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*Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics*. Washington, DC: The National Academies Press, 2003.

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"A remarkable book."

-- John F. Nash, Jr., 1994 Nobel Prize Winner in Economics

"...mind-expanding..."

-- Mark Haddon in

"There have been a lot of books and plays about eccentric mathematicians, but Bernhard Riemann blows the stereotype away. He had a quiet family life, was shy, and didn�t go crazy like John Nash. It's nice to read about someone ordinary who was perhaps as bright a mathematician as has ever been. Derbyshire goes into great depth, and the math is quite difficult. If you're interested in it, there it is -- the real equations. But if you're not, you can skip it. This is one of the best mathematical biographies I've read -- and I've read a lot."

-- Jef Raskin in

"...[this book] will reward the effort paid to [it]... the most demanding, and for that reason most rewarding, is probably Derbyshire's."

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"The most detailed, and consequently the most rewarding account of the Riemann Hypothesis is John Derbyshire's

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"John Derbyshire's

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"Mr. Derbyshire's tone is warm and witty, and reading his book, I felt as though he was sitting next to me, guiding my ascent into one of math's more rarefied fields. ... Many people have terror on sight when it comes to the arcane symbols of mathematics, and they might not consider picking up a book about a problem the greatest minds in the world haven't solved. That would be a shame; like any great teacher, John Derbyshire's passion for his subject transforms unfamiliar and difficult material into a genuinely enjoyable and enlightening experience."

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"In

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"For those interested in the mathematics of the Riemann Hypothesis, a background in algebra, geometry, and introductory calculus should be sufficient. But surely most everyone can enjoy Mr. Derbyshire's lucid and informatively anecdotal description of the thinkers who contributed to our understanding of prime numbers. ... John Derbyshire's

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"Alternating between telling Riemann's life story and presenting a mathematical primer on the elements of his hypothesis, Derbyshire elegantly explores a vexing topic."

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"In common with almost all books of this kind, there are parts that you will skim, and which these are will depend on your mathematical background--but the bits you do read will be extremely well explained. A major and most unusual strength of the book, which even experts will enjoy, is a sort of intimacy between the author and the zeta function itself. ... The chapters of Derbyshire's book alternate between mathematical ones and more historical ones, a device that works well."

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"...Riemann and his colleagues come to life as real characters and not just adjectives for conjectures and theorems. ... Parts of

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"The Riemann hypothesis, as Derbyshire shows through approachable examples and colorful quotes from leading mathematicians, has now acquired a life of its own. It is hardly easy to explain, but Derbyshire does his very best. He also takes his time to do so. ... [a] difficult but rewarding book..."

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"Derbyshire's book includes significantly more mathematics than the other [two books on the Riemann Hypothesis], but it is still accessible to anyone comfortable with simple mathematical formulas. The author's goal is to explain Riemann's connection between the primes and the zeros of the zeta function, as well as other important 20th-century mathematical developments. For Derbyshire to have pulled his objective off so successfully is a remarkable achievement. ...for readers who seek a deeper level of understanding of the hypothesis and more biographical details about Riemann, Derbyshire's remarkable book is, in my view, a gem."

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"Derbyshire begins with a riveting account of Riemann's times... I like the historical account, which is well woven and accurate as far as I could check. A fair picture of the problem is presented... Altogether the author has succeeded in writing a very readable and interesting book. The appendix provides a funny song describing the Riemann hypothesis, written by Tom Apostol in 1955. It makes a fitting finish, showing that mathematicians also have a light side."

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"...Derbyshire is a talented expositor determined to make the reader understand some serious mathematics. A general reader with some memory of high school algebra who is willing to concentrate will come away with a grasp of what the problem is and why insiders are excited. Mathematicians in other fields will deepen any superficial understanding they may have, as well as picking up some new ideas on how to explain mathematical ideas. ...Late in his book, Derbyshire ambitiously but successfully unpacks [Riemann's] short and difficult [1859] paper... Explaining from a standing start what the Riemann zeta function and its zeros are in only half a book is not easy, and Derbyshire proves himself a leading mathematical communicator in being able to do it."

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"Derbyshire, a

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"[Derbyshire's] layout is unusual; he uses the odd-numbered chapters for the mathematical story and the even-numbered chapters for the history. This approach works very well -- the difficult technical pieces are interlaced with an entertaining and well-told historical narrative. A less technically inclined reader might concentrate on the history and lightly skim the odd-numbered chapters. On the other hand, the mathematically inclined should not skip the even-numbered chapters -- they tell a good story that should not be missed."

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"Derbyshire attempts to walk the reader slowly up the mathematical slope... the reader willing to work through Derbyshire's presentation will understand something of Riemann's insights."

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"[Derbyshire] has written a wonderful book. He does not fudge the mathematics ...for the most important audience of non-mathematicians--those young ones who might consider

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"This is a striking and brilliant book, in many ways the most ambitious science-for-the-public attempt I have ever read. John Derbyshire undertakes a task which is (we are more or less convinced by the end) impossible, and yet the book succeeds, and at its best it is beautiful. ...the book is compelling ... Derbyshire writes with a novelist's eye and ear, and a novelist's feel for the concrete image, the telling detail, the come-hither sentence."

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"...a historical adventure. Chapters alternate between broad-scale historical accounts and detailed mathematical presentation. ... His historical chapters link mathematical developments to the lives and personalities of the mathematicians involved and are full of interesting stories."

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"Three things help to make this math book accessible. The first is the breezy conversational style. ... The second element that makes this book accessible is its alternating chapters on technical and historical matters. ... Finally, the third factor that makes this book accessible is its numerical examples."

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"[Derbyshire] first takes readers through well-organized mathematical fundamentals in order to give them a good understanding of Riemann's discovery and its consequences. ...an excellent introduction for nonspecialists."

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"...brilliantly written..."

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"...presents more technical details about the hypothesis and will probably attract math recreationists... It requires, however, only a college-prep level of knowledge because of its crystalline explanations."

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"...a wonderfully lucid and captivating explanation and history of the hypothesis and of the life and times of Bernhard Riemann. ...Derbyshire's lively account helps the reader get a 'feel' for the Riemann hypothesis, as well as a good overview of the mathematics."

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"An informative, comprehensive, well written account of the unsolved problem that most mathematicians regard as the most important open problem in the field. Derbyshire not only tells the historical story behind the problem -- the people stuff -- he also includes all the mathematics needed to understand what the problem is about and how people are trying to solve it."

-- Keith Devlin, Stanford University, author of

"John Derbyshire's book has fascinating historical vignettes that link mathematical problem to persons and events."

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"The Riemann Hypothesis is one of the deepest of all unsolved problems in mathematics. Unfortunately it is difficult to state exactly what the hypothesis is. It is high time that someone would write a book explaining the hypothesis in ways understandable by ordinary mathematicians and even by laymen. Three cheers to John Derbyshire for having finally done it."

-- Martin Gardner, "Mathematical Games" columnist for

"John Derbyshire's tour de force

-- Arthur Jaffe, Harvard University

"...a good introduction -- and an infuriating challenge."

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"Every so often I read something mathematical and I fall in love with math all over again. Oh, I'm not that bright, mathematically speaking. ... In any event, I recently bought John Derbyshire's

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"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. ... 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."

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"In

-- Amazon.com

"Riemann's life and work form the subject of John Derbyshire's touching biography

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"...a nice history..."

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