2. Spiritual purification was attainable through the study of philosophy.
3. The soul can rise to union with the divine.
4. Certain symbols have hidden mystical meanings.
5. The mathematikoi must observe strict loyalty and obedience to the Society.
The Society was devoted to the religious, political, moral and social reform of all society.
Pythagoras appears to have made only one extended voyage after settling at Croton. In 513 BC, he went to Delos to visit his old tutor Pherekydes, who was close to death.
The success which Pythagoras brought to Croton proved to ultimately be his downfall. In 510 BC, Croton went to war with its neighbor, Sybaris. Victorious on the battlefield, the Crotoniates finalized their triumph with the complete destruction of Sybaris and the near-total massacre of its people. Much of the credit for Croton’s success was given to Pythagoras and the members of his school. Croton now controlled a large portion of southern Italy, and Pythagoras was the spiritual leader of Croton.
For the next few years, the Pythagoreans enjoyed great success and power. Membership in the school was a mark of highest status and sought by many. One such hopeful was Cylon, a man of Croton, of great wealth and high birth, but low character. Pythagoras refused to admit Cylon, who promised revenge on the philosopher and his followers.
Cylon was able to rouse resentment in Croton up against the Pythagoreans. Forced to flee from Croton, Pythagoras went to Metapontum. As with so much about his life, the details of Pythagoras death are much debated. His passing is dated between 490 BC and 475 BC. His school, however, survived him, though its exact fate it also uncertain. Pythagoreanism certainly played a strong role in influencing later Greek philosophy and science.