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Product Details

• Amazon Sales Rank: #14293 in Books
• Published on: 2004-05-01
• Original language: English
• Number of items: 1
• Binding: Paperback
• 448 pages

Amazon.co.uk Review
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, Amazon.com

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Customer Reviews

The Greatest Unsolved Mathematical Problem
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".

Do not buy any others
I have read this book and one of the other two 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:

1+1/2+1/3+1/4+...

to the product of the inverses of the prime numbers

(1/2)*(1/3)*(1/5)*(1/7)*(1/11)*.....

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.

This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.

I cannot do more than endorse the other reviewers' praise for this classic-to-be.

A fabulous read
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it!