April 29, 2003
Prime numbers are the atoms of arithmetic, the building blocks for all other numbers. In school, we are taught that a prime is one that cannot be divided evenly by any other number except one and itself. What we are not taught is that primes represent the most tantalizing mystery in the pursuit of human knowledge. How can one predict when the next prime number will occur? Is there a formula that could generate primes? Where is the pattern behind these elusive numbers? These questions have formed a riddle that has confounded mathematicians since the ancient Greeks. The answer would revolutionize the world of math, and much more.
Nearly 150 years ago, a German mathematician named Bernard Riemann came as close as anyone has ever come to solving this problem. In 1859 he presented a paper on the subject of prime numbers to the Berlin Academy. At the heart of his presentation was an idea – a hypothesis – that seems to reveal a magical harmony between primes and other numbers. It was an idea that Riemann argued was very likely to be true. But after his death, his housekeeper burned all of his personal papers, and to this day, no one knows whether he ever found the proof.
By now, the Riemann Hypothesis has become the number one obsession for the world’s leading mathematicians. Considered to be even more difficult and more important than Fermat’s Last Theorem, Riemann’s solution would serve as a periodic table in charting the entire mathematical universe. But it has implications that go far beyond math. It is of tremendous importance in business, since prime numbers are the linchpin for security in banking and e-commerce. It is also the idea that brings together vastly different areas of science, with critical ramifications for Quantum Mechanics, Chaos Theory, and the future of computing. Pioneers in each of these fields are racing to crack the code, and a prize of one million dollars has been offered to the winner.
In this remarkable book, Marcus du Sautoy tells a story of eccentric and brilliant men, and of the unquenchable thirst for knowledge that has driven some to madness and others to glory. Illuminating, authoritative, and extremely engaging, The Music of the Primes provides the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.
Marcus du Sautoy is a professor of mathematics at the University of Oxford and a research fellow at the Royal Society. A frequent contributor on mathematics to The Times and BBC radio, he lives in London.