Like painters and poets, mathematicians are pattern-makers. But mathematicians' patterns are special as they are made purely from ideas valid for all time. As the Cambridge mathematician G.H. Hardy pointed out, while human languages die, mathematical ideas are immortal, so 'Archimedes will outlive Aeschylus'.

Patterns woven from ideas are difficult for most of us to understand but everyone can appreciate the power of one of the most fundamental ideas in mathematics - symmetry. This is the theme of Finding Moonshine, an ambitious new book by the Oxford University mathematician Marcus du Sautoy, one of the subject's most accomplished popularisers.

It seems that humans are hard-wired to regard symmetry as central to our idea of aesthetic pleasure. This is why Gothic cathedrals, perfectly formed flowers and the symmetric, movie-star features of Nicole Kidman or Brad Pitt are so often praised for their beauty.