Prime Obsession

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.

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A class of its own - Rated
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. I have always felt that advanced pure mathematics is as worthy an art as painting or sculpture, and the great mathematicians as worthy artists as Van Gogh etc. But because of the inaccessibility of the subject matter to the layman this great art couldn't be widely-enough shared. With more books like Prime Obsession this wrong will be righted.

Challenging, but worth it - Rated
The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate:

"Has anyone proved the Riemann Hypothesis?"

Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis.

Interesting - Rated
I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though.

A popularisation the focuses on the actual mathematics - Rated
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.

Do not buy any others - Rated
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.