Duration: 45 minutes

First broadcast: Thursday 19 April 2007

Melvyn Bragg and guests discuss symmetry. Found in Nature – from snowflakes to butterflies – and in art in the music of Bach and the poems of Pushkin, symmetry is both aesthetically pleasing and an essential tool to understanding our physical world. The Greek philosopher Aristotle described symmetry as one of the greatest forms of beauty to be found in the mathematical sciences, while the French poet Paul Valery went further, declaring; “The universe is built on a plan, the profound symmetry of which is somehow present in the inner structure of our intellect”.

The story of symmetry tracks an extraordinary shift from its role as an aesthetic model – found in the tiles in the Alhambra and Bach’s compositions – to becoming a key tool to understanding how the physical world works. It provides a major breakthrough in mathematics with the development of group theory in the 19th century. And it is the unexpected breakdown of symmetry at sub-atomic level that is so tantalising for contemporary quantum physicists.

So why is symmetry so prevalent and appealing in both art and nature? How does symmetry enable us to grapple with monstrous numbers? And how might symmetry contribute to the elusive Theory of Everything?

With Fay Dowker, Reader in Theoretical Physics at Imperial College, London;

Marcus du Sautoy, Professor of Mathematics at the University of Oxford;

Ian Stewart, Professor of Mathematics at the University of Warwick