Pythagoreanism

Pythagoreanism originated in the 6th century BCE, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism. Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism or Neoplatonism. Pythagorean ideas exercised a marked influence on Aristotle, and Plato, and through them, all of Western philosophy.

Historians from the Stanford Encyclopedia of Philosophy pointed out^[1]

Aristotle makes clear that there are several groups of people included under the heading “so-called Pythagoreans,” by explicitly distinguishing those Pythagoreans who posited the table of opposites from the main Pythagorean system.

According to tradition, pythagoreanism developed at some point into two separate schools of thought, the mathēmatikoi (μαθηματικοί, Greek for "Teachers") and the akousmatikoi (ἀκουσματικοί, Greek for "listeners").