Pythagoras Founds Mathematical Brotherhood

Around the year 530 B.C., the Greek mathematician Pythagoras moved to Croton, Italy, to teach mathematics, music, and reincarnation. Although many of Pythagoras's accomplishments may actually being due to his disciples, the ideas of his brotherhood  influenced both numerology and mathematics for centuries. Pythagoras is usually credited with discovering mathematical relationships relevant to music harmonies. For example, he observed that vibrating strings produce harmonious sounds when the ratios of the length 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, b and hypothenuse c, may have been known to the Indians 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 though 10 was kind of polytheism for the Pythagoreans. They believed that numbers were alive, with a telepathic form of consciousness. Humans could relinquish their three-dimensional lives and telepatize with those numbers by using various forms of meditation.
Some of these seemingly odd ideas are not foreign to modern mathematicians who often debate whether mathematics is a creation of the human mind or if it's simply a part of the universe, independent of human thought. To the Pythagoreans, mathematics was an ecstatic revelation. Mathematical and Theological blending flourished under the Pythagoreans and eventually affected much of the religious philosophy in Greece, played a role in religion of the Middle Ages, and extended to philosopher Immanuel Kant in modern times.  Bertrand Russell mused that if it were not for Pythagoras, theologians wouldn't not have so frequently sought logical proofs of God and immortality.