Michael Shermer is probably best known as Scientific American ’s resident sceptic – a man who has what seems the wickedly enjoyable job of going around finding fault with other people’s beliefs – a sort of modern day court jester without (presumably – I’ve never seen him) the funny costume and bells. In this classic, originally published in 1997 but reviewed in a new UK edition, he gives a powerful argument for taking the sceptical viewpoint. Although along the same lines as Carl Sagan’s  The Demon Haunted World ,  this book works alongside Sagan’s masterpiece, rather than competing with it. It focuses more on why we believe strange things, and also very usefully expands out from the paranormal and pseudoscience to include pseudohistory, a topic I hadn’t even realized existed. Shermer is something of a convert to scepticism, so has a convert’s fervour, but none of the unpleasant aggressiveness of the likes of Randi and Dawkins. Instead he gently shows us how strange ...

An autobiography by as big a name in science as James Watson, one of the discoverers of the structure of DNA, is one of those rare moments that perhaps can be over-anticipated to the point of disappointment when it arrives. Sadly, this was the case with  Avoid Boring People . It covers the period from his birth to the mid 1970s, but does so in a strangely detached, rather affected style. You never get the feeling that you are seeing the real person, but rather a dim view into the past through fogged lenses. As is often the case the early family history is a bit dull, but things liven up when Watson gets to school – but rather than soaring from here, it’s only certain little areas, such as political battles at Harvard, that shine through with any great brilliance. Perhaps most surprising is the almost summary approach to the DNA work. One suspects that Watson thinks it has all been done before – not least in his own  The Double Helix , written when he was much younger...

This is one of the very few books we have been unable to give a straightforward star rating. The reason is that it has been important to separate the idea and the execution. More on this later. A Certain Ambiguity  is a novel, but a novel with the explicit intention of putting across information about mathematics. This might seem a very new thing to do, but in fact has plenty of historical precedent. For example, when Galileo wrote his two great books, they were in the form of dialogues between fictional characters. Of course they weren’t novels – the novel form didn’t exist – but they did make use of human discussion to help get across complex points to a more general reader. In A Certain Ambiguity we meet Ravi Kapoor who travels from India to America to further his education, and finds himself increasingly fascinated by both maths and his grandfather, who was a mathematician and had been in the US himself. The storyline interwines Ravi’s experience at college with a gradual ...