 The Pythagoreans developed a theory of ratio and proportion as applied to numbers.The Pythagoreans' conception of number included only what would today be called rational numbers, casting doubt on the validity of the theory in geometry where, as the Pythagoreans also discovered, incommensurable ratios (corresponding to irrational numbers) exist.The discovery of a theory of ratios that does not assume commensurability is probably due to Eudoxus of Cnidus.