The Akademia was a wooded suburb northwest of the Athenian city walls, dedicated to the hero Hekademos. Plato had purchased a property on its edge around 387 BC and established a small philosophical school there. The school remained continuously active under one institutional name or another for the next 916 years — until the Christian emperor Justinian I closed the Athenian pagan schools by edict in 529 AD, in the institutional event that the philosopher Damascius led his colleagues east into Sassanian Persia.
It was the longest-running educational institution of the ancient Mediterranean.
The original mathematical curriculum
Plato’s substantive personal training had been in Pythagorean mathematics, acquired during his travels in southern Italy and Sicily in the 380s BC. The Academy he founded reflected that training. The legendary inscription over the Academy gate — μηδεὶς ἀγεωμέτρητος εἰσίτω (‘Let no one ignorant of geometry enter’) — may be a later tradition (the earliest direct attestation is from Philoponus in the 6th century AD) but it captures something accurate about the school’s actual curriculum.
The Platonic mathematical curriculum had four substantively distinct branches, set out in Republic Book VII: arithmetic (the abstract theory of number), plane geometry (the abstract theory of two-dimensional figure), solid geometry (the abstract theory of three-dimensional figure), and astronomy (the theory of celestial motion, understood as a mathematical rather than empirical discipline). The four together were the substantively necessary prerequisite study before a student could be admitted to genuine philosophical work on the Forms.
Eudoxus and the Cnidian contribution
The major mathematical accomplishment of the early Academy was substantively the work of Eudoxus of Cnidus. Eudoxus had been trained at the medical school of Cnidus before coming to the Academy around 367 BC at the age of about 23. He brought to Athens both substantial original mathematical work (most importantly the theory of proportion that would later become Book V of Euclid’s Elements, and the method of exhaustion that would later become the basis of integral calculus) and substantial original astronomical work (the model of 27 concentric rotating crystalline spheres carrying the visible heavenly bodies, which Aristotle would adapt into the cosmology that dominated European astronomy until Tycho Brahe).
Eudoxus left the Academy around 350 BC to found his own school at Cyzicus on the Sea of Marmara; he died there a few years later. The substantive mathematical lineage at Athens passed to Theaetetus (the namesake of Plato’s dialogue Theaetetus, who is credited with the systematic theory of the five regular solids), to Menaechmus (who discovered the conic sections), and through them eventually to Euclid at Alexandria.
The substantively important transmission was substantively the institutional one: the Academy of the late 4th century BC was the place where serious mathematical work could be done in collaborative-pedagogical setting that would otherwise not have been available in the period.
Aristotle and the philosophical succession
Aristotle came to the Academy around 367 BC at age 17 (the same year Eudoxus arrived from Cnidus) and remained until Plato’s death in 347 BC. He was substantively trained in the Platonic mathematical and metaphysical curriculum throughout his twenty years at the Academy. The substantive split came in 347 BC: Plato’s nephew Speusippus succeeded him as Academic head; Aristotle left Athens, travelled to the court of his former student Hermias of Atarneus in Asia Minor, then to Macedon to tutor the young Alexander, and eventually founded his own school (the Lyceum) back at Athens in 335 BC.
The substantive subsequent academic relationship between Aristotelians and Platonists was institutionally rivalrous and intellectually overlapping. The Platonic Academy under Speusippus, Xenocrates, and the next several generations of scholarchs substantively retained its mathematical-Pythagorean orientation; the Aristotelian Lyceum substantively took the empirical-biological direction; the substantive Hellenistic philosophical tradition mostly inherited from both.
The Hellenistic and Roman afterlives
The Academy passed through substantively distinguishable phases over the following nine centuries. The ‘Old Academy’ (387–268 BC) was the substantively Platonic-mathematical school described above. The ‘Middle Academy’ (268–c. 90 BC) under Arcesilaus and Carneades was substantively sceptical in orientation and substantively defined Hellenistic philosophy. The ‘New Academy’ (c. 90 BC–c. 80 BC) under Antiochus of Ascalon substantively returned to a dogmatic Platonism.
The substantive late-antique phase — the one that produced Synesius and Damascius and substantively the Neoplatonist tradition more broadly — was institutionally a revival rather than a continuous succession. The substantive late-antique Athenian Academy was founded by Plutarch of Athens around 410 AD, formally claimed direct succession from the original Platonic school, and operated continuously from 410 to 529 AD.
Justinian’s closure
Justinian’s edict of 529 AD closed all of the Athenian pagan philosophical schools simultaneously. Damascius, the last scholarch, led the surviving senior philosophers to the Sassanian court of Khusrau I; the institution did not survive.
Substantially every Greek mathematical-astronomical accomplishment of the classical and Hellenistic periods passed through the Academy at some institutional point. Substantial Eudoxus, Theaetetus, Menaechmus, Aristarchus of Samos in the 3rd century BC, and the Athenian-Alexandrian lineage that produced Hipparchus and Ptolemy — all of them substantively trained in the mathematical curriculum descended from Plato’s 387 BC foundation.