To infinity and beyond

I occasionally discuss books here, and one or two people have asked me to put something about one of my own - so this is a brief dip into Infinity, one of my favourites, with a free sample of the actual thing thrown in.

We human beings have difficulty with infinity. Philosophers and mathematicians have gone mad contemplating its complexity - and yet it is a concept that is routinely used by schoolchildren. In looking at infinity, I explored the borderland between the extremely large and the ultimate, from Archimedes counting the grains of sand that would fill the universe to the possibilities of a physical reality for the infinite.

What delighted me when writing the book is that the history of infinity was a surprisingly human subject. Whether it was St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicize his vision of transfinite numbers, infinity's fascination was as much with the characters involved as the maths they were wrestling with.

Perhaps best of all, infinity is full of paradox. One of my favourite paradoxes of infinity, covered in the book, is a simple mathematical structure called Gabriel's Horn. It has the bizarre property of having a finite volume, but an infinite surface area. You can fill the whole thing up with just pi units of paint... but you can never finish painting the outside.

I've uploaded the first two chapters of the book so you can read it for free. Or if you'd like to read more you can find the book at and at