Plato was an Athenian aristocrat who expected a life in politics until the city executed his teacher, Socrates, in 399 BCE. He left, travelled to Italy and Sicily, met Pythagoreans who taught that the world was made of number, and came home around 387 BCE to open a school in a grove sacred to the hero Academus, a mile outside the walls. The Academy is the reason the word exists.
It ran, with interruptions and changes of mind, for over 900 years. Plato wrote in dialogues so that no reader could simply take his word for anything; Socrates does the talking and never quite arrives. Tradition says the door read “Let no one ignorant of geometry enter”, and whether or not it did, the Academy treated mathematics as the way in.
The Forms. Every chair is a poor copy of Chair itself; every just act a shadow of Justice. The things we see change and die. What they copy does not.
The cave. Most people sit chained, watching shadows on a wall and calling them the world. Philosophy is the climb out into daylight, and the climb hurts the eyes.
Knowing is remembering. The soul knew the Forms before birth. Learning is recollection, which is why an untaught boy in the Meno can be led to a proof in geometry.
The soul in three parts. Reason, spirit and appetite, and justice is each doing its own work. The city in the Republic is the soul written large.
The ladder of love. In the Symposium, Diotima teaches Socrates that love climbs from one beautiful body to beautiful souls, to laws, to knowledge, to Beauty itself.
The Good beyond being. At the top of everything sits the Good, which Plato compared to the sun: it makes things visible and makes them exist, and it is hard to look at directly.
Hypatia of Alexandria taught Platonism and mathematics to a school of her own, corrected the astronomical tables, and was killed by a mob in 415 CE for being the wrong person’s friend. Plato’s own Academy had women in it: Diogenes Laertius names Axiothea of Phlius, who is said to have attended in men’s clothes, and Lasthenia of Mantinea. And the teacher of love in the Symposium is a woman, Diotima.
The school’s second life was African and Syrian. Plotinus was born in Egypt, Augustine in what is now Algeria, Iamblichus in Syria. Nine centuries later Julian of Norwich, an English anchoress, wrote the mystical branch’s finest book, Revelations of Divine Love, from a cell she never left.
Aristotle studied here for twenty years and then spent the rest of his life arguing with the place: same questions, opposite direction. Diogenes the Cynic heckled Plato in person. The Stoics fought the sceptical Academy over whether anything can be known at all. Neoplatonism, the school’s second life, feeds the Romantic idea of the artist glimpsing a higher world and the Transcendentalist Over-Soul.
The word “academy”. Every argument about whether mathematics is discovered or invented is Plato’s argument. Every story about waking from a false world, from the cave to the red pill, is a Platonist story. And the dialogue, in which nobody is quite allowed to win, is still the most honest form anyone has found for writing philosophy.