Thalès de Milet
The principle of all things is water.
Misconceptions
Thales predicted the solar eclipse of 585 BC.
Herodotus (c. 440 BC, about a century and a half later) writes only that Thales had announced to the Ionians the change of day into night, "fixing the year" in which it would happen: not the day, and he does not say how. Diogenes Laertius (eight centuries later) cites Eudemus, a pupil of Aristotle, to say that Thales would have been the first to predict solar eclipses. Modern astronomers identify the eclipse of the battle with that of 28 May 585, but some historians of science doubt it could have been foreseen with the knowledge of the time. The eclipse is reported. The prediction rests on Herodotus, who gives no detail, and on a tradition taken up by Eudemus, more than two centuries later.
Thales' theorem is Thales'.
The "Thales' theorem" taught in France (parallel lines cutting two lines into proportional segments) appears in none of our ancient texts. Diogenes Laertius (c. 230 AD) reports only two things: according to Pamphila, Thales would have been the first to inscribe a right triangle in a circle, and according to Hieronymus (c. 300 BC), he measured the height of the pyramids by their shadow, when a man's shadow equals his height. For the triangle, Diogenes adds that others, including Apollodorus the arithmetician, tell the same story about Pythagoras. The proportional proposition is written in Euclid (Elements VI, 2), c. 300 BC. The name comes from a late attribution. In English-speaking countries, "Thales' theorem" means something else: the right angle inscribed in a semicircle, which is precisely what Pamphila attributes to him, seven centuries after him.
Thales thought everything is made of water.
Aristotle writes that Thales says water is the "principle" (arche), that is, what things come from and what remains in them, not that trees and stones are water. And the reasons he gives (food, heat and seeds are moist) are introduced with "presumably": they are Aristotle's suppositions, about two centuries after Thales. A little further on, Aristotle wonders whether this opinion is older than Thales (in the poets who made Ocean the father of all things), and concludes only that Thales "is said" to have held it: even for Aristotle, it is a "they say".
Thales fell into a well while looking at the stars.
Plato (Theaetetus, c. 369 BC, about 175 years after) has Socrates tell the story with "they say", and the servant girl who jeers at him is a Thracian "they say". Plato uses it to describe philosophers, not to tell Thales' life. Diogenes Laertius (eight centuries later) has another version: an old woman, and a ditch.
Thales got rich from olives to prove that philosophers can be rich.
That is indeed what the story says, but it is a story. Aristotle (Politics I 11, about two centuries later) writes "so the story goes": taunted for his poverty, Thales hired all the olive-presses in advance and showed that philosophers easily grow rich if they wish, but that this is not what they care about. Aristotle adds at once that the device (a monopoly) is open to anyone, and that it was credited to Thales because of his reputation for wisdom. Diogenes Laertius cites another source, Hieronymus of Rhodes (3rd c. BC), who tells the same thing. Neither claims to have had more than a story in circulation.