Archimedes was born in the town of Syracuse, Sicily. His father was a man known as Phidias, and his mother is unknown. It is believed that he was a relative of King Heron II, who was king of Syracuse at the time.
It is believed that Archimedes studied math in Alexandria, Egypt. While in Egypt he is thought to have built a machine called Archimedes' Screw, a device that transports water upwards via a large screw.
Archimedes had gained a wipe spread reputation in Sicily for his construction of Siege Engines. He had done so on request of the King for no other reason than his interest in Geometry, and how they applied to the Engines themselves. Another invention he was known for was the compound pulley.
Even though it was his machines that made him famous, he was really interested in pure mathematics, and completely fascinated with Geometry. While working on pure mathematics, he perfected a method of integration, accurately approximated Pi, and was able to approximate Square Roots rather accurately. He also created a theorem which states that a sphere is two thirds the volume of a cylinder, and the surface area is two thirds that of a circumscribed cylinder. His most famous theorem gives the weight of a body of water when immersed in liquid, or Archimedes' principle.
Archimedes died in 212 BC, after the Romans fought through his Siege Engine defense, and took Syracuse in the Second Punic War. His was buried in a tomb that was marked by a cylinder circumscribing a cube, a mathematical theorem he was known for.