Rating: 
Summary: I've been waiting for this book for 30 years!
Review: Prime Obsession is the first truly accesible introduction to the Reimann hypothesis I've ever seen. The author isn't afraid to go through a lot of the details required to understand what's at stake with a sense of assurance, personality and humor that makes this book a true classic in the popular literature of mathematics. I'd put it in a class with Nagel and Newman's wonderful book on Godel's Theorem. Though there is a fair amount of mathematical diligence required, very little advanced mathematical knowledge is needed. The treatment of complex functions, for example, takes some head scratching thought to follow along; but the effort is well rewarded. There is also a good bit of interesting biographical and historical information woven throughout the book, but this clearly takes second place to Darbyshire's -- very succesful in my view -- effort to lay out the basic mathematical plot line of the Reimann hypothesis in relatively complete detail.
Rating: 
Summary: A Pleasing Trip Through a Small Part of Math Land
Review: "This isn't magic. There's a reason this stuff works," my high school math teacher used to say. Of course, there are some contentions, hypotheses, in math where we don't know if they work, if they are true.For professional mathematicians, one of the most important of these is the Riemann Hypothesis. Everlasting fame amongst mathematicians, and, incidentally, a million dollars is waiting for the person who can nail the truth of the "RH" down. Unlike some famous math problems, the gist of the RH is not readily apparent to most non-mathematicians. Derbyshire has to spend some time explaining what is meant by "All non-trivial zeros of the zeta function have real part one-half." And, as someone whose formal math instruction ended with four years of high school math and who reads the very occasional popular math book by Gleick, Peterson, or Paulos, I'm pretty much the target audience Derbyshire pitches that explanation to. The book's style reminded me of the science histories of James Burke. But where Burke's work is a pinball version of history, caroming from person to person, theory to theory, Derbyshire's is a train of mathematical explanation covering the work leading up to, and proceeding from, the RH. Occasionally, Derbyshire stops at some station, pulls up the blind, and looks at some area of tangential interest: famous mathematicians including Gauss, Hilbert, Russell, Dyson, and Turing (who thought RH untrue and attempted to build a computing device to disprove it); German educational reforms of the early 19th century; the Cambridge Five spies; and, most often, since this book is ostensibly a biography of him, the life of Bernhard Riemann. But it's not long before we're back on that math train again. This is not to shortchange the non-math interludes of the book. Derbyshire's quick asides gave me a lot of ideas for further reading. And, if less than half of the book's 422 pages cover Riemann's life, you still get some idea of his protean mind so important not only to mathematics but modern physics. Derbyshire's claim that, if you don't understand the RH after he explains it you never will, seems credible. I won't claim I immediately followed his chain of explanations the first time around. But that had more to do with trying to read this book in 15 minute intervals over a week rather than Derbyshire's prose. Upon reviewing many sections again, things became clearer. The book briefly notes some of the consequences of RH, practical and theoretical. A lot of math is based on the assumption it's true. And the RH may have some mysterious relation to the world of quantum physics. In the commercial and military worlds, where encryption methods based on prime numbers are important, the RH, which has to do with the distribution of primes, may have significant importance if proved true. I think one of the best things about this book is that, briefly, in a simple way, a non-mathematician like me can get some small idea of the excitement mathematicians feel upon discovering some curious pattern in the world of numbers. The only complaint I have with this book is its format. Is it too much to ask that, in the age of computerized typesetting and with an author whose footnotes are all worth reading, that we put those footnotes at the bottom of the relevant page and not at the end of the book?
Rating:
Summary: Zeta functions and a golden key make a great book
Review: Since Andrew Wiles's proof of Fermat's Last Theorem in 1994, the title of 'World's Most Famous and Fascinating Mathematical Problem' belongs to Bernhard Riemann's hypothesis, stated thus - 'All non-trivial zeroes of the zeta function have real part one-half.' In 1859, the 32 year old Riemann was made a corresponding member of the Berlin Academy. Like all such honorees, he presented a paper detailing his current research. Entitled 'On the Number of Prime Numbers Less Than a Given Quantity', it attempted to find a general rule / formula for determining the existence of prime numbers. During his presentation, Riemann made an off-the-cuff comment that has obsessed mathematicians for over a century.
John Derbyshire's 'Prime Obsession' is a history of Riemann, prime numbers, and the great importance of his hypothesis. As I am not a mathematician, I can't say whether math experts will enjoy the book. But I enjoyed it very much, not least because of Mr Derbyshire's wonderful writing. He is an engaging and personable writer, and his mathematical discussions are as clear and precise as anyone could wish. And much of the math is explained in 'real world' terms. Anyone who has taken a calculus course should be fine. The structure of the book is an extension of its subject - the odd-numbered chapters handle the mathematics and the even-numbered ones discuss the history and importance of Riemann's hypothesis, or RH, as Mr Derbyshire terms it. There are detailed graphs and notes, and a fun appendix which features a song about RH. And for anyone who thinks math is boring, there are lots of entertaining mathematicians and anecdotes along the way. You may ask yourself why anyone cares about prime numbers and proving a formula for their prediction. For mathematicians, the sheer joy of tackling an 'impossible' problem is enough. For everyone else, Mr Derbyshire has several answers, ranging from cryptography to quantum mechanics to the computer you're using right now. Riemann's hypothesis casts a shadow in the unlikeliest places. To date, the hypothesis is considered true. No counter-example has been found.... yet. But the search continues and, as further incentive for study, the Clay Institute is offering a million-dollar prize to anyone who proves or disproves it. Mr Derbyshire does not believe the prize will be claimed soon. Work on RH proceeds in fits and starts, with no end in sight. I highly recommend this book, which I picked up on a whim and couldn't put down. I only wish Mr Derbyshire had taught my college math courses. His love of the subject is contagious. I enjoyed Simon Singh's book on Fermat's Last Theorem, but 'Prime Obsession' was even better.
Rating:
Summary: Perfect, for the right reader
Review: An excellent popularization, should serve as a model for how advanced mathematics can be explained to the general public. Derbyshire sets the level of math required right where it should be (assumes the reader got a full dose of high school math but not necessarily anything since then), and his weaving of the historical and mathematical threads is masterful. I have a Ph.D. in math and I learned much more than I expected from the book -- even though there is nothing beyond a tiny bit of calculus, Derbyshire has many fresh ways of looking at standard mathematical material. If you want more of the math, get Harold Edwards's indispensable book "Riemann's Zeta Function" (available as a Dover book).
Rating:
Summary: The greatest problem
Review: This book is probably the greatest work on the subject which is easily accessible to a layman. I think, however, that in order to make this book a pleasant read, you have to know some calculus, and you need to have a good grip on pre-calculus mathematics. The author introduces the mathematical aspects the reader needs to know, but if the reader has learned the necessary math previously, the book will be a much easier read. The reader will also be able to comprehend the mathematical ideas which are usually taught only at the graduate level.
Rating:
Summary: Very good book.
Review: I was hesitant to read this because I know the author's background is in political writing but this is a very well written and thorough book
Rating:
Summary: The best history of the Riemann Hypothesis
Review: There are now three books on the Riemann Hypothesis readily
available for those interested on the history of this
famous problem. Prime Obsession is the book to choose if you
want to see the mathematics involved. John Derbyshire is
a mathematician with a talent for writing so that both the
history and the mathematics are covered well. By cleverly
alternating the chapters with math and history, Derbyshire
lets you decide how you want to read the book. I read Stewart,
Devlin, Gardner, Peterson, and any other writer who explains
mathematics to the public. Mr. Derbysire's book is as good as
it gets.
Rating:
Summary: Excellent Reading for Math and Non-Math Types
Review: Mr. Derbyshire has written an absolutely excellent book on the Riemann hypothesis. The Riemann hypothesis, which relates to prime and complex numbers, has yet to be proved. It is the most famous unproved problem in mathematics. In fact, the first person to prove the Riemann hypothesis will be awarded a large sum of money from the Clay Mathematics Institute. Mr. Derbyshire's book is perfect for folks like me with a mathematics background and also for those who lack formal training but are interested nonetheless. The mathematics are very well explained, and much of the book requires no understanding of mathematics at all. "Prime Obsession" is easily the most accessible book ever written on the Riemann hypothesis. Pure mathematics is more of a mysterious art than a science, and this work serves to illuminate one very important mathematical mystery. This book is on my shelf, and it should be on yours too!
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: A great read!
Review: What an extraordinary book. It's beautifully written, with wit and style, and is a joy to read. Derbyshire provides some wonderful new insight into both mathematics and mathematicians. The mathematically inclined will enjoy the personal stories and historical context he attaches to the famous figures with whom they are only mathematically acquainted.
The proofs and clear and elegantly presented, and lead one down a path toward understanding the beauty and importance of the Riemann Hypothesis.
The highlight of the book for me was the connection he was ultimately able to make with modern physics. If you've ever wondered what pure number theory is really good for, this is the book to read!
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