Marcus du Sautoy's The Music of the Spheres is a difficult, enlightening and enjoyable read. Because of the abstract nature of mathematics, some of the concepts might be difficult to understand on first reading. But careful reading will be rewarded with du Sautoy's infectious excitement about the nature of math, discovery and human obsession. Some readers may not share du Sautoy's passion for math, but lovers of mathematics, science, puzzles, and nature will find the book hard to put down.

From prehistoric man through ancient Greecian times on into modern times, all through the world the elusive prime numbers have fascinated certain minds. Faced with the problem of determining when the next prime number will occur, many scientists have locked themselves in rooms, figuring, calculating, making logical moves or intuitive leaps. For those of us not particularly enamoured of math, all this excitement seems like a tempest in a teapot. But we are probably unaware of the practical applications of primes in encryption, security, credit card use etc. Nor are we aware of the cosmically patterned way in which various kinds of number patterns – the triangular numbers, the Fibonnaci numbers, the golden ration, the primes – echo eerily, elegantly and orderly throughout the physical world. In short, the ubiquitous nature of patterns and math in science can bring a smile of awe to both the logical and the spiritual mind.

Du Sautoy gives his readers a history of an obsession, particularly the mathematical fever known as the obsession with Riemann's hypothesis. (Hypotheses, conjectures and theorems abound in science.) The problem for these mathematics is to turn the Riemann Hypothesis into the Riemann Theorem. And to do that a proof is needed.

The Riemann Hypothesis deals with one of the longest unsolved math puzzles, the question of how to predict – in an elegant mathematical proof – when prime numbers will occur. A prime number is a number that is not divisible by any other number, i.e. 2, 3, 5, 7, 11. One might think that primes would decrease after a while, but primes seem to go on into infinity (but the question of infinity is another mathematical question). The answer has not been found as yet but mathematicians along the way have come up with other discoveries that touch on the strange qualities of primes. There will probably be more discoveries with the advance of quantum physics, music, computers and chaos theory – and with the mathematical belief that proofs and patterns are there waiting to be discovered and realized.

Of course, natural discoveries are always amazing, "Eureka!" kinds of things. Something that has been there all the time is suddenly seen through hard work, intuitive leaps, new sciences, lateral thinking or new ways of thinking. Discoveries are made on the backs of other discoveries. Du Sautoy's excitement about math comes from his conviction that the discoveries in mathematics are unlike those of other sciences. In mathematics, each generation "builds on the achievement of the last without fear of collapse." In the future, du Sautoy says, chemists might have to re-do and reassess the periodic table of elements, when new discoveries further question the "elemental" structures of atoms, quarks, et al. But the number one will always lead to the number two which will always lead ....well, you get the picture.

Mathematics is also something which (and this is where philosophers have a problem with pure mathematics) exists outside the mind. It is a kind of absolute truth that corresponding elements in nature and the universe continually reaffirm. In short, it is orderly and almost theological in its omnipresence, unsearchability, depth, subtlety, elegance "foresight" and beauty. Yes, we're talking about math here.

Du Sautoy's research is copious and panoramic. Weaving in historical accounts and diagrams, he shows his reader the history and concepts behind the obsession with primes. Along the way, we nibble on tasty little historical gems and pick up fun and intriguing mathematical facts. For instance, eight perfect shuffles of a card deck will bring the card pack back to its original order, and certain cicadas have developed reproductive time cycles based on prime numbers. And who would have guessed that there are musical resonances – pattern drums, the mathematicians call them – to everything from DNA to astronomy.

But this story is primarily about the obsessed men and women with one thing on their minds. Primes have changed the world, of course, and been practical in many ways. The Music of the Primes shows us the power of certain numbers and their mark on history. Many concepts have appeared because of the search for primes, specifically Riemann's use of imaginary numbers and imaginary mirrors, a hypothesis which still needs to be seen in a perfectly elegant, human, non-computerized proof. No doubt, the proof will come. And when it comes, it will not only be elegantly beautiful, but simple. And it will open new views onto previously unseen vistas.