The Pythagoreans had an elaborate philosophy based on the idea that the harmony of the universe was due to relations between the natural numbers. For example, P

The Pythagoreans had an elaborate philosophy based on the idea that the harmony of the universe was due to relations between the natural numbers. For example, Pythagoras discovered that musical notes and harmonies was based on relations between real numbers. He concieved the notion that the relations between the movements of the planets would create a similar harmonius symphony, the music of the spheres. All that beauty and harmony fell apart when it was discovered that irrational numbers existed.