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Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers Paperback – May 9, 2006
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Top Customer Reviews
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.
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).
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?
Most Recent Customer Reviews
I greatly enjoyed Prof. Rockmore's clear, non-jargon laden prose. He explains abstract, yet extremely important mathematical ideas with lucidity. I recommend this book highly.Published 1 month ago by Charles E. Witteck
Rockmore's narrative couched within all the historical background of Riemann and his contemporaries was not only interesting but it provided a path to understand all the why's of... Read morePublished 2 months ago by AthleTech
There are quite some titles available on the subject so far. This book gives a very complete overview of all the mathematicians that have been working to solve the Riemann... Read morePublished on November 24, 2013 by Martijn13Maart1970
This book is not only a review of the issues, personalities and history of this great problem, but also an assessment of why it matters. A fascinating read.Published on February 5, 2013 by James Kent Brink
I had high hope when I saw the title and the bio of the author. But I was left bewildered after going through the book. Read morePublished on May 26, 2011 by fantans
I don't know what it is with the latest books trying to popularize certain branches of contemporary and modern science, but it seems to me that poetic and decorated language now... Read morePublished on May 27, 2007 by Gerke M. Preussner
How do you write a book about mathematics and numbers without any? I got lost in the sea of abstract forced analogies and ended up more confused, irritated, and lost than I had... Read morePublished on May 12, 2007 by Sanjeev Naik
I felt very irritated by reading this book. Many analogies and side stories lead to loose the focused main subject. Read morePublished on April 13, 2007 by TS
This wasn't any good as a hardback and reissuing it
in paperback doesn't change matters.
To get an idea of what you are in for, see the reviews
of... Read more