Infinity. How often do you think about it? I mean really think about the idea that something could go on forever? Have you thought about what the end of the universe might look like? Or whether there is a physical boundary to it? If there is a boundary, what is beyond it? More universes? Are they infinite?

What about the infinitely small? An atom’s radiation, for example, will never completely disperse, it will get smaller and smaller, halving each time while never reaching zero. This too is infinity and so too is a wheel that keeps spinning, unbroken by the things that would cause friction and slow it down. So many ideas behind infinity, it deals with an endless cycle, the infinitely large and the infinitely small and it is no wonder we take it for granted. Sometimes I wonder whether that is a good think; think about mathematical paradoxes a little too much, a little too often and it’s likely to make your head hurt.

That is why Barrow has written this fascinating book. It makes us really think about the concept of infinity and appreciate it’s place in the making of human civilisation – from mathematics and science to art and culture, the infinite has baffled us, well, um, infinitely. Since human civilisation first devised counting, we must have wondered whether their could be an upper limit. The answer is, of course, no but that hasn’t stopped people asking the question to begin with. All we need to do is add 1 to largest number we can think of and we have an even larger number. Infinity goes on forever.

This is the story of infinity, rather like an autobiography if a concept could have such a thing, from the height of the middle ages and the golden age of mathematics, this book is as practical as it is theoretical. It presents paradoxes to ponder and concepts to chew over. Sometimes, it gets quite heavy but the author tackles them in a way that doesn’t / shouldn’t put people off.

In many ways, it is not an easy read. You won’t need a background in physics but if you hated the subject or are one of those people who avoids popular science likes the plague, you may struggle through this. Try to stick with it though, because it is well written and engaging and you might just learn something.