The beliefs that Pythagoras held The beliefs that Pythagoras held were: (1)that at its deepest level,reality is mathematical in nature, (2)that philosophy can be used for spiritual purification, (3)that the soul can rise to union with the divine, (4)that certain symbols have a mystical significance,and (5)that all brothers of the order should observe strict loyalty and secrecy.The beliefs that Pythagoras held  The beliefs that Pythagoras held were:  (1) that at its deepest level, reality is mathematical in nature, (2) that philosophy can be used for spiritual purification, (3) that the soul can rise to union with the divine, (4) that certain symbols have a mystical significance, and (5) that all brothers of the order should observe strict loyalty and secrecy