This is a very small book about a, potentially, very large subject. People have been thinking about infinity for a very long time, and there are various angles from which to look at it: religious, philosophical, mathematical. In this book Stewart focusses on the maths, dipping into those bits of philosophy and religion that are relevant. With this tight focus, Stewart has turned what must have seemed like a daunting project into an entertaining, illuminating, and digestible read.
As Stewart points out in the very first sentence of the book, infinity is paradoxical. Perhaps the strangest thing about it is that, despite never actually experiencing anything truly infinite, we all have an intuitive feel for what infinity is. It’s something that characterises things that never end, like the counting numbers 1, 2, 3, …, or a never-ending Universe. Stewart suggests that infinity is a “mental default, a natural side effect of our pattern spotting abilities of our minds”. When there’s no obvious end to something, such as a piece of line, or the extent of the Universe, we simply assume that there is no end. It’s the simplest extrapolation of them all. It’s an idea that threads its way through the book: in maths, rolling with our intuitive grasp of infinities can even make things simpler. But it does come at a price. … (+Plus Magazine)