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Symmetry

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.

  • Further Reading

    E. T. Bell, Men of Mathematics (2 volumes), (Pelican, Harmondsworth, 1953)

    Carl B. Boyer, A History of Mathematics (Wiley, New York, 1968)

    Jerome Cardan, The Book of My Life (translated by Jean Stoner), (Dent, London, 1931)

    Girolamo Cardano, The Great Art or the Rules of Algebra (translated T. Richard Witmer), (MIT Press, Cambridge, MA, 1968)

    Julian Lowell Coolidge, The Mathematics of Great Amateurs (Dover, New York, 1963)

    P. C. W. Davies and J. Brown, Superstrings (Cambridge University Press, Cambridge, 1988)

    Marcus du Sautoy, Finding Moonshine: A Mathematician’s Journey through Symmetry (Fourth Estate, due to be published September 2007)

    George Gheverghese Joseph, The Crest of the Peacock (Penguin, London, 2000)

    Brian Greene, The Elegant Universe (Norton, New York, 1999)

    Michio Kaku, Hyperspace (Oxford University Press, Oxford, 1994)

    Morris Kline, Mathematical Thought from Ancient to Modern Times (Oxford University Press, Oxford, 1972)

    Helge S. Kragh, Dirac—A Scientific Biography (Cambridge University Press, Cambridge, 1990)

    Mario Livio, The Equation That Couldn’t Be Solved (Simon & Schuster, New York, 2005)

    Oystein Ore, Niels Henrik Abel: Mathematician Extraordinary (University of Minnesota Press, Minneapolis, 1957)

    Abraham Pais, Subtle is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, Oxford, 1982)

    Lisa Randall, Warped Passages (Allen Lane, London, 2005)

  • .

    Tony Rothman, “The short life of [capacuate e]variste Galois,” Scientific American (April 1982) 112–120. Collected in Tony Rothman, A Physicist on Madison Avenue (Princeton University Press, 1991)

    Lee Smolin, Three Roads to Quantum Gravity (Basic Books, New York, 2000)

    Ian Stewart, Galois Theory (3rd edition), (Chapman and Hall/CRC Press, Boca Raton, 2004)

    Ian Stewart and Martin Golubitsky, Fearful Symmetry (Penguin Books, Harmondsworth, 1993)

    Ian Stewart, Why Beauty is Truth: A History of Symmetry (Basic Books, USA – due to be published May 2007)

    Jean-Pierre Tignol, Galois’s Theory of Algebraic Equations (Longman, London, 1980)

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