Archimedes did not work in mathematics.
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 . Unlike his inventions , the mathematical writings of Archimedes were little known in antiquity .