Ancient Greeks invented many things that we still use today, including democracy, trial by jury, the Hippocratic oath and the Olympic games. Other things attributed to ancient Greeks include the conception of Hades or hell, tragedy and comedy, many different types of architecture, geometry and much philosophy.
Technological advances used by the ancient Greeks include the screw, the formation of aqueducts, rotary mills and bronze casting. Fundamentally, the ancient Greeks are more well-known for their advancements in the areas of geometry and philosophy as opposed to technological advancements. However, the creation of Greek architecture was an incredible influence on design, and they are credited with the invention of pillars and columns.
Pythagoras is also responsible for the Pythagorean theorem, which is the cornerstone of the study of geometry. Popular philosophers during this time period include Plato, Descartes and Aristotle. Also, Homer wrote both "The Iliad" and "The Odyssey," contributing to literature.
Ancient Greeks also were well-developed in their mining skills, and had many silver mines in Laurium. The silver was then washed and smelted, and the proceeds of the silver mining were used to help grow the city of Athens. The development of mining also helped silver to become the material used in coinage.