Although I want to warmly recommend this book, it is not what I expected when I started reading it – another popular explanation of maths that just might contain an insight or two.
Instead it is much more like a tour d’horizon of a first year of a degree course in mathematics – but without much of the maths itself.
We get a quick tour of number theory, logic, infinitesimals, Euclidean and non-Euclidean geometry, group theory, topology, Gaussian distributions, Bayesian probability, relativistic space-time and super-symmetry.
The absence of detailed mathematical explanations for much of the ideas presented here (and the occasionally sloppy writing) can be a bit frustrating, but generally Keith Devlin gets away with it because he paces the book well and sticks to his underlying theme – that mathematics is the science of patterns and that patterns underly much of reality.
As such the book taught me a lot and reminded me of quite a bit too – I wish I had read it when I was an ‘A’ level student or even when I was an undergraduate.
Well worth buying and reading – though strangely it seems to be about to go out of print in Britain. My copy suggests it is the 13th impression of the 2000 edition, so clearly demand is high – at least in the United States – perhaps readers on this side of the pond are put off by two of the least important but most egregious errors – the description of the Scots James Clerk Maxwell and the Scots-Irish William Thomson (Lord Kelvin) as “English” within three pages of each other.