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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

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Author: John Derbyshire
Publisher: Plume Books
Category: Book

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Rating: 5.0 out of 5 stars

12 reviews
Sales Rank: 5685

Media: Paperback
Edition: Reprint
Number Of Items: 1
Pages: 448
Shipping Weight (lbs): 0.8
Dimensions (in): 8 x 5.5 x 1

ISBN: 0452285259
Dewey Decimal Number: 512.73
EAN: 9780452285255
ASIN: 0452285259

Publication Date: May 2004
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Also Available In:

•	Hardcover - Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

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Editorial Reviews:

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, Andre 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

Customer Reviews: Read 7 more reviews...

5 out of 5 stars

A popularisation the focuses on the actual mathematics January 5, 2008
2 out of 2 found this review helpful

Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.

This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.

No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical.

5 out of 5 stars

Do not buy any others April 12, 2007
13 out of 13 found this review helpful

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.
It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so 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: 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 is because of the techniques that Riemann invented in his paper.

Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it.

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.

5 out of 5 stars

A fabulous read January 19, 2005
33 out of 36 found this review helpful

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!

5 out of 5 stars

Riemann Hypothesis December 4, 2004
14 out of 16 found this review helpful

This book by John Derbyshire is absolutely fantastic. Giving a thorough insight into the history of Riemann, and mathematics for that matter, provides the reader with a fuller knowledge before the author tries to smash through the hypothesis bit by bit. Breaking down the ideas mathematicians have developed over the past 140 years in trying to solve this greatest 'unsolved' problem in mathematics, Derbyshire gives the reader the feeling that Riemann truly was a fantastic mathematician and his innovative ideas are truly unique. The proof in which is that this hypothesis is still today unsolved. If you want a book about this complex hypothesis, I reccomend this. Easily illustrated and not too difficult to understand, Derbyshire makes this hypothesis seem so trivial in complexity and worthiness to the lay mathematician, yet to those with a keener knowledge this book relays the hidden answers beautifully.

5 out of 5 stars

Prime Obssesion - prime choice! September 15, 2004
12 out of 15 found this review helpful

This an excellent book. It discusses the history of, and background to, the intractable problem of understanding the distribution of prime numbers. In doing this the author draws upon the cultural, educational and political events that were intimately related to the zeta function and the mathematicians involved with it. I found this book utterly compelling and I was particularly delighted by the author's drawing together of broader European historical events in a non-trivial way. It was astonishing to read of the political and educational reforms of tsarist Russia and their repercussions for European education today.

The mathematical discussion is remarkably lucid. Only in a couple of places did I feel that the author was asking the reader to take on trust his arguments. Occasionally I tripped over the writing style, but the story being told was so compelling that this hardly mattered.

Anyone who is interested in an holistic approach to our cultural development should be delighted by this book.