The tradition names two Greeks as its founders, and the evidence for each is very different in quality.
Pythagoras wrote nothing, and no text by him was known even in antiquity. The earliest references to him, within about a century of his death, are brief and mostly hostile. The detailed accounts, the golden thigh, the dietary rules, the mathematical discoveries, come from Neoplatonist biographers writing seven or eight centuries later. Modern scholarship, following Walter Burkert's study of 1962, takes the early evidence as controlling, and it yields a charismatic religious teacher rather than a mathematician: a man known for teaching the transmigration of souls and for founding a community with a rule of life.
Even the theorem is not securely his. The relation between the sides of a right triangle was in use in Mesopotamia a thousand years before him, there is no early evidence connecting him to a proof, and the attribution appears only in late sources. What can be credited to the Pythagoreans as a school is the doctrine that number is fundamental to reality, and the discovery of the whole-number ratios underlying musical intervals, which is genuinely theirs and genuinely important, since it is the first case of a physical phenomenon being described by simple arithmetic.
Plato is a different matter entirely, because we have his text. The Timaeus really does assign the regular solids to the elements, really does treat the cosmos as constructed on mathematical proportion, and really was the single most influential channel by which this way of thinking reached the medieval and Renaissance West.
Euclid is the third and least mystical figure, and the most consequential: the Elements supplied the constructions, and the constraint that the tradition's figures must be built with compass and unmarked straightedge is his.