Customer Reviews

Stalking the Riemann Hypothesis

5 star:		(4)
4 star:		(1)
3 star:		(1)
2 star:		(4)
1 star:		(5)

 

 

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.

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.

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.

This is the latest and we hope the last book on the
RH at least until the thing is solved. It is not
at all clear what audience the author was aiming
for but if he is afraid even to spell out such
basics as the euler product, then clearly the whole
enterprise is doomed. The first third of the book -
in which the maxim 'a picture (formula) is worth a
thousand words' is inverted - is essentially
a total loss. The only redeeming features are sections
on the connection to quantum chaos and to random matrices.
Still, considering the resources available to the author,
one expected much more.

When Albert Einstein sought the mathematics to bring his general theory of relativity to life, he found his solution in the works of none other than Bernard Reimann.

And although Reimann died young (at 39) apparently the special math necessary for relativity was not Reimann's only masterstroke.

He also developed a theta function or formula for predicting the placement of prime numbers in the number line. As you may recall from elementary mathematics, prime numbers are those numbers only divisible by themselves and one.

Though casual thought on the matter may initially lead one to conclude that prime numbers would eventually be exhausted (indeed the higher you go the more rare they do become) mathematical proofs dating back to Euclid show that like the integer line they accompany they go on forever.

But again figuring out how they can be located algorithmically within that forever was long a mathematics holy grail until 1859 when Bernard Reimann posited a hypothesis for locating them. His hypothesis or zeta function involves incredibly complicated mathematics certainly beyond the scope of this book so if you want to understand it you may do better to read Reimann's Zeta Function.

However if you want the outlines of search that goes from ancient Greece all the way to modern times, this book makes quick accessible reading.

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. (quite quickly I admit) I am confused by what the author tries to achieve. To a math inclined reader, it does not convey the depth of the materials around Riemann hypothesis --- it does not even define zeta function, let alone explaining its connection to prime number theory or other math objects. On the other hand, I cannot imagine how a lay person would enjoy the book --- there is no life in anything described in the book.

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 when I began reading the book. 80 pages into the book, I give up and will read Derbyshire's book, about which I have read good things.

Disclaimer: I am not a mathematician by training but have a science/engineering background. Even if I did not understand all the details, I had hoped the book would at least grip my attention and make me want to learn more.

What a contrast (and a frustrating one at that) attempting to read this book was...especially considering I just finished reading QED - The strange theory of light and matter by Richard Feynman. There couldn't be two contrasting writing styles!

In 1900 Dave Hilbert, the most famous mathematician of his day, and quite likely of any day, gave a speech where he listed 23 mathematical problems that he expected to be solved during the 1900's. Most of the problems got solved, several by the invention of new fields of mathematics. Problem Number 8 was simply "Prove the Riemann Hypothesis." It wasn't solved. (To see the other 22, do a Google Search.)

Riemann wrote a short paper on prime numbers stating his hypothesis. He then became very ill and died at the age of thirty-nine. The proof has remained elusive for a century and a half. While watching the play "Proof" I found myself wondering if this was the "Proof" in the play.

This book is the story of the recent attempts to prove Riemann's hypothesis. It doesn't use any (or very little) mathematics so it is much easier for the layman to read. But the problem isn't solved, after you read the book perhaps you will. If you do, you would be a good candidate for the Fields medal the math equivalent of the Nobel.

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 sells better than scientific clarity and educational value. This book serves more as a general overview into a wide range of more or less related open and solved problems in mathematics and physics rather than an interesting introduction into the problem of prime number distribution and the Riemann hypothesis. The many analogies, which are often explained in too much detail, do not only distract from the main topic, but often lack a considerable amount of relevance. In several cases they don't even lead to any meaningful conclusion for the particular problem at hand. Near the end of the book, the author somewhat succeeds to "close the circle", but overall this work leaves much to be desired. In my opinion a great opportunity to explain the book's topic to a general audience was missed.

The author's failed attempt to be cute and clever is very annoying. I guess he wanted to follow the style of Hofstadter, Paulos, Berlinski, and others. The problem is he's just not a good writer.