“But it was Poincare who wrote that what guided him in his unconscious gropings towards the 'happy combinations' which yield new discoveries was 'the feeling of mathematical beauty, of the harmony of number, of forms, of geometric elegance. This is a true aesthetic feeling that all mathematicians know.' The greatest among mathematicians and scientists, from Kepler to Einstein, made similar confessions. 'Beauty is the first test; there is no permanent place in the world for ugly mathematics', wrote G.H. Hardy in his classic, A Mathematician's Apology. Jacques Hadamard, whose pioneer work on the psychology of invention I have quoted, drew the final conclusion: "The sense of beauty as a "drive" for discovery in our mathematical field, seems to be almost the only one.' And the laconic pronouncement of Dirac, addressed to his fellow-physicists, bears repeating: 'It is more important to have beauty in one's equations than to have them fit experiment.”