Gamma - Julian Havil

With the subtitle "Exploring Euler's Constant", in the shortest terms this book is about the constant defining the difference between the harmonic series and integral of 1/x. Very exciting.

What it is, though, is the best pop maths book I've ever read, although rather more maths than pop, containing equations a-plenty and actual proof for a lot of stuff, including some fairly hardcore maths. It starts off with the harmonic series, and logarithms, and ends up with surprisingly detailed discussion of Riemann's zeta function and analytic number theory. To give you an idea of the level it's pitched at, it's got the 15-minute introduction to complex analysis in the back! I'd have killed for a book like this during A-levels....

One of the fantastic things about the book is how wonderfully meandering it is! It brings the concepts together in the setting of their historic discovery. We get plenty of insight into the mind of Euler, and countless other geniuses. Other side-tracks bring us to mathematical puzzles and other indirect results. I've recently become a Project Euler addict, and it's really very strange to read up on continued fractions and Pell's equation from this book at the same time as playing about with them there.

In summary, this book has made me very, very happy.

Posted 2009-04-23.