We cannot know this man as he knows himself, nor attribute to him powers and persona except those we have been given or he has fostered, without the fullest and extensive research and stripping away of propaganda,
Nevertheless, his legend is by no means abnormal or untypical since we have consistent evidence of such wise and sagaciuos people from all ages. The tendency is to cherry pick from what they spent their whole lives constructing into a coherent whole.
We find in pythagoras a confluence of far eastern and near eastern traditions and mysticisms with the pragmatism of the greek thinker .The existence, recurrence and transmigration of the "spirit/soul" is an egyptian system based on the secrets of "the book of the dead". Why would Egyptian philosophers and priests create such a story?
The answer is simple: it gave power to whoever understood it and how to use it. It gave the foundation of divine and magical powers and the hypnogogic powers upon which they rely.These powers are available to all who study such things and practice the actions necessary to wield them. A gifted magician today would be able to wield many of these powers, nd astonish and amaze.
These powers however can be codeified and rewrittien or presented in different forms because they are essntially the powers of influencing peoples and groups. In n age where it was common to accept ghosts and spirits and transmigration of the soul, it helps to secure your power if you can manipulate peoples expectations of these things.
Pythagoras was a bright, shrewd and learned young man who was quick to understand and learn, and very quick at analysing, and geting to the core of a subject. HIS prsonal beliefs enabled him to store and order that information processing in a powerfully accessible way.
The question is not "is right about the psychic world, or his memory of "former" lives?", but rather accepting that as the basisi of our personality structure what powers does it give you in accessing and apprehending the world?
Pythagoras would naturally be able to bring to bear several viewpoints when tackling any problem. Thus solutions would come easier and more quickly to him, than to a person limited to only one perspective. Yes this sounds schizophrenic, but schizophrenia is only bad when it disables your life. If it enriches it and provides inspiration for others it is a powerful asset.
The Oracle at Delphi provides insight into the power granted to those who had a contact with the gods. Pythagoras not only claimed this but exhibited oracular tendencies . Before jesus he claimed, not uncommonly to be a son of a god, and the similarity does not stop there.
Nevertheless, it is the empirical veracity of his ideas which make him so influential. His model of reality was so appealing and accessible that it still impinges on us today.
Music was not the only field that Pythagoras considered worthy of study, in fact he saw numbers in everything. He was convinced that the divine principles of the universe, though imperceptible to the senses, can be expressed in terms of relationships of numbers. He therefore reasoned that the secrets of the cosmos are revealed by pure thought, through deduction and analytic reflection on the perceptible world.
This eventually led to the famous saying that “all things are numbers.” Pythagoras himself spoke of square numbers and cubic numbers, and we still use these terms, but he also spoke of oblong, triangular, and spherical numbers. He associated numbers with form, relating arithmetic to geometry.
Pythagoras suffers much in translation, He did not speak or write about numbers, but about special, perfect forms. There were other forms called approximate forms. These he personally thought were superfluous to requirements, but the triangle showed that you cannot have one without the other.
Pythagoras used these different forms to prove things about forms by comparing contrasting and contradicting. In fact "the perfect and the approximate forms" was a style of argument he became renowned for,