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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Hardcover – 15 Apr 2003

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Product details

  • Hardcover: 448 pages
  • Publisher: Henry (Joseph) Press (15 April 2003)
  • Language: English
  • ISBN-10: 0309085497
  • ISBN-13: 979-0309085495
  • Product Dimensions: 22.8 x 14.8 x 3.1 cm
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (47 customer reviews)
  • Amazon Bestsellers Rank: 730,474 in Books (See Top 100 in Books)

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Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to discover one of the greatest problems in mathematics. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem, which was to find proof of the conjecture "all non-trivial zeros of the zeta function have real part one-half".

That statement may be nonsense to anyone but a mathematician but Derbyshire walks the reader through the decades of reasoning that led to the Riemann Hypothesis in a way that makes it perfectly clear. Riemann never proved the statement and it remains unsolved to this day.

Prime Obsession offers alternating chapters of step-by-step maths 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 and allows 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, GH 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,

About the Author

John Derbyshire

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First Sentence
In August 1859, Bernhard Riemann was made a corresponding member of the Berlin Academy, a great honor for a young mathematician (he was 32). Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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49 of 49 people found the following review helpful By Andrew Hanna on 19 May 2003
Format: Hardcover
Prime Obsession, is a wonderful book based on the history and insight of the brilliant mathematician, Bernhard Riemann. As the title suggests, the main aim of the book is to give the reader a clear and understandable definition of what the Riemann Hypothesis actually is. To do this, Derbyshire has structured the book so the reader is given a chapter of mathematical tools, followed by a chapter of the history of Riemann and other great mathematicians, such as Gauss, Euler, Hardy, followed by a math chapter etc... However, don't let the math sections put you off this book, as Derbyshire explains, he uses minimal calculus to get the reader through the book. He takes the reader though basic analysis, then onto prime numbers, domain streching, followed by what he calls the Golden Key which uses the Euler product. Then he introduces basic complex number theory, and finally he pulls them all together to start to explain the RH (Riemann Hypothesis). Riemanns ideas and visualizations of complex functions are difficult to comprehend for even the most accomplished mathematician, but Derbyshire employs a method that any lay person can understand perfectly, using his "Argument Ant". Any person interested in mathematics, should read this book, as it serves as a wonderful insight into one of the greatest mathematicians, and problems that has ever existed. And for those who are just interested in the RH but were never quite sure where the zeros come from, then the chapter on domain streching and subsequent chapters will make it all clear. This is the best popular science book I have read since Feynmans "QED: The strange theory of light and matter".
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43 of 43 people found the following review helpful By Hamptonshirewonder on 13 April 2007
Format: Paperback Verified Purchase
I have read this book and two of the other three popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.

"Prime obsession" emphasises the centrality of the other parts of Riemann's paper apart from the famous Hypothesis. By doing this it helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous Hypothesis. The Prime Number Theorem states, roughly that: as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason the Prime Number Theorem could be proved, irrespective of Riemann's Hypothesis' truth, is because of the techniques that Riemann invented in his 1859 paper.

Riemann's starting point was to generalise Euler's formula which relates the sum of the reciprocals of natural numbers:


to the product of the inverses of the prime numbers


Derbyshire's explanation is far clearer and much easier to follow than those in the other popularisations.

This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.
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20 of 21 people found the following review helpful By Simon Pollack on 18 Dec 2008
Format: Paperback
I am a bit of a junkie for books on maths, revisiting my degree of 15-20 years ago. The quality varies a lot though and I am very often disappointed. This I supose is not surprising: I want not to be patronised but I also want accessibility, context (historical, personal), and some insight into the underlying beauty of the mathematics in question. But this book pushes all the right buttons.

The Riemann Hypothesis is really quite advanced - you wouldn't find much in-depth study of it in any compulsory modules of undergraduate courses. But Derbyshire brings it to life. The book is challenging but accessible, and ultimately a very fulfilling read.

I think the key to his success is the interleaving of chapters on the lives of the protagonists with those on the maths leading up to and surrounding the Hypothesis. Because an understanding of the relevant mathematics helps understand the importance of a given mathematician's life, and an understanding of historical context helps bring the maths to life, these chapters are mutually reinforcing. As such the whole is greater than the sum of the parts (I think I might just have found that 1+1>2). And because so many of the great mathematicians contributed to the foundations of number theory and analysis, and many subsequently worked on the Riemann Hypothesis itself, this book kind of doubles as a selective history of modern (from Newton) mathematics.

I can't recommend this book enough. Even for those with no background in maths, but with an enquiring spirit, there is enough here (crucially, without turgidity) to dimly comprehend the profound beauty and true mystery of maths. It makes you believe somehow in the Platonic Ideals and that those blessed with true insight get closer to them than the rest of us.
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