Brian Clegg – Infinity, the Quest to Think the Unthinkable.

The concept of infinity is one of those slightly misunderstood scientific ideas. Everyone thinks they know what it means, but Brian Clegg's book is about showing that the concept itself has had a complex history. For children, “infinity is the biggest number there is”, I remember being very young and announcing to bemused parents that I was going to “count to infinity”.

Clegg's examination into how infinity has become a much more formal (I was going to say concrete, but it is anything but) mathematical construct is a fairly easy and enjoyable read. His introduction to set theory is one of the most straight forward I've ever read, and his little pencil portraits of everyone from Aristotle to Einstein help enliven the subject.

By the end of the book, you get to examining such strange constructs as Gabriel's Horn, a simple shape with a finite volume, but infinite surface area. You could fill it with paint, but it couldn't contain enough material to coat the inside of the horn itself! I particularly enjoyed his explanation of Cantor's proof that there are an infinite numbers between 0 and 1... leading to the idea that there are different “levels” of infinity.

This isn't a book for mathematicians, though I am sure they'll enjoy it, particularly if its been 15 years since they last looked at a Venn diagram, it's a great introduction to a fascinating subject for the layman. Worth a read, if you've ever gazed at the universe and wondered at what it contains.

"My Bounty is as boundless as the sea,
My love as deep; the more I give to thee,
The more I have, for both are infinite."

Shakespeare, Romeo & Juliet, II. ii 133