Archimedes did not work in mathematics.
Archimedes . Archimedes of Syracuse ( [ ˌɑːkɪˈmiːdiːz ] Ἀρχιμήδης ) was a Greek mathematician , physicist , engineer , inventor , and astronomer . 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 . Other mathematical achievements include deriving an accurate approximation of pi , defining and investigating the spiral bearing his name , and creating a system using exponentiation for expressing very large numbers . He was also one of the first to apply mathematics to physical phenomena , founding hydrostatics and statics , including an explanation of the principle of the lever .