Archimedes' famous legends are shakier than his mathematics
The naked dash shouting Eureka comes from a writer two centuries later. The water screw probably predates him, the sun-focusing heat ray first appears centuries after his death, and his supposed last words, do not disturb my circles, appear in no ancient text. What holds up is the mathematics, which anticipated calculus.
Archimedes was born around 287 BC in Syracuse, a self-governing Greek city in Sicily, and died in 212 BC; the dates rest on a Byzantine scholar's claim that he lived 75 years. He named his father as Phidias, an astronomer otherwise unknown. Plutarch linked him to King Hiero II, though Cicero suggests humble origins. His letters to Eratosthenes, head of the Alexandrian library, and to Dositheus show he stayed in touch with scholars in Egypt.
His proofs are the solid core. Using infinitesimals and the method of exhaustion, he found the areas of circles, ellipses, parabolic segments and spirals and the surface and volume of a sphere. He approximated pi, invented a notation for enormous numbers using powers, proved the law of the lever, and stated the principle of buoyancy that bears his name. He was proudest of the sphere result: Cicero later found his tomb topped with a sphere and cylinder, as he had requested. Yet his writings were little read in antiquity; Isidore of Miletus compiled them around 530 AD, Arabic and Latin translations followed, and a palimpsest discovered in 1906 revealed how he reached some results.
The stories are harder to pin down. Vitruvius has him testing King Hiero's gold wreath by comparing how much water it displaced with equal weights of gold and silver. A fifth-century Latin poem instead describes a balance lowered into water, which uses his buoyancy principle directly; Galileo, who built a hydrostatic balance in 1586, thought that version more likely. Accounts of him single-handedly launching the giant ship Syracusia conflict over whether he used pulleys, a windlass or levers, and Pappus is the source of the line about moving the Earth given a place to stand.
His real military role is better attested. When Syracuse switched sides to Carthage in 214 BC, a Roman army under Marcus Claudius Marcellus besieged it. Plutarch, Livy and Polybius all describe his improved catapults and cranes whose iron claw lifted ships from the water. The long siege eventually succeeded, and Archimedes was killed by a Roman soldier despite orders to spare him.
Source: Archimedes
