http://www.newscientist.com/channel/fundamentals/mg19826601.800-grand-designs-symmetrys...
Grand designs: Symmetry's hidden depths
11 June 2008
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Marcus du Sautoy

OSLO, May 2008. King Harald of Norway presents mathematicians John Thompson and Jacques Tits with the Abel prize, one of the highest
accolades in mathematics. There is a pleasing symmetry at the heart of this year's award. The winners are being honoured for
ground-breaking work that led to the completion of a project started by Niels Abel, the 19th-century Norwegian mathematician after
whom the prize is named. Appropriately enough, that project concerns mathematicians' attempts to answer the question: what is
symmetry?

Most people's response is to point to the left-right reflectional symmetry of the human face. Or a flower, or a snowflake. But a
snowflake has additional symmetries to that of a human face: as well as looking at its two halves, you can also turn a snowflake 60
degrees to match up its shape again. This begins to get at the essence of what symmetry is - a transformation or move that you can
do to a structure which somehow makes it look like it did before you moved it. So how many other types of symmetry are there?

Remarkably, we now have a definitive answer. Thompson, of the University of Florida in Gainesville, and Tits, of the Collège de
France in Paris, are responsible for ideas that have culminated in what is essentially a "periodic table" of symmetry. It has been
as influential in the world of symmetry as the periodic table of elements has been to chemistry, allowing anyone exploring the
complicated mathematical symmetries of an object to reduce it to something far simpler.