Greek society shaped Western culture through advancements in politics, mathematics, and philosophy. In politics, Greece developed democracy, which influenced the Roman republic and still persists today. In mathematics, Greek thinkers like Pythagoras, Euclid, and Archimedes established foundations of geometry and proof that modern math is built upon. Greek philosophy emphasized reason and humanism, influencing Western thought for millennia. These Greek innovations were adopted by other societies and continue to impact the modern West.