The Riemann Hypothesis

This is not the book to learn much of the technicalities of the problem. But if you are interested in the human stories around it, this is a great book.

a good introduction for this subject.

Leaves the reader somewhat disappointed.I picked up this book with great expectations, having read the publisher's publicity. To be frank, I was left disappointed. The book tells the reader very little about the wonderful and mysterious character of the Riemann hypothesis and leaves both mathematical novices and those who know about the intricacies of higher Mathematics dissatisfied. This is indeed a pity!Having said this, Mr Sabbagh's story is eminently readable and enlightening. The book has many sections that are in effect a diary of the conversations with various Mathematicians. These give an insight into the thought processes, passions, motivations, and rivalries that exist in the select community of Number Theorists. The pen portraits of the main protagonists is quite interesting even though it sheds little light on the character of the Riemann hypothesis and how it enthralls those working on its proof.The toolkits covering a set of brief synopsis of Infinite series and the Euler identity should be useful to the lay (but Mathematically capable) reader, but the appendix on the De Brandes proof is rather obscure.Overall, an OK book if the reader wants a gentle introduction to the subject and act clever in passing conversation at parties, but, sadly, this book fails to educate and enlighten in the real sense!

I think potential readers of this intriguing book need to bear in mind the following: (1) you do not need to understand Riemann's hypothesis to enjoy this book and (2) Mr. Sabbagh does a very fine job of outlining Riemann's hypothesis in layman's terms. Riemann's hypothesis is not easily grasped; what Sabbagh wants to do is to enhance your understanding of it. There is no pretense here that the hypothesis in all its complexity is being conveyed. In fact, near the book's end, he concedes that "you know almost nothing [about R's hypothesis] compared to what there is to know. The hypothesis itself is an outcome of Riemann's zeta function which is the sum of the series 1 + 1/2^s +1/3^s...1/n^s, which means 1 + 1/2^a+ib + 1/3^a+ib (where i is an imaginary number). All sorts of values are possible, but the values of interest center on the Riemann zeta function when it becomes zero. These zeroes, as its turns out, fall on what is known as the "critical strip" and their graph is linked to the fluctation of the primes, which are themselves the building blocks for all the other numbers. The hypothesis is that all the "significant" zeroes line on the critical strip. The proof has become the Mount Everest of mathematics, but it remains unscaled. Many mathematicians, who perhaps found the hypothesis disarmingly approachable, have died before reaching the summit.Sabbagh does want you to understand the hypothesis, but he is also trying to delve into the community of mathematicians generally -- what they are like as people -- in an effort to make them more accessible as well. Inevitably, in this area, Sabbagh often reads like an anthropologist documenting the ritualistic "abnormalities" of some primitive Amazonian sub-culture. What I found surprising is not that Sabbagh finds that the thought processes of mathematicians rarely intersect with that of non-mathematicians; rather what I found striking were the similarities with the "rest of us." They can be collaborative yet guarded, brave yet insecure, intuitive but distrustful of intuition. Several he finds are lousy at simple computations (but brilliant on abstractions). They are a colorful lot, but they are not high IQ aliens from another world. The portrait of Louis de Branges is especially fascinating and forms a strong sub-plot within Sabbagh's text.I don't plow through many books like this, but I do recommend The Riemann Hypothesis. Like Sarah Flannery's "In Code" (which has an excellent chapter on prime numbers), The Riemann Hypothesis is suited for, and ought to be attractive to a wide audience.

good book

As a math hobbyist, I've been very eager to learn more about the Riemann Hypothesis. I ordered this book a couple weks ago, and fell ill this week -- so I had some time to spend reading.I didn't get very far before I found a rather glaring error. On page eighteen, the author explains one method for showing that there's no largest prime number. He asserts that:(2 * 3 * 5 * 7 * 11 * 13 * 17 + 1) / 7is equal to2 * 3 * 5 * 7 * 11 * 13 * 17 + (1/7)which is not correct. The left-hand term actually evaluates to2 * 3 * 5 * 11 * 13 * 17 + (1/7).Maybe I'll revise my review after I read more; perhaps the book really does deserve my trust. But after an early blunder like this in a simple topic, maybe I won't read any further.Less astute readers might not have caught this and later become confused. Maybe, in the deeper topics, I won't be able to proof the text and become confused or disillusioned by other errors.

Though the subject matter itself is interesting, Sabbagh's treatment of it is not to my liking and is hampered by several glaring errors in arithmetic which also showcase inadequate proofreading. In addition - and I'm almost shocked to have to say this of a book published in 2004 - the typography is of very poor quality. In many cases, it's bad enough to render equations (especially ones containing superscripts or subscripts) unreadable. The text looks to me like the result of 1960s-era phototypesetting, not the digital typography I'd expect from a technical book published in the last 35 years.

In this tome about one of the most celebrated conjectures in Mathematics today, there are actually more words attributed to some person not fathoming why the multiplication of two negative numbers yields a positive number than there are to Andrew Wiles and Fermat's Last Theorem. The author spends far too much time on basic concepts while ignoring the major aspects of the Riemann Hypothesis theory. If I wanted basic concepts, I would have read other books. Consequently, this book turns out to be a real disappointment. I returned my copy back to Amazon and instead ordered Prime Obsession. You will learn a lot more from Prime Obsession!