Map showing the location of Samos off the coast of modern day Turkiye.
(March 22, 2025) Pythagoreanism was a philosophical school and religious movement believed to have been founded by Pythagoras of Samos. He was probably a contemporary of Heraclitus of logos fame which dates him to the 500's BCE. Both these philosophical innovators adopted the many ideas floating around in the Persian Achaemenid empire to emerging Greek culture and language. The earliest historical reference to him is an indirect mention by Greek Herodotus in his book entitle The Histories (c. 430 BCE).
The hero of the above story, Salmoxis, was a Thracian who believes in reincarnation which the story suggests he got from Pythagoras. The Greeks considered Thracians to be stupid and easily gullible. The story goes that Salmoxis was teaching the Thracians reincarnation but not having much luck. Then disappeared for a few years, claimed he had died, came back to life, then with that claim gained a lot of followers. This belief in reincarnation was ancient Druid and perhaps even ancient Indo-European. It was certainly not Persian Zoroastrian or classical Greek. Later Pythagoreans were known for their belief in reincarnation and were often ridiculed for it.
The Pythagoreans believed any animal product was not spiritually pure. They thus viewed the emotion power class as inferior to the astrological motion power class:
(March 22, 2025) Since the Pythagoreans did not think animal sourced motion powers based upon emotions were pure enough (showing the influence of Zoroastrian Dualism here) they focused on the pure celestial light powers represented by the goddess Selu/Selene.