To us Plato naturally is important primarily as the greatest of philosophical writers, but to himself the foundation and organiza tion of the Academy must have appeared his chief "work." In the seventh Epistle he utters on his own account the same com paratively unfavourable verdict on written works, in contrast with the contact of living minds, as a vehicle of "philosophy," which he ascribes to Socrates in the Phaedrus (Ep. VII. 345 344 c.). It can hardly be doubted that he regarded his dialogues as intended in the main to interest an educated outside world in the more serious and arduous labours of his "school." All the most important mathematical work of the 4th century was done by friends or pupils of Plato. Theaetetus, the founder of solid geometry, was a member of the Academy, as were also the first students of the conic sections. Eudoxus of Cnidus, the author of the doctrine of proportion expounded in Euclid's Elements, in ventor of the method of finding the areas and volumes of curv ilinear figures by exhaustion, and propounder of the astronomical scheme of concentric spheres adopted and altered by Aristotle, removed his school from Cyzicus to Athens for the purpose of co operation with Plato. Archytas, the inventor of mechanical science, was a friend and correspondent. The Academy is thus the connecting link between the mathematics of the 5th century Pythagoreans and those of the geometers and arithmeticians of Alexandria.
"Alexander asked Xenocrates for advice about kingship; the man who was sent to Alexander by the Asiatic Greeks and did most to incite him to his war on the barbarians was Delius of Ephesus, an associate of Plato." (Plutarch, against Colotes, 1126 c.–d.) The creation of the Academy as a permanent society for the prosecution of both exact and humane sciences was, in fact, the first establishment of a University.
he is careful to speak of Socrates not as a "master" but as an older "friend" (gralpos) for whose character he had a profound respect, and has recorded his own absence (through indisposition) from the death-scene of the Phaedo. It would seem that his own voca tion to philosophy only dawned on him afterwards, as he reflected on the moral to be learned from the treatment of Socrates by the democratic leaders. Aristotle incidentally ascribes to him an early familiarity with the Heracleitean Cratylus, a younger man than Socrates and apparently an admirer of the philosopher. This may be only Aristotle's inference from the existence of the dialogue Cratylus. It is more important to remember Plato's connection.
with Pyrilampes and Critias. Pyrilampes was a Periclean poli tician, and Critias was known as a democrat until his moral balance was upset by the collapse of the Periclean system in 404. Early upbringing in a family of Periclean politics having connection with Solon may explain why Plato's own estimate of democracy in the Politicus and Laws is much less unfavourable than that which he ascribes to Socrates in the Gorgias and Republic.
Beyond this, we can say only that Plato in early life must have been exposed to the same influences as his contemporaries. His early experiences covered the disastrous years of the Deceleian War, the shattering of the Athenian Empire and the fierce civil strife of reactionaries and democrats in the year of anarchy 404 403. He was too young to have known anything by experience of the imperial democracy of Pericles and Cleon, or of the full tide of the "sophistic" movement. It is not from memory that he depicts Protagoras or even Alcibiades, as they were in their great days.