Monday, February 23, 2009

Prime Obsession

Book Review : Prime Obsession
Author : John Derbyshire
My rating : 5 out of 5 stars

Don't get deceived by the shortened title - this is not a B-grade movie. The complete title of the book is "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics".

The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It was one of the problems in Hilbert's list and today carries a prize of one million dollars for proving it. Now that Fermat's Last Theorem has been proved, maybe this is the greatest unsolved problems in math as the title says. But the problem (NOT the solution) posed by Fermat's last theorem is very simple to understand. The Riemann Hypothesis is quite another story.

I am no mathematician. So I do not even understand what it means when I read "All non-trivial zeros of the zeta function have real part one-half." Much less the deep relationship about the distribution of primes. That's where John Derbyshire's book comes in. It does a fabulous job of explaining what the heck that means and why is it even related to the prime numbers.

There is a lot more to like in this book than just that. It may seem impossible, but this book about math reads like a gripping mystery novel and is as much a page turner as any fiction I have read. I simply could not put it down. I found myself reading this late into night and getting up early the next morning, looking forward to continue reading. For a book to do that - especially when it is about an intricate mathematical conjecture - is truly amazing.

The book is presented in an interesting format. It is as much about the actual mathematics around the hypothesis as it is about the history, story and lives of the mathematicians who have worked on the Prime Number Theorem. So Derbyshire neatly divides the math and history in alternate chapters. Anyone who does not have enough inclination to go through the mathematical material can simply skip alternate chapters and still enjoy the book. But I would not advice doing that even though the math is quite involved. You need some math background and willingness to work on it. But Derbyshire starts from very basic concepts in algebra. Even if you have forgotten some simple stuff like logarithms, he walks you through it. Taking one step at a time. For anyone who used to love math, the efforts will be handsomely rewarded. And believe me - it is this series of mathematical chapters that reads like a hard-to-put-down novel.

The historical chapters are amazing as well. The book introduces the reader about the lives and times of Euler, Gauss, Hardy, Hilbert and many other mathematicians including of course Riemann. This series of chapters is very moving because the author's obvious affection for the great mathematicians and passion for explaining their achievements.

I highly recommend this book. There are a lot of good books that explain high level physics to a layman. Math is completely abstract. Hence more difficult to explain. Derbyshire took on a very ambitious project. It's one thing to talk about the number pi - but making Riemann Hypothesis accessible to a layman is a great achievement. It deserves a place on any list of "must read" books.

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