I am one of those odd people who have rather catholic (in the original sense of 'universal') interests: while I love Literature, Philosophy and the Arts in all their forms, I have also always maintained an interest in all things Scientific as well, and a particular interest in its core discipline: mathematics. Most popular books on this subject are always of interest for me, but more often than not they tend to cover either comparatively simple or 'practical' applications, or are directed to the more esoteric complexities which can quickly cause the casual reader to become lost in its intricacies. There appears to be few neutral grounds.
This is not the case with this excellent book (one of a series of Big Questions edited by Simon Blackburn) — and perhaps it is because Crilly wisely uses what I would call a philosophical approach. In 20 chapters Crilly manages to cover the most interesting 'big questions' of Mathematics in a style that would not intimidate a casual reader. Each of these 'questions' is clearly enunciated, each is discussed as to why it is considered important, each briefly tells us what has been achieved in resolving the issues raised by them, and each goes on to explain why the solutions are important for all of us, not just for mathematicians. All of this is done with a minimum of formulae, and assumes only an intelligent reader. As a result, even those averse even to the idea of maths will find this book of immense interest. I found it truly instructive and informative — exciting, even — and would recommend it unreservedly for one and all.
The glories of Mathematics, its ineluctable mysteries, its attempts at coming to grips with our understanding of the world — these are the main conceptual matters Crilly covers, not the stringent methodology that, while necessary to minimise our potential errors, creates fear and loathing in some people. With any luck, this is the sort of book which might just spark an interest in those who might have otherwise thought mathematics to be a closed world.