Since its inception by Bernhard Riemann in 1859, every pure mathematician has longed for a proof for the Riemann hypothesis. So great is the interest in its solution that in 2001, an American foundation put up prize money of US$1 million to the first person the demonstrate that the hypothesis is correct. The Riemann hypothesis refers to prime numbers -- those that cannot be divided by any whole number except 1 (for example: 2, 3, 5, 7, 11, 13, 17, 19, 23...). For example, 19cannot be split into smaller whole numbers, in the way that an atom cannot be split into smaller atoms. Riemann's hypothesis seeks to explain where every single prime to infinity will occur. It is a mind-bending problem that encapsulates a profound mystery at the heart of our counting system, one that mathematicians speak about in awed terms. Karl Sabbagh's glorious, highly inventive book makes even the airiest peaks of maths accessible. He uses anecdotes, history and jokes and makes vivid characters out of the eccentric figures racing to solve the problem. His triumphant book, in the end, is a brilliant explanation of numbers and a profound meditation on the ultimate meaning of mathematics.