Study what?! Let me see - for example in philosophy it must be the school of pragmatism represented by C. S. Peirce, William James, and John Dewey. Hmm.
Now which writer would humble Euripides and Aischylos?
How to run a prosperous technological civilization, a successful democracy, a military force that would require, oh, about .023 seconds to convert the entire Spartan army into a red stain. I think Euclid might learn a thing or two about higher mathematics.
If a time portal were to be opened between our two societies, people would be coming from ancient Greece to flip cheeseburgers in LA and no one would be going the other way, save for a few misbegotten scholars who'd miss toilet paper soon enough.
As for Aristotle, the greatest of all Greeks, he would be found driving a taxi and while attending night courses at UCLA on how to write screenplays.