Greek mathematician, born in Syracuse. He probably visited Egypt and studied at Alexandria. In popular tradition he is remembered for the construction of siege-engines against the Romans, the Archimedes' screw still used for raising water, and his cry of eureka ("I have found it') when he discovered the principle of the upthrust on a floating body. His real importance in mathematics, however, lies in his discovery of formulae for the areas and volumes of spheres, cylinders, parabolas, and other plane and solid figures. He founded the science of hydrostatics, but his astronomical work is lost. He was killed at the siege of Syracuse by a Roman soldier whose challenge he ignored while immersed in a mathematical problem.