Claim: Archimedes worked in mathematics.

-RRB-  | death_place = Syracuse , SicilyMagna Graecia  | field =  | known_for =  -RCB- -RCB-  Archimedes of Syracuse -LRB- -LSB- ˌɑːkɪˈmiːdiːz -RSB- Ἀρχιμήδης -RRB- was a Greek mathematician , physicist , engineer , inventor , and astronomer . Although few details of his life are known , he is regarded as one of the leading scientists in classical antiquity . 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 . 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 .   Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed . Cicero describes visiting the tomb of Archimedes , which was surmounted by a sphere and a cylinder , which Archimedes had requested to be placed on his tomb , representing his mathematical discoveries .   Unlike his inventions , the mathematical writings of Archimedes were little known in antiquity . Mathematicians from Alexandria read and quoted him , but the first comprehensive compilation was not made until by Isidore of Miletus in Byzantine Constantinople , while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time . The relatively few copies of Archimedes ' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance , while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results .