Stalking the Riemann Hypothesis [Hardcover]

Dan Rockmore (Author)

Book Description

ISBN-10: 0224062530 | ISBN-13: 978-0224062534 | Publication Date: April 21, 2005 | Edition: First Edition

Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bountry. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.

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

• Hardcover: 304 pages
• Publisher: Jonathan Cape Ltd; First Edition edition (April 21, 2005)
• Language: English
• ISBN-10: 0224062530
• ISBN-13: 978-0224062534
• Product Dimensions: 9.3 x 6.1 x 1.3 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 2.7 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #2,967,166 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

24 of 27 people found the following review helpful:

4.0 out of 5 stars Another fine book on the Riemann Hypothesis., July 20, 2005

By 

Lester D. Taylor (Professor of Economics (Emeritus), University of Arizona, Tucson, AZ USA) - See all my reviews
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This review is from: Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers (Hardcover)

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.

20 of 23 people found the following review helpful:

3.0 out of 5 stars An Ode to Higher Mathematics, August 11, 2005

By 

J. Brian Watkins (Laie, Hawaii) - See all my reviews
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This review is from: Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers (Hardcover)

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.

15 of 18 people found the following review helpful:

5.0 out of 5 stars Engaging and elegant introduction to the Riemann hypothesis, April 21, 2005

By 

Cristopher Moore - See all my reviews
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This review is from: Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers (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.