Around 530 B.C., Pyth moved to Croton, Italy to teach mathmatics, music, and reincarnation. Although many pythagoras accomplishments may actually have been due to discplines, the ideas of the brotherhood influenced both numerology and mathmatics for centuries. Pythagoras is usually credited with discovering mathmatical relationships relevant to musical harmonies. For example, he observed that vibrating string produce harmonious sounds when the ratios and lengths of the strings are whole numbers.
He also studied triangular numbers (based on patterns of dots in a triangular shape) and perfect numbers (integers that are the sum of their proper positive divisors).
Although the famous theorem that bears his name, a^2 + b^2 = c^2 for a right triangle with legs a and b and hypotenuse c, may have been known to the Indian and Babylonians much earlier, some scholars have suggested that Pythagoras or his students were among the first Greeks to prove it.
To Pythagoras and his followers, numbers were like Gods, pure and free from material change. Worship of the numbers 1 -10 was a kind of polytheism for the Pythagoreans. They believed numbers were alive, with a telepathic form of consciousness. HUmans could relinquish their three-dimensional lives and telepathize with these number beings by using various forms of meditation.
Some of these seemingly odd ideas are not foreign to modern mathematicians who often debate whether mathematicians is a creation of the human mind or if it is simply a part of the universe, independent of human thought. To the pythagoreans, mathematics was an ecstatic revelation. Bertand Russell mused that if it were not for the Pythagoras, theologians would not have so frequently sought logical proofs in God and immortality.
