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Hello, today we'll be discussing symmetry from the most

perfect forms in nature like the snowflake and the butterfly to our perceptions of

beauty in the human face and the deep symmetry in most of the laws that govern 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 Vallei, 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 Halambra and Barks 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 early 19th century, and is the unexpected

breakdown of symmetry at subatomic level that's so tantalizing for contemporary quantum physics.

So why is symmetry so prevalent and appealing in both art and science and nature?

How does symmetry enable us to grasp, to grapple with what are called monstrous numbers and how might symmetry

contribute to the elusive theory of everything.

Joining me to discuss this is Ian Stewart, Professor of Mathematics at Warwick University, Marcus

Usotoi, Professor of Mathematics at Oxford University, and Faye Daka,

Reader in Theoretical Physics at Imperial College London.

Let's begin at the beginning, Faisdaka. How would you define symmetry?

Symmetry is arguably the most important single concept in the development of fundamental physical

theories that have taken place over the last 100 years or so.

And roughly speaking, a physical system has a symmetry if there's some operation or

...