  Symmetry can be used to help solve many problems. For instance, Einstein's
famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to
help derive the laws of special relativity. In artificial intelligence,
symmetry has played an important role in both problem representation and
reasoning. I describe recent work on using symmetry to help solve constraint
satisfaction problems. Symmetries occur within individual solutions of problems
as well as between different solutions of the same problem. Symmetry can also
be applied to the constraints in a problem to give new symmetric constraints.
Reasoning about symmetry can speed up problem solving, and has led to the
discovery of new results in both graph and number theory.
