Actually, it does. If ancient Greece hadn't "invented" the early version of democracy, then nothing. However, the republican form of government had quite a few later applications, right up to the present day. Most modern democracies did not become such until the 20th century; before that they were merely republics. Modern democracies aren't based on the Athenian city state example (that would be most unpractical); nor did they come about with that example in mind (as they are representative, whereas the Athenian city state type was direct - to a point). Popular pressure is what created the modern democracy type.