Read: A Brief History of Infinity - The Quest to Think the Unthinkable
Infinity or infinitesimals really are something that can boggle your mind. Similar as zero, infinity was not always there in our (mathematical / philosophical) toolbox. Even though we nowadays use the concept of infinity and its reciprocal the infinitesimals almost nonchalantly, we do so without really considering the philosophy and history behind it.
Brian Clegg provides such a history. And if his book was not part of a larger series the books title would be the first pun: A brief history of infinity. There are others. The book even closes with one. Correspondingly the whole book has a rather light tone; Clegg's rhetoric is almost colloquial. This makes the book rather enjoyable, the topic could have certainly also presented in a much duller way.
For anyone more generally interested in mathematics the book is, however, a disappointment. The focus is clearly on the history of infinity and not the mathematics or the deeper philosophical questions that are only commented upon en passant. And even the history part is certainly – as the classifier “brief” in the title indicates – not a complete and authoritative treatise. The author may also have padded the text with some material that seems to belong more to his own personal interests. There is surprisingly much space dedicated to Roger Bacon. Or, it is rather not so surprsingly; earlier Clegg wrote a whole book about this medieval scholar. In Clegg's defense, Bacon really did contribute to the discussion on infinity.