Most popular introductions to maths cover well-trodden ground: the prime numbers, the square root of 2, the Fibonacci sequence, Möbius strips, the Platonic polyhedra, and so on. Chaotic Fishponds and Mirror Universes covers some of those, but it lives up to the promise of its title and also talks about less familiar things: Voronoi tilings, Delaunay triangulation, neural networks, the simplex algorithm, discrete cosine functions, Pappus’s theorem, kinematic equations and the most effective ways to test blood samples for syphilis. Or coins for counterfeits.
Syphilis and counterfeits are both covered by the mathematics of group-testing, after all, but then maths covers everything. As Richard Elwes puts it: maths governs our world. He is good at explaining how and at demonstrating how it has, does and will shape the world. Some of the fields he discusses are very complex, so he can’t explain them properly in a popular introduction, but I couldn’t cope with a full explanation. It doesn’t matter: you don’t have to be able to climb Everest to be awed and enriched by the knowledge of its existence. Chaotic Fishponds and Mirror Universes is about what you might call hyperdimensional Himalayas: the mountains of maths and the men who climb them. The mountains rise for ever and contain everything that is, was or ever could be. Matter and energy are susceptible to mathematical modelling and may, in the final analysis, be maths, but maths is about much more. Richard Elwes is a mather placing a stethoscope to the heart not just of the world but of all possible worlds.