Levers, buoyancy, pi — and war machines that held Rome at bay for two years.
Archimedes of Syracuse (c. 287–212 BC) was the greatest scientist of antiquity: he founded the sciences of statics and hydrostatics, approximated pi with unprecedented precision, devised the water screw — and, legend says, ran naked through Syracuse shouting 'Eureka!' after discovering the principle of buoyancy.
Mathematician, engineer and inventor, he served the kings of Syracuse and turned his genius to war when Rome besieged his city, holding off the legions for two years before dying — by a Roman soldier's sword — in 212 BC.
Archimedes was born around 287 BC in Syracuse, the powerful Greek city-state on Sicily's east coast, and tradition holds that he studied in Alexandria, the great center of Hellenistic learning. He was a kinsman and confidant of King Hiero II, who reigned for half a century.
The famous 'Eureka' story comes from the Roman writer Vitruvius: Hiero suspected his goldsmith of debasing a votive crown with silver, and Archimedes, stepping into his bath and watching the water rise, saw how to measure the crown's volume — and its purity — by displacement. Whether he truly ran home naked, the principle of buoyancy he stated is exact: a body immersed in fluid is buoyed up by a force equal to the weight of the fluid displaced.
In 'Measurement of a Circle' he proved that pi lies between 3 10/71 and 3 1/7 — the first rigorous bounds, accurate enough for all practical use for a thousand years. In 'On the Sphere and Cylinder' he showed that a sphere's surface and volume are two-thirds those of its circumscribing cylinder, a result he prized so highly it was carved on his tomb.
His 'method of exhaustion' — slicing curved shapes into ever-finer pieces to compute their areas — anticipated integral calculus by nearly two thousand years. The Archimedes Palimpsest, a prayer book scraped over his erased writings and recovered with modern imaging, revealed works lost for a millennium.
'Give me a place to stand, and I will move the Earth,' he is reported to have said of the lever — and he proved the mathematics of levers, pulleys and the center of gravity. The water screw that still bears his name raised water from mines and fields, and is still used in irrigation today.
When Rome besieged Syracuse in 214 BC, his cranes and catapults — 'iron hands' that plucked ships from the water, stones that smashed hulls — held the most professional army on earth at bay for two years. When the city fell in 212, the Roman general Marcellus had ordered his life spared; a soldier killed him anyway, over a mathematical diagram drawn in the sand.
