The Music of the Primes

This is a homage to mathematics, and in particular to that mysterious elite of maths known as prime numbers - for the uninitiated, whole numbers that cannot be divided exactly by two smaller numbers: 2, 3, 5 and 7 to 1,000,039 and beyond. It has to be said that if you don't already know what a prime number is, you may be baffled by large chunks of this work - written by an eminent mathematician who does have a tendency to assume readers won't be thrown by statements such as, 'Fermat had been right in his claim that the equation x^n + y^n = z^n has no solutions when n is bigger than 2.'Yet that would be a pity, because this is a fascinating work capable of offering at least a glimpse into the magical parallel universe of people who talk like that. Mathematicians are often regarded as arrogant because, according to du Sautoy, their subject has a permanence resting on the certainty of proof. Unlike scientific hypotheses, which may be moderated by new evidence or discarded altogether, mathematical proof is forever - what the ancient Greeks established about maths remains true today. So the great names of mathematics march through these pages with their reputations forever intact, never to be overruled by mathematicians of the future. And from Greeks onwards, mathematicians have been fascinated by primes. The problem is this. Primes get fewer the higher you count. There is no way of predicting the next prime to come. Yet there is no limit to the number of primes, as various intriguing thought experiments herein demonstrate. And it matters because the potential significance of primes is immense. This is a natural language - there is a species of cicada which emerges only every 17 years (17 is prime), presumably to avoid potential predators working to non-prime cycles. It has resonances with problems in particle physics, and immense practical application - computer security relies on primes, and without them modern business would collapse. And primes are a potential universal, intergalactic language - if we are ever to communicate with aliens, primes could well form the vocabulary for making contact. So mathematics' ultimate accolade will pass to the person who solves its most difficult outstanding problem: to understand how primes are distributed throughout the universe of numbers; to prove the Riemann hypothesis which proposes that there is harmony in this apparent sea of randomness. And the remarkable thing about this book, if you read it, is that if and when the discovery occurs - with who knows what ramifications for our future - you will want to know all about it. (Kirkus UK)