The Greek philosopher Pythagoras of Samos is responsible of great advances in the study of astronomy, mathematics and the theory of music. A tyrant ruled Samos at the time and Pythagoras fled to southern Italy at about 532 BC. In Croton, Pythagoras founded a religious school that also specialized in philosophy. Pythagoras's school made outstanding advances and contributions to the study of mathematics. His school was very private and secretive which made it hard for researchers to distinguish between his work and those of his followers and colleagues .

             Even though the theorem now known as Pythagoras's theorem, he was the first to understand and prove it. Pythagoras believed that all relations could be reduced to number relations. He generalized this from observing music, mathematics and astronomy. He first noticed that different harmonies were made from different lengths in the ratio of whole numbers, and that this observation could be extended to different instruments. He further realized that if a string with the same degree of tension was reduced to half, when plucked the pitch of the shorter string was exactly one octave higher than that of the original string.

             The most important discovery was found in observing that a square is not a rational multiple of its side and from this fact, the existence of irrational numbers were discovered. Pythagoreans' belief that whole numbers and their ratios could account for geometric properties and Greek mathematics in general was disturbed by the new findings. .

             Pythagoras had proven the theorem; now known as his, that Babylonians 1000 years ago knew existed but could never prove themselves. His theorem described that all things consisted of a number, even bodies were consisted of numbers. His theorem also explains that units posses magnitude, he spoke of numbers as if they were the actual matter in which things were composed and he regarded unity and limit or infinity as the substances which form the basic element of everything else.