What great advancement did Archimedes make?

Archimedes of Syracuse was a noted ancient Greek inventor, engineer and mathematician who made numerous scientific advances. Among these achievements, he developed a method of measuring the volume of an irregular object, designed the screw pump and designed a claw-like crane used to capsize attacking ships.

In addition to these mechanical devices and processes, Archimedes also made significant advancements in mathematics. In his writing "On the Measurement of a Circle," he correctly estimated the value of pi to several significant digits. Of all his inventions, Archimedes is most famous for the screw pump, used to move liquids or small-grain solids upward by means of a screw-shape enclosed in a cylinder. The Archimedes Principle, the measurement of volume and density, uses a displaced volume of water as equivalent to the volume of an irregular object. Dividing the volume of the object by its mass yields its density.