author : James R. Newman

I have always had a soft spot for this book: it was what made me excited about mathematics. Back in the dimly-remembered mists of the early 70s -- I was about 14 -- my maths teacher lent me his copy, and it just blew my mind. For the first time I realised there was more to maths than the, admittedly interesting, but rather uninspiring, topics in our school text books. I certainly didn't understand all of what I was reading at the time, but it let me glimpse exotic and fascinating lands, and I wanted to find out more. (I don't suppose I could honestly claim to understand all of it even now -- the Banach-Tarski paradox, for example, still gives me a headache!) I believe it is important occasionally to read things one doesn't understand -- it broadens horizons, and stimulates the mental taste buds with something a bit spicier than the usual predigested pap. (But it is also important to realise that that one doesn't understand it, rather than to integrate it as a load of gobbeldygook into one's world model -- that way lies crank science.)

In retrospect, this is just one of the early popular maths book. Topics include large numbers (introducing the googol), infinities, probability, non-Euclidean geometry, calculus, topology, mathematical games -- all with an emphasis on the weird and paradoxical. There is even a section on fractal curves (not yet called that, of course). The 1940s academic prose style may seem a little precious now, but there is some very deep stuff indeed in here, and it's still well worth a read, whether you are 14, or rather older!