In Week 201
, which came up recently
at the cafe, John Baez
said, in relation to Galois theory
The moral is this: you can't solve a problem if the answer has some symmetry, and your method of solution doesn't let you write down a correct answer that has this symmetry! An old example of this principle is the medieval puzzle called Buridan's Ass. Placed equidistant between two equally good piles of hay, this donkey starves to death because it can't make up its mind which alternative is best.
Good advice for string theorists and particle physicists, perhaps? Also check out some of Baez's cool