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The Music of the Primes by Marcus du Sautoy, HarperCollins/Fourth Estate, $24.95/£18.99, ISBN 0066210704 Reviewed by Ben Longstaff

MANY of the most beautiful ideas in mathematics have the irresistible appeal of familiar old children’s stories. Even if you know how the plot unfolds, you can’t help listening spellbound until the end. The same charm surrounds the many anecdotes about the lives, triumphs and tragedies of the mathematicians who have unearthed these gems for us – their chance encounters, bizarre wagers, peculiar habits and reassuringly human flaws.

Playing brilliantly with these facets of the subject, Oxford professor Marcus du Sautoy’s The Music of the Primes takes on the story of the greatest unsolved problem in mathematics, an amazing prediction made by the 19th-century pioneer Georg Riemann in his momentous and tantalising paper of 1859. Riemann was a mathematical visionary whose insights into the prime numbers are still being unravelled today. Though the primes seem to be dotted along the stream of numbers at random, Riemann’s masterstroke was to make an inspired guess at the method in nature’s apparent madness. His hypothesis concerns the exact distribution of prime numbers. The world’s best maths brains have been trying to prove him right – or wrong – ever since.

Du Sautoy’s narrative conjures up the characters and their profound ideas with wonderful verve and a poetic gift for explanation. It is enormously entertaining stuff. He also uncovers a staggering depth and richness to the Universe that should leave you in awe.