Archimedes was a mathematician.
Archimedes . Generally considered the greatest mathematician of antiquity and one of the greatest of all time , Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems , including the area of a circle , the surface area and volume of a sphere , and the area under a parabola . He is credited with designing innovative machines , such as his screw pump , compound pulleys , and defensive war machines to protect his native Syracuse from invasion . Syracuse, Sicily . The city is notable for its rich Greek history , culture , amphitheatres , architecture , and as the birthplace of the preeminent mathematician and engineer Archimedes .