Rating: 
Summary: Complex Math Made Very Understandable and Interesting
Review: Although this book deals with a subject that no-one would sensibly place in a category below "Very Advanced," John Derbyshire treats his subject as well as any math author I've ever read, and I've read a lot of math books over the past 40-some years.My formal math education ended after a standard introductory calculus course as an undergrad. However, I have always been, and remain, extremely interested in math -- a math aficianado if you will. As such, I've self-taught myself a lot of math -- including a lot of very advanced math -- over the past 40 years; ergo, my reading of a great many math books. And without doubt, Derbyshire's book is the finest math book I've yet to read. I suspect Derbyshire started with the hypothesis that his readers are not familiar (or only familiar in a passing sense) with high-level, advanced math, and perhaps might even suffer from math anxiety. Any such readers, however, should have absolutely no fears. Derbyshire's exposition is superb. He clearly defines everything the reader needs to know to grasp AND understand fully the more advanced parts of the book. The book is clearly well designed to convey the information he wants or needs of convey and masterfully explains what would otherwise be quite difficult to understand. Without any doubt this is by far the best book on any advanced and complicated subject -- the best book on ANY math subject (including a book on something as simple as how to add one and one) -- I have ever read. Without sacrificing the complexity of the subject, Derbyshire has written his book in a very readable and interesting manner. And he does all this while making the subject so interesting you can hardly wait for someone to finally prove Riemann's Hypothesis and Riemann's zeta function so we can read Derbyshire's account of that landmark event in the history of mathematics.
Rating:
Summary: Enjoyable even for the specialist
Review: As a math graduate student, I find a lot of "popular" math books rather boring, incorrect or both. "Prime Obsession", however, is not in any of those categories.
The mix of history chapters and math chapters makes it easy for the mathematically inclined to skip some of the easy explanations, and for the math phobic to skip them completely. They are, however, well written and quite enjoyable to read; it can be difficult to grasp the entirety of the Riemann Hypothesis by reading scientific papers, and Derbyshire does a superb job explaining the hypothesis and its importance in mathematics.
The historical and biographical chapters are detailed and very enjoyable to read. The author touches on the greatest figures of modern mathematics, and his respect for all of them, even the most eccentric, is admirable.
This is one of the best non-technical math books I've ever read, and a must (I believe) for anyone contemplating a career in mathematics. It might be best read in high school or early college, but if you missed it then -- it's never too late. I believe it can be enjoyed even after you've seen a lot of stuff.
Rating:
Summary: A very readable book
Review: For some reason, the subject of this book has been very popular recently; I've seen at least 4 books on the Riemann Hypothesis and the distribution of prime numbers in the past year or 2, this among them. I think this book is one of the best of the set.
The author attempts to write the book at a level accessible to someone with a very small background in mathematics, even nearly omitting the use of calculus (though he finds that he cannot totally omit calculus). I can't easily put myself in the place of his intended reader, since my mathematical background is rather better than that, but I still think this book is better at putting a highly abstruse mathematical topic within reach of the general public than most authors can manage.
The book melds history with mathematics, I think quite successfully, giving the reader a chance to learn about some of the people involved as well as learning what interests mathematicians so much about the Riemann hypothesis.
If you are not math-phobic, you might like this book. try it!
Rating: 
Summary: Read this one for the pure entertainment value of it all.
Review: I found this to be a rather delightful book with its arrangement of chapters alternating between historical point of view back to mathematical progress and then back to historical. I found it very entertaining to read about the lives of the great mathematicians involved in developing the prime number theory and furthering the study of the Riemann Hypothesis. Mathematics is littered with such interesting characters that even a liberal arts major can enjoy these expository stories of their lives. The only downside to this whole book is that he takes too much time for the non-math inclined readers to get 'caught up' with their basic skills before he jumps to anything interesting. If you have a background that is strong through calculus, then you could probably avoid reading all the math-based chapters up through the end of the prime number theory section of the book, and you most likely woud not have missed a thing.
Rating:
Summary: Maths for Leisure
Review: I love the way this book was written. If you are looking for a layman's introduction to the various aspects of maths, particularly number theory and analysis, you will not be disappointed. Anecdotes are found all over the book with very interesting historical background of the work that has gone behind trying to prove the RH. The author has cleverly interspersed the historical and mathematical chapters to give a good mix on his writing.
I would have given the book a 5 star if not for the last few chapters of the book which in my opinion, the author was too impatient to end it. He took great pains to introduce readers to series and limits in the front but skip through quite a number of difficult concepts at the back. Those of you who are not too good at calculus may be lost towards the end of the book.
Nevertheless, just reading the historical chapters is already worth your reading time. I must say that at the end of the day, I learnt some new ways of explaining maths concepts and finished the book feeling rather awe-struck and satisfied.
Rating:
Summary: Zeta Function Fun
Review: I was first skeptical that this book was going to be too elementary, with too much history and not enough math. This is not the case as Derbyshire has put together an excellent book covering such topics as Hermitian matrices, the logarithmic integral, and the p-adic numbers among others. It is odd though, since at times Derbyshire will stop to remind the reader of something as simple as "-3 times -3 is 9, not -9." Luckily he will only pause for a sentence and then continue straight on to the more interesting math.
This book builds up to explaining what Riemann showed in his landmark paper where he proposed the hypothesis. This involves deriving the prime counting function in terms of the zeta function zeros. At that point the reader will understand the relevance of the zeros, but not necessarily the importance of the hypothesis which states where to find those zeros. While the hypothesis does put a stronger bound on the prime couting function as Derbushire explains, the main reason to solve it is because it's there. This may be disappointing for some, but the jounrey is well worth it.
I recommend this book for readers who want to learn about the zeta function and have a basic knowledge of number theory and calculus. The combination of math and history was better than I expected, and the book is enlightening in both areas.
Rating: 
Summary: Decent history, but the author never gets to the point.
Review: If you were to write a book about a 400 page book on the Riemann Hypothesis, about what page would you describe why that particular problem is important? Page 5, 10? Well, Derbeyshire weaves in and out of tangents and refuses to get to the point until after 320 pages. While it is obvious he knows what he's talking about, the author does not move to a single point.
He alternates between the history and the mathematics of the Riemann hypothesis chapter by chapter. The history is fun and interesting, but it was hard to see what he was talking about because he never seemed to explain the title of the book, "Prime obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics". Why is the greatest unsolved problem in mathematics? Why is it called Prime obsession when on the surface it looks the formula has nothing to do with prime numbers? He only tells you near the end, giving no context to most of the book.
He utterly fails at the mathematics part. For example, he'll start to get somewhere, but will end up with phrase, "let's first look at...". And he'll explain in annoying detail the most basic, ninth grade mathematics instead of finishing his initial thought. For example, he is about to explain the Zeta function and it seems like he is about to tell you about it, but then suddenly bores you with power rules. You know, the stuff you learned eighth grade. a to X times a to the Y equals a to the (X + Y). He'll bore you with this stuff. This would be fine, if he prefaced every chapter with "if you know this, then skip to...", but he doesn't, so you're stuck sifting through the most basic information to get what you need. Truly annoying.
If you do decide to read this (I hope you don't), and have actually completed high school and some college mathematics, then you should skip all odd chapters, with the following exceptions (pages 43-47, 75-81, 100-105, 216-218, 233-237, 302-310, 327-349). There you go, I saved you immense time and effort. Does this mean that nearly half the book is useless? Yes, useless and tedious.
Rating:
Summary: An author not afraid of the math
Review: In 1859, Bernhard Riemann, one of the greatest mathematicians of his day, wrote a paper about the distribution of prime numbers. In that paper as an incidental remark he wrote, "All non-trivial zeros of the zeta function have real part one-half." Riemann had no proof that this was true but he suspected that it was true based on his intuition and his understanding of prime numbers. For nearly 150 years, mathematicians have been trying to either prove or disprove Riemann's hypothesis.
Writing a book about something as obscure as the zeta function for the non-mathematician is a daunting proposition but John Derbyshire is up to the challenge. In a book on a topic like this, you expect the author to not be afraid to discuss complicated mathematics. By starting off slowly and holding our hands as he moves through the math, Derbyshire makes complex mathematical functions understandable even to someone who hasn't looked at calculus in more than twenty years. So even if non-trivial zeros, natural logs, and prime number distribution theories sound over your head, Derbyshire will explain it in a way that will make it clear and interesting. Derbyshire breaks the book up so that the odd-numbered chapters cover mathematical details and the even-numbered chapters cover historical background of the story. So even if you do get lost in the math, you still can still follow the story which is fascinating in itself.
At the time of writing this review, a possible solution proving the Riemann hypothesis to be true has been produced by Louis de Branges of Purdue University. That makes "Prime Obsession" both fascinating and timely.
Rating:
Summary: The Work of an Accomplished and Clever Teacher
Review: Not only is the author a gifted prose stylist, this book actually had me engrossed in higher mathematics. Face it, though number theory can be beguiling--my introduction was the fine biography of Erdos by Paul Hoffman--many of the recent popular works on mathematics are difficult and too often leave the reader disappointed. To this reviewer, Prime Obsession is every bit as fun to read as the latest pulp fiction but after the story is over, this work leaves the reader with a gift of understanding.
What made Prime Obsession so fun to read was the excellent balance between exposition of the story and exposition of the underlying ideas. This book was not afraid to go deeper into the mathematics than similar works, such as The Music of the Primes by du Sautoy. Derbyshire alternated between chapters of narrative with chapters purely about the underlying mathematics. Not only did the author produce a compelling story but the science was surpassingly well taught--the understanding of the zeta function engendered in the reader adds punch to the story. It is always nice to have at least a little knowledge of what is going on.
Although the typical non-mathematician who chooses to read this book will already appreciate the intellectual achievements of Berhard Riemann, it is the gift of Derbyshire's work that with a reasonable investment of thought any reader can begin to glimpse the beauty and elegance of higher mathematics.
This book was so good that as soon as I finished I ran out and bought "Seeing Calvin Coolidge in a Dream"; frankly, that says it all. This is a must read.
Rating:
Summary: Fascinating book
Review: Prime Obsession is a great book.
John Derbyshire does a great job of taking a most obscure mathematical topic and makes it not only interesting, but also readable.
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