In 1859, Bernhard Riemann, one of the greatest mathematicians of his day, wrote a paper about the distribution of prime numbers. In that paper as an incidental remark he wrote, "All non-trivial zeros of the zeta function have real part one-half." Riemann had no proof that this was true but he suspected that it was true based on his intuition and his understanding of prime numbers. For nearly 150 years, mathematicians have been trying to either prove or disprove Riemann's hypothesis.
Writing a book about something as obscure as the zeta function for the non-mathematician is a daunting proposition but John Derbyshire is up to the challenge. In a book on a topic like this, you expect the author to not be afraid to discuss complicated mathematics. By starting off slowly and holding our hands as he moves through the math, Derbyshire makes complex mathematical functions understandable even to someone who hasn't looked at calculus in more than twenty years. So even if non-trivial zeros, natural logs, and prime number distribution theories sound over your head, Derbyshire will explain it in a way that will make it clear and interesting. Derbyshire breaks the book up so that the odd-numbered chapters cover mathematical details and the even-numbered chapters cover historical background of the story. So even if you do get lost in the math, you still can still follow the story which is fascinating in itself.
At the time of writing this review, a possible solution proving the Riemann hypothesis to be true has been produced by Louis de Branges of Purdue University. That makes "Prime Obsession" both fascinating and timely.
This earned 5 stars on Amazon. The book is published by Joseph Henry Press.
The review can be seen on Amazon on My Amazon Reviews page.