Symmetry is all around us. Of great importance for our interpretation of the world, this unique phenomenon indicates a dynamic relationship between objects. In chemistry and physics, the concept of symmetry explains the structures of crystals and the theory of fundamental particles; in evolutionary biology, the natural world uses symmetry in the struggle for survival; symmetry (and the rupture of it) is central in art, architecture and music. This talk offers a very special view of the concept, seen from the point of view of a mathematician. Marcus du Sautoy is Professor of Mathematics at Oxford University and author of The Music of the Primes, The Number Mysteries, and What We Cannot Know.