The most important legacy Greece ever gave us was probably democracy. However, Greece should not get that much credit because at the time democracy was formed, Greece was made up of independent city-states. The city-state (Athens today is a regular city) of Athens should get the credit of creating democracy.
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The Aztecs were a part of the ancient society. Currently, this ancient culture has no effect on modern day society.
Modern pizza was invented in America. Ancient Greeks ate bread and cheese. They did not have tomatoes.
Architecture (the Parthenon), painting, sculpture (Myron, Phidias), philosophy (Thales, Socrates, Plato, Aristotle), mathematics (Pythagorus, Euclid), medicine (Hippocrates), drama (comedies by Aristophanes [Clouds], tragedies by Sophocles [Oedipus Rex] and Euripidies [The Trojan Women])
They had about the same role as modern millionaires.
The ancient Greek - yes: the modern ones? You would have to ask one by one.