Archimedes

By Kaveh Hosseini

Give me a place to stand, and I will move the Earth. Archimedes of Syracuse said it, and unlike most boasters, he could nearly prove it. The greatest mathematician of antiquity and the greatest engineer of the ancient world were the same man — a combination that made him both a legend and, in the end, a casualty of war.

Born around 287 BCE in Syracuse, the Greek city-state on Sicily's coast, Archimedes likely studied in Alexandria before returning home to serve King Hiero II as a kind of one-man research institute. His mathematics is staggering. In The Measurement of a Circle he trapped pi between 3 10/71 and 3 1/7 — bounds so tight they stood for centuries. In On the Sphere and Cylinder — the work he was proudest of, with its results engraved on his tomb — he proved the surface area and volume of the sphere. In The Method, a treatise lost until a palimpsest resurfaced in 1906, he revealed his secret: he discovered his theorems by mechanical reasoning, imagining geometric figures as physical weights balanced on a lever, then proved them rigorously. It is the closest any ancient came to integral calculus.

His physics was equally original. On the Equilibrium of Planes founded statics and the mathematics of levers. On Floating Bodies founded hydrostatics, proving the principle that a body immersed in fluid is buoyed up by the weight of the fluid it displaces — the famous "Eureka" moment, when he leapt from his bath and ran naked through Syracuse having solved Hiero's problem of the possibly debased gold crown. He designed the water screw that still bears his name, compound pulleys, and war machines of terrifying ingenuity.

Those machines defined his death. When Rome besieged Syracuse in 214 BCE, the seventy-something Archimedes turned the harbor into a slaughterhouse: cranes that lifted ships by the prow and dashed them on rocks, catapults of every range, mirrors — the sources claim — that set ships ablaze with focused sunlight. The Romans were so rattled that, the historian Polybius wrote, the mere sight of a rope over the wall sent them fleeing. When the city fell in 212, the Roman general Marcellus had ordered Archimedes spared; a soldier found him absorbed in geometric diagrams drawn in the dust and, when the old man protested the disturbance, killed him. "Do not disturb my circles," tradition has him say. Rome conquered Syracuse; it could not conquer the mind that had defended it.

Impact on civilization

Archimedes founded two branches of physics — statics and hydrostatics — and brought mathematics within a hair's breadth of the calculus, two thousand years early. His method of exhaustion became the model for rigorous analysis; his war machines showed that abstract mathematics could be turned into worldly power; and his legend — the bath, the lever, the circles in the dust — made him the archetype of the scientist for every generation since. Modern engineering still works in his shadow.