Archimedes

Archimedes was a Greek mathematician, physicist and engineer from Syracuse in Sicily who lived from about 287 BCE until 212 BCE. He worked out the mathematics of the lever, floating bodies, the sphere and the circle, and he is credited with devices such as the Archimedes screw. He was killed when Roman forces captured Syracuse during the Second Punic War.

Early life of Archimedes

Archimedes was born in Syracuse, a Greek city on the island of Sicily, around 287 BCE. We know the name of his father, Phidias, an astronomer, only because Archimedes mentions it in his book The Sand Reckoner. A biography written by his friend Heracleides has not survived, so little else about his early years is certain.

Plutarch says Archimedes was a friend and relative of King Hieron II of Syracuse, and The Sand Reckoner is dedicated to Hieron’s son Gelon. Many scholars think he studied in Alexandria with the successors of Euclid. The World History Encyclopedia adds that he made friends there with Eratosthenes and Conon of Samos before returning to Syracuse to work for the king.

Career and major work of Archimedes

Archimedes served the court of Syracuse as a mathematician and as a practical problem-solver. His surviving treatises include two books On the Equilibrium of Planes, Quadrature of the Parabola, two books On the Sphere and Cylinder, On Spirals, On Conoids and Spheroids, two books On Floating Bodies, Measurement of a Circle and The Sand Reckoner. A further work, The Method, came to light in the summer of 1906, when the Danish scholar Johan Ludvig Heiberg found it in a 10th-century manuscript.

That manuscript is now called the Archimedes Palimpsest. A palimpsest is a manuscript whose original text was scraped away so the parchment could be reused. The Walters Art Museum in Baltimore states that it holds seven of his treatises, that it is the only surviving copy of On Floating Bodies in the original Greek, and that it is the unique source for The Method. An anonymous collector bought it at auction in 1998 and deposited it at the museum in 1999 for conservation and study.

Plutarch reports that Archimedes designed war machines for Hieron and that they were used against the Romans under Marcellus in the siege of 212 BCE. Plutarch adds that Archimedes regarded such devices as amusements in geometry rather than serious work.

Ideas and contributions of Archimedes

In geometry, Archimedes showed in On the Sphere and Cylinder that the surface of a sphere is four times the area of its great circle and that its volume is two-thirds that of the cylinder around it. In Measurement of a Circle he fitted regular polygons with 96 sides inside and outside a circle and concluded that pi lies between 3 10/71 and 3 1/7. In Quadrature of the Parabola he found the area of a segment cut off from a parabola by a straight line.

The Method shows how he found many of his results by balancing imagined slices of a figure against one another, then confirmed them with strict proofs. The MacTutor biography says his methods anticipated the integral calculus. The Sand Reckoner proposes a number system able to express numbers as large as 8 times 10 to the power 63, in modern notation, and argues that this is large enough to count the grains of sand that would fill the universe.

In mechanics, he found the centers of gravity of plane figures and solids and set out the law of the lever in On the Equilibrium of Planes. In On Floating Bodies he laid the foundations of hydrostatics, the study of fluids at rest, and stated what is now called Archimedes’ principle: in modern terms, a body immersed in a fluid is pushed up by a force equal to the weight of the fluid it displaces. The principle remains basic to fluid mechanics and to ship design.

The Archimedes screw, a pump built from a spiral inside a tube, is credited to him. MacTutor reports that some authors say he invented it in Egypt, and it is still used in many parts of the world. Plutarch also tells of a compound pulley that let him pull a fully loaded ship across the shore with little effort.

Death and tomb of Archimedes

Archimedes was killed in 212 BCE when the Romans took Syracuse. The accounts differ on the details. In the version reported by the World History Encyclopedia, a soldier told him to follow, and Archimedes refused because he was absorbed in a calculation. Another version says soldiers killed him because they thought he was carrying gold.

He had asked for a sphere inside a cylinder, with the ratio between them, to be carved on his tomb. In 75 BCE the Roman orator Cicero, serving in Sicily, looked for the tomb and found it overgrown with brambles, identified by a small column bearing a sphere and a cylinder.

Legacy of Archimedes

MacTutor calls Archimedes the greatest mathematician of his age. His methods for finding areas and volumes influenced later work leading to calculus, and the recovery of The Method in 1906 gave historians a rare view of how he actually discovered his results. A 2005 release from the Walters Art Museum described X-ray fluorescence imaging that made it possible to read previously unknown mathematical texts in the palimpsest.

Legends and disputed claims about Archimedes

The best-known story is that Archimedes, asked to test whether a crown was pure gold, noticed while bathing that his body displaced water and ran through the streets shouting Eureka. The Roman architect Vitruvius tells it about two centuries later. The World History Encyclopedia points out that Archimedes’ own On Floating Bodies never mentions the crown, so the story is best treated as a legend.

Stories of a heat ray, or burning mirrors, used against Roman ships are also debated, and the World History Encyclopedia says that both their existence and their efficacy remain uncertain. Some scholars suggest Archimedes as the likely inventor of the Antikythera mechanism, a geared device that modeled the heavens, because Cicero describes similar instruments by him. Others attribute that device to Hipparchus or different makers, so the question remains open.

Editorially reviewed by Specialty Digest Editorial TeamLast reviewed November 4, 2026Researched and drafted with AI assistanceReport an issue