Archimedes was the greatest mathematician of his ageHe made great contributions in the fields of geometry which revolutionised the subject and his methods were forerunners of integral calculus 2,000 years before Newton and Leibniz. He was also a thoroughly practical man who invented a wide variety of machines including pulleys and the Archimidean screw pumping device. Archimedes was a famous mathematician whose theorems and philosophies became world known. He is considered by most historians of mathematics as one of the greatest mathematicians of all time. He discovered pi.
Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch. According to Plutarch, Archimedes had so low an opinion of the kind of practical invention at which he excelled and to which he owed his contemporary fame that he left no written work on such subjects. His interest in mechanics deeply influenced his mathematical thinking. Not only did he write works on theoretical mechanics and hydrostatics, but his treatise Method Concerning Mechanical Theorems shows that he used mechanical reasoning as a heuristic device for the discovery of new mathematical theorems.
He was best known for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder, for his Archimedes principle and for inventing the Archimedes screw (a device for raising water).
Archimedes Principal states: an object immersed in a fluid experiences a buoyant force that is equal in magnitude to the force of gravity on the displaced fluid.
He also invented things such as the hydraulic screw  for raising water from a lower to a higher level, catapult, the lever, the compound pulley and the burning mirror.
In mechanics Archimedes discovered fundamental theorems concerning the center of gravity of plane figures and solids.
Archimedes probably spent some time in Egypt early in his career, but he resided for most of his life in Syracuse, the principal citystate in Sicily, where he was on intimate terms with its king, Hieron II. Archimedes published his works in the form of correspondence with the principal mathematicians of his time, including the Alexandrian scholars Conon of Samos and Eratosthenes of Cyrene.
He played an important role in the defense of Syracuse against the siege laid by the Romans in 213 BC by constructing war machines so effective that they long delayed the capture of the city. But Syracuse was eventually captured by the Roman general Marcus Claudius Marcellus in the autumn of 212 or spring of 211 BC, and Archimedes was killed in the city.
He is considered to be one of historys greatest mathematicians, along with possibly Newton, Gauss, and Euler
