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Dr Riemann鈥檚 Zeros by Karl Sabbagh, Atlantic Books, 拢14.99, ISBN 1843541009 Reviewed by Roy Herbert

THERE is a story of a woman on a train who was intrigued by a fellow passenger reading a book and laughing out loud from time to time. He left his seat and the book behind. She snatched the chance to look at it. It was page after page of calculations. She concluded that it was best to find another seat.

Karl Sabbagh鈥檚 book aims to show that mathematicians are human. His central topic is Riemann鈥檚 hypothesis, a famous and intractable problem that has been keeping mathematicians鈥� brows knitted for about 150 years. It concerns the distribution of prime numbers 鈥� those that can be divided only by 1 and themselves: 2, 3, 5, 7, 11 and so on. There are strange features to their pattern of occurrence, tantalising prospects of finding an order that can allow them to be predicted, but which is always beyond reach.

There鈥檚 a million dollars waiting for anyone who can find and prove a solution to Riemann鈥檚 hypothesis. Every now and then someone announces the latest huge number that has been found to be a prime, but the hypothesis itself remains unproven, a mathematical lure of obsessional attraction. Sabbagh packs around the story a discussion of the properties of numbers that fascinate the indefatigable solution seekers, their work and personalities 鈥� satisfyingly eccentric in many instances. Whether this is enough to carry an ordinary reader through is hard to decide. It is certainly worth a try and there is an excellent section called 鈥淭oolkits鈥� to help anyone who is rusty on the basics.