Who was Archimedes?
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.
Last updated: October 2026
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 of Syracuse lived roughly from 287 to 212 BCE, in a Greek city on the east coast of Sicily that was among the richest and most powerful in the Mediterranean. Syracuse was a crossroads: a Greek colony with ties to Corinth, a rival of Carthage, and a city that would soon be caught between the two superpowers of the western Mediterranean, Rome and Carthage. Archimedes was born into the city's elite — his father, Phidias, was an astronomer — and he studied in Alexandria, the great centre of learning in Egypt, before returning to Syracuse, where he spent his life under the patronage of King Hiero II.
We know Archimedes almost entirely through his own writings and through later admirers. Unlike many ancient thinkers, he was both a theoretician and an engineer: he proved theorems of pure geometry with a rigour that would not be surpassed for nearly two thousand years, and he built machines that terrified armies. The Roman writer Plutarch, who is our main source for his life, says Archimedes regarded his practical inventions as "sordid and ignoble" beside pure mathematics — yet it was the inventions that made him famous, and that would, in the end, cost him his life.
The most famous story about Archimedes is the one about the crown. King Hiero had commissioned a golden crown and suspected the goldsmith of mixing in silver. He asked Archimedes to determine whether the crown was pure gold without damaging it. The solution, legend says, came to Archimedes in the bath: noticing the water displaced by his body, he realised that the volume of an irregular object could be measured by the water it displaces, and that an object's density — its weight divided by its volume — would reveal whether it was pure gold. He leapt from the bath and ran naked through the streets crying "Eureka!" — "I have found it!"
The story is almost certainly embellished, but the principle it carries is real and is still called Archimedes' principle: a body immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. That is why ships float and balloons rise. Archimedes set out the theory of floating bodies in his treatise On Floating Bodies, which also explored the stability of ships — the first work of naval architecture, and a text whose second half was lost until the rediscovery of the Archimedes Palimpsest in the twentieth century.
Archimedes' most quoted remark concerns the lever: "Give me a place to stand, and I will move the earth." The law of the lever — that a small force applied at a great distance from a fulcrum balances a large force near it — was his, and he built on it a science of mechanics that included pulleys, the screw that still bears his name, and compound machines. The Archimedes screw, a helical pump for raising water, is still used in irrigation and sewage treatment today. Tradition also credits him with a system of mirrors or lenses that set Roman ships alight — a story modern experiments have tested with mixed results, and which most historians regard as legend.
The war machines were real enough. When Rome besieged Syracuse in 213–212 BCE, during the Second Punic War, Archimedes' defences held the Roman army and fleet at bay for two years: catapults with adjustable ranges, cranes that lifted ships from the water and dropped them, and, according to Plutarch, grappling devices that seized vessels by the prow. The Roman commander Marcellus is said to have complained that he was fighting a "geometrical Briareus", a hundred-handed monster. Syracuse fell in 212 BCE, through treachery during a festival, and Archimedes was killed by a Roman soldier — according to legend, while he was working on a diagram, telling the intruder, "Do not disturb my circles." Marcellus, who had ordered that he be spared, was said to have mourned him.
Archimedes' mathematics was his greatest achievement, and it anticipated the calculus by nearly two millennia. In Measurement of a Circle, he proved that the ratio of a circle's circumference to its diameter — pi — lies between 223/71 and 22/7, by inscribing and circumscribing polygons of up to ninety-six sides. In Quadrature of the Parabola, he found the area of a segment of a parabola using the method of exhaustion, a technique of approximating a curved area by ever-finer polygons that is, in essence, integration. In On the Sphere and Cylinder, he proved that the surface area and volume of a sphere are two-thirds those of the cylinder that encloses it — a result he was so proud of that, according to tradition, a sphere and cylinder were carved on his tomb.
In The Sand Reckoner, Archimedes devised a system for expressing numbers larger than any in ordinary Greek usage, to show that even the number of grains of sand that would fill the universe could be written down — an early meditation on the infinite and on the power of notation. And in The Method, a work lost until the twentieth century, he revealed how he actually discovered his results: by imagining shapes sliced into infinitely many pieces and weighed against each other, a technique of infinitesimals that he then proved rigorously by exhaustion. It is the closest any ancient thinker came to integral calculus.
Archimedes' works survived through Byzantine copies, and his influence on the scientific revolution was profound: Galileo called him the greatest mathematician, and his methods shaped the work of Newton and Leibniz. But the fullest picture of his thought came only in modern times. In 1906, the Danish scholar Johan Ludvig Heiberg discovered in a prayer book in Constantinople a palimpsest — a manuscript whose parchment had been scraped and reused — containing lost works of Archimedes, including The Method and the only surviving Greek text of On Floating Bodies. The manuscript was sold at auction in 1998 and subjected to years of imaging and conservation, revealing texts that had been invisible for centuries.
Archimedes remains the archetype of the mathematical physicist: a thinker who moved freely between pure theory and practical machines, who could calculate pi to two decimal places and defend a city, who glimpsed infinity and died over a diagram in the dust. The "Eureka" moment has become the universal image of discovery. The reality was harder and finer: a lifetime of rigour, imagination and work, preserved by luck across two thousand years.
- Archimedes, The Works of Archimedes, edited and translated by T. L. Heath.
- Reviel Netz, The Works of Archimedes (Cambridge, new translation and commentary).
- Reviel Netz and William Noel, The Archimedes Codex — on the Palimpsest.
- Plutarch, Life of Marcellus — the ancient source for the siege of Syracuse.
- Encyclopaedia Britannica, "Archimedes".