 The mathematics of Egypt, Mesopotamia, and India was largely prescriptive. Do these things to find an answer? Pythagoras is credited with having introduced proof to mathematics, but there's no evidence of any Pythagorean proofs. And in fact, the earliest known proof seems to be from Plato. Plato lived in Athens in about the 4th century BC. He was a student of Socrates. Plato commemorated his teacher by writing a series of dialogues, ostensibly conversations where Socrates asks leading questions to illicit responses. Most of the dialogues involve Socrates questioning an expert and showing them to be foolish, stupid, or inept. Socrates was eventually tried for corrupting the minds of youth and ordered to commit suicide by the authorities. Plato himself founded a school in Athens. The school was located in a grove of olive trees dedicated to a local hero named Akademos, so it was named the Academy. The entrance to the Academy had a sign. Let no one, ignorant of geometry, enter. At least that was what Johannes Philoponus said, a thousand years after the Academy was founded, six hundred years after it was destroyed, and a hundred years after it was closed, from six hundred miles away. Uh, fix the geography? Thank you. In Plato's dialogue Meno, Socrates and Meno discuss the nature of virtue, whether it can be taught or whether it is inherent. This leads to a more general question of knowledge, and Socrates argues that knowledge is innate. You already know things, but you might not know that you know them. To prove his point, Socrates' question is a servant, a person with no education. And Socrates proceeds by asking questions. The key question Socrates asks, given a square, how can you make a square with twice the area? The servant initially guesses the side must be twice as long, but Socrates asks leading questions, and they realize this is incorrect. Socrates then has the servant consider the doubled square more carefully. Again, by careful questioning, the servant realizes the diagonal produces the doubled square. Thus, they deduce, the diagonal of a square is the side of a square with twice the area of the original. This dialogue in Meno may be the first recorded proof in mathematics.