breathing room between passages of mathematics. This is a lively account of one of the central problems of modern science. Jared Wunsch
Copyright © American Library Association. All rights reserved --This text refers to an out of print or unavailable edition of this title.
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Product Details

  • Paperback: 304 pages
  • Publisher: Vintage; Reprint edition (May 9, 2006)
  • Language: English
  • ISBN-10: 0375727728
  • ISBN-13: 978-0375727726
  • Product Dimensions: 5 x 0.6 x 8 inches
  • Shipping Weight: 12.6 ounces (View shipping rates and policies)
  • Average Customer Review: 3.1 out of 5 stars  See all reviews (20 customer reviews)
  • Amazon Best Sellers Rank: #203,981 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Lester D. Taylor on July 20, 2005
Format: Hardcover Verified Purchase
This is another fine book on the Riemann Hypothesis that, in my view, strongly complements the volumes by John Derbyshire and Marcus du Sautoy. Readers of the book should have some prior exposure to the Riemann Hypothesis (including a basic understanding of complex variables), some understanding of linear algebra, and a modicum of understanding of quantum physics. I say this because, unlike for Derbyshire and du Sautoy, the mathematics underlying the Riemann Hypothesis are more talked about than developed. The strengths of the book are (1) the author's strong historical perspective, (2) his ability to make extremely esoteric mathematical concepts understandable (and fun!), and (3)a better discussion than provided by either Derbyshire or du Sautoy of the connection between the distribution of the zeta zeroes and the distribution of the prime numbers -- in short, why it is that the Riemann Hypothesis is viewed amongst mathematicians as being so important.
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Format: Hardcover Verified Purchase
OK, let's just stipulate that this guy loves mathematics--me, I'm just oddly fascinated with a topic so esoteric that it takes a graduate degree just to decipher the several alphabets that have been sacrificed to the needs of mathematical symbology. It appears as though I am not alone.

However, Dr. Rockmore is staking out a different turf than the other books. His goal seems not to be geared towards explaining the difficult topics so much as giving a lay reader an introduction to the various issues that pertain to the problem of the Riemann Hypothesis. Metaphor and simile are not the best tools for describing higher mathematics. My only criticism of this book is that while it touches on everything it actually explains very little. At first, having read the Sabbagh and Derbyshire books, this was frustrating; however, it becomes clear that the purpose of this book is very different.

"Stalking the Riemann Hypothesis" is more in the nature of "Einstein's Dreams" by Alan Lightman. It is more an attempt to convey the mathematician's wonder and curiosity than an understanding of the underlying science; seen in this light, I felt the book succeeded.
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Format: Hardcover Verified Purchase
Chapter 7 of this book refers to a curious incident about Stieltjes. In 1885 he claimed he had proved the Riemann Hypothesis.

Announcing his discovery in the journal of the French Academy of sciences he said:

"I have managed to put this proposition beyond doubt by means of a rigorous proof."

Erm ... Except that he didn't actually provide any proof at all. Besides that, I guess it was OK. Perhaps the margin was too small to contain it?

All joking aside, what was going on here? Stieltjes was a very respectable and highly original mathematician. Why the reticence to provide the claimed proof? Vanity, when he realised it was flawed? Perhaps, like Mr. Micawber, he thought that "something will turn up" if he kept working on it.

Dan Rockmore, the mathematician author of this book, points out that the primary record of Stieltjes's investigation of the Riemann Hypothesis is to be found in the Stieltjes-Hermite correspondence. In these letters Stieltjes mentions he has hit upon some "marvellous cancellations". Shades of Fermat's Last Theorem.

Stieltjes' plan of attack on the problem involved taking the reciprocal of the zeta function and involves the Möbius inversion formula.

For more details of this curious business see pages 98-99 of this book.

You will also find an account of it in Derbyshire's book (pages 160-61).
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Format: Hardcover
Rockmore's treatment of the Riemann hypothesis does the challenging job of introducing lay readers to the Prime Number theorem, the Euler factorization, Mobius inversion, and the eigenvalues of random matrices. The history is covered beautifully, detailing the partial successes and false starts along the way. Rockmore assumes very little on the part of the reader, and if you're already familiar with the complex plane and infinite series you will read between the lines a bit (actual equations are confined to footnotes) but even mathematically-inclined readers can gain a lot from the book. I enjoyed it a great deal.
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Format: Paperback
This little book with a populist and entertaining narrative is a great read for those fascinated by the mathematical concepts they may have heard about but put off by the formidable complexities of number theory. It is full of intriguing metaphors for abstract concepts, historical anecdotes, and key developments in mathematics and physics that have surprising relations to the Riemann hypothesis. The amazing fact is that the zeros of Riemann’s zeta function reflect the distribution of the prime numbers, but a rigorous proof is still lacking.

The book starts out well by conveying the excitement and mystery that have always surrounded prime numbers, going back to the Greeks, including Euclid’s proof of the infinitude of primes. Here the mathematics is very elementary. Later key terms from more abstract modern mathematical investigations are introduced but their meanings are typically illustrated by analogies, unless pictures are available, such as for the Poincare’ disk, which illustrates hyperbolic geometry and its chaotic trajectories that are suggestive of the randomness of the prime numbers.

For the mathematically trained reader, an appendix containing formulas and citations would have been useful to reduce the guesswork. Many terms, such as “pair correlation” and “Tracy-Widom distributions”, will seem somewhat mysterious to many readers. Nevertheless they can be alluring guideposts to the curious, providing a useful framework for grasping the “big picture”, especially if you have Wikipedia at your fingertips to see what the mathematics actually looks like.

Numerical investigations and an abundance of other evidence demonstrates that the Riemann hypothesis is almost certainly true, but the excitement is in the chase. What new worlds of mathematics will be needed to actually prove it, and are we almost there?
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