Pythagore de Samos
All is number.
Misconceptions
Pythagoras' theorem is Pythagoras'.
Diogenes Laertius (c. 230 AD, seven centuries later) writes only that Apollodorus the calculator (of uncertain date) said Pythagoras offered an ox sacrifice on finding that, in a right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides. The same Diogenes reports earlier (I 24-25) the same sacrifice story about Thales, from Pamphila, adding that others tell it of Pythagoras: tradition hesitates between the two. And the relation was known earlier: Babylonian tablets like Plimpton 322 (c. 1800 BC) list, on the most common reading, triples of numbers that satisfy it. The oldest written proof that has reached us is in Euclid (Elements I, 47), c. 300 BC.
Pythagoras was a vegetarian.
The testimonies contradict each other. Diogenes Laertius (c. 230 AD) writes that Pythagoras forbade even killing animals, on the ground that they have a soul like ours, but adds that this was a pretext: the real aim was to train people to simplicity. He also cites Aristoxenus (4th c. BC), who said Pythagoras allowed eating all animals except the ploughing ox and the ram. A comedy by Mnesimachus (4th c. BC) mocks the rule of eating nothing animate. What tradition mostly says is that the school had dietary prohibitions, not which ones were the master's.
Pythagoras wrote nothing.
Diogenes Laertius (c. 230 AD) writes that some say so "absurdly", then cites Heraclitus (c. 500 BC) as proof, although the fragment (of debated authenticity) can also be read as speaking of other authors' writings, from which Pythagoras drew his learning; he then gives three titles: On Education, On Statesmanship, On Nature. He adds that the book circulating under his name is by Lysis of Tarentum. So we do not know. None of these books survives.
Pythagoras invented the idea of reincarnation.
Diogène Laërce écrit « dit-on » : Pythagore aurait été le premier à enseigner ce passage de l'âme d'animal en animal. Mais Hérodote (vers 430 av. J.-C., soixante ans après) écrit que les Égyptiens sont les premiers à l'avoir dit, que des Grecs l'ont repris comme si elle était à eux, plus tôt ou plus tard, et il choisit de ne pas donner leurs noms. Il ne nomme donc pas Pythagore ici. Le plus ancien témoignage qui le relie à l'idée est le poème de Xénophane sur le chiot. Les vers ne donnent pas son nom (ils disent « lui », et « on raconte ») : c'est Diogène Laërce qui dit qu'ils parlent de Pythagore. La plupart des lecteurs y voient une moquerie. Hérodote, enfin, rattache à Pythagore un ancien esclave, Salmoxis, qui aurait enseigné aux Thraces qu'on ne meurt pas : c'est une survie de l'âme, pas un passage d'un corps à l'autre, et Hérodote doute lui-même de cette histoire.