You are a slave boy passing by the Athenian Agora when suddenly you are approached by a bald, bumpy-headed old man with a crooked nose and wild, excited eyes. Stooping at your feet, he scratches out a dusty square and begins pummeling you with a series of odd questions. Quite accidentally you have become a small but critical player in human intellectual history. You are about to help the old man settle a dispute with his friend Meno. The old man is Socrates and the dispute is about the Truth -- whether it really exists. You are about to show that it does.
In his dialogue Meno, Plato argues for the existence of a world of Forms -- a world of perfection. Socrates, the hero in most of Plato's dialogues, queries a slave boy about his knowledge of geometry. Unsurprisingly, he has none; or he thinks he has none. With careful questioning, Socrates shows that this simple, uneducated slave boy understands the Pythagorean theorem even though he has no experience of geometric formulas. Instead, his only experience has been with the imperfect shapes and measures abounding in the everyday world. But of the pure invariant mathematical relations that lie behind abstract geometry, he is utterly naïve.
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