[.ca] Prime Obsession: Bernhard Riemann & the Greatest ... (ISBN 0309085497)

From Amazon.com:
Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself parses as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae. In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. --Therese Littleton

Complex Math Made Very Understandable and Interesting:
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.

splendid (though heavy math):
This book should be the first one to appear in Amazon's listings for the Riemann Hypothesis, yet doesn't even appear in the top ten. It gives fascinating historical background to a very real Riemann and his friends, traces developments to the present day in a conversational tone, and somehow manages to take the reader through the details of what the RH says so that you actually understand it. Recommended with one reservation; to understand the chapters (every other one) which bring one to understand the RH, you will need to make a considerable investment in reading and rereading to make it. That is not for the faint of heart. However, the other half of the book can be enjoyed by anyone who likes general science history books.

What a piece of work a man is!:
"Prime Obsession" is a fascinating book for several reasons: the author explains a difficult topic with such clarity that it's simply amazing. For those who are more skilled in math, this book would also be very enjoyable to read, except that they might find some of his explanations redundant because he really assumes that the we don't know anything (and I mean anything!). Mr. Derbyshire obviously understands the topic quite well himself. He has written an amazing book for everyone to enjoy. 200 years since Riemann first presented the problem, we are still desperately trying to solve it, and one day, you never know... what a piece of work a man is!

Good overview:
This book accomplishes two things very well. It explains the history behind the Riemann Hypothesis and also the relevant mathematics. I like how the author structured the book and also how he simplified the math somewhat. However, the math contained in this book can be challenging if you don't have any background. I would recommend a basic understanding of calculus if you want to understand the math. However, the math is kept separate from the history, so if you just want a historical overview, then this book will also work well. I recommend this book to anyone interested in math and math history.

An Excellent Read, Highly Recommended:
Prime Obsession is an excellent popularization of the Riemann Hypothesis. I found John Derbyshire's presentation of the math to be very approachable by non-mathematicians like myself. It's taken slow, one basic step at a time, and spread across a well written and fascinating history of Bernhard Riemann and other key players. Simply put, you do not need an advance degree in mathematics to enjoy this book. My math bakground is limited to 2 semesters of calculus 20 years ago and I haven't used it since. For me, John Derbyshire's approach was both refreshing and entertaining. If you've got even the faintest interest in math, you will find this book rewarding.