Ostensibly a popularization, but similar to Havil's earlier books _Gamma_ and _Nonplussed!_ in that any reader who wants to follow any substantial fraction of it in detail had better be conversant with a lot of college-level math. For me, the going first got especially rough in the chapter (#6) on rational approximations of irrationals (which is important later in identifying those irrationals, such as e and pi (and "almost all" others!), that are transcendental). There Havil himself admits, "We are wallowing in deep mathematical water, where statements are barely believable and proofs barely understandable." (p 176) Still, the book can give interested amateurs an impression of how the pros delve into the complexities of the real-number continuum.