Just as the US publishers of  Harry Potter and the Philosopher’s Stone  reckoned the US public couldn’t cope with the word ‘philosopher’ and changed the title, this is called Fermat’s Enigma  in the US (it could also be because of another book of the same name by Amir Aczel). But crazy assumptions from publishers apart, it’s the superb story of a bizarre little problem that no one could solve until the ever-wily mathematician Fermat scribbled in a margin that he had a wonderful solution, only there wasn’t room to write it down. Fermat may well have been boasting, but it threw down a gauntlet to hundreds of mathematicians who were to follow until it was finally achieved in the 20th century. Don’t worry if the maths doesn’t interest you – the story will, both in its historical context and in the insight into the work and nature of modern mathematicians. In some ways the star of the book is Andrew Wiles, the British Mathematician who pretty well single-handedly cracked ...

An eloquent plea for reason and the scientific method when the media are pumping unexplained phenomena and X-Files fiction at us all the time. There’s nothing wrong at all with science fiction or fantasy, as long as we are aware that’s what it is – but Sagan points out just how easy it is for us to believe that the ‘truth is out there’ just because we want it to be. Everything from presidents consulting horoscopes to witch burning and miracle cures come under Sagan’s logical but still human eye. Whether your demons are traditional or modern world alien abductors, spirit mediums or faith healers, he painstakingly shows that we are much more likely to invent the supernatural than to experience it for real. Although Sagan goes on a bit, it’s a great counter to wide-eyed acceptance – as useful in business as it is in dealing with the unexplained. The cover asks ‘Are we on the brink of a new Dark Age of irrationality and superstition?’ and it’s a question anyone with an interest in science...

Not in quite the same class as Singh’s definitive  Fermat’s Last Theorem , but still a fascinating survey of the history of code making from the earliest days, through thewartime Enigma machines to the present day complexity of 128 bit encryption. The great thing about the book is probably not the mathematical complexity of modern codes and ciphers but the very human studies of the use and need to transmit secret messages, from the ancient Greeks writing on a messengers bald head, then waiting for the hair to regrow, through the cipher that doomed Mary Queen of Scots to the race to crack the World War II Enigma machines. One of Simon Singh’s great strengths is being able to get across complex principles in a way that the everyday reader doesn’t find intimidating. This shines through in The Code Book I don’t know if recent editions have the rather cringe-making ‘cipher challenge’ in the back – we can but hope this has disappeared by now – but this shouldn’t put anyone off. Wh...

The  book on the most amazing development in mathematics since the introduction of the zero – chaos theory. Has a nice dramatic style that highlights the importance of the people involved in the maths, but can’t detract from the remarkable implications of this fundamentally new understanding of how almost everything really works, rather than the approximations we are used to in science… … at least, that’s certainly the feeling you’ll get when you read the book. But then you take a step back and think, okay, what chaos done for the world since 1987 (or thereabouts) when the book first came out. And you have to say – very little. Chaos is fascinating, but usually turns out to be fundamentally impractical. Does this detract from the book? Not at all. It’s still a fascinating read after all these years, and even if the best chaos can give us is Jeff Goldblum in Jurassic Park it doesn’t cease to intrigue. Paperback:    Using these links earns us commission at no...