Archimedes

Archimedes was born around 287 BCE in Syracuse, a Greek city in Sicily. That year is derived from the Byzantine scholar Tzetzes' claim that he lived for seventy-five years. In The Sand Reckoner he names his father as Phidias, an astronomer about whom nothing else is known.

Plutarch calls him a relative of King Hiero II of Syracuse, while Cicero and others point to a humble origin. Whether he ever studied in Alexandria is unknown; his surviving works are addressed to scholars there, such as Dositheus and Eratosthenes. An ancient biography has been lost, so many details of his life remain uncertain.

Archimedes investigated areas and volumes using the method of exhaustion. In On the Sphere and Cylinder he showed that the volume and surface area of a sphere are two thirds of those of the circumscribed cylinder. In Measurement of a Circle he estimated π between 223/71 and 22/7; in Quadrature of the Parabola he determined the area of a parabolic segment.

He was one of the first to apply mathematics to physics. In On the Equilibrium of Planes he proved the law of the lever and used centres of gravity; in On Floating Bodies he formulated the law of buoyancy that bears his name. In The Sand Reckoner he developed a system for expressing very large numbers and estimated the apparent diameter of the sun.

Ancient authors attribute devices to him, such as pulley systems, defensive machines and a planetarium. His Method, a letter to Eratosthenes, describes how he found results by mechanical reasoning before proving them rigorously. That text is known only from a palimpsest identified in 1906.

In the third century BCE Syracuse was one of the largest and richest Greek cities, ruled by Hiero II. After the First Punic War Hiero remained an ally of Rome, which brought his city long peace and prosperity. After his death in 215 BCE, Syracuse took the side of Carthage in the Second Punic War.

Alexandria, with its Museum and Library, was the centre of Greek science; mathematicians from all around the Mediterranean exchanged texts and problems there. Scholars often worked for rulers and cities and were usually also engineers, astronomers or philosophers. Archimedes wrote in the Doric Greek of Syracuse.

In antiquity Archimedes was famous above all for his mechanical ingenuity. Polybius, Livy and Plutarch describe improved catapults and cranes that lifted Roman ships and sank them, which prolonged the siege of Syracuse. Cicero relates that Marcellus brought two planetaria by Archimedes to Rome, one of which was placed in a temple.

His mathematical writings were little known in antiquity. Alexandrian mathematicians read and quoted him, but the first comprehensive collection was made only around 530 CE by Isidore of Miletus in Constantinople; commentaries by Eutocius from the same period made them more accessible. His mathematics thus initially reached mainly a small circle.

Archimedes was killed in 212 BCE when Syracuse fell. Livy says he was killed by a soldier who did not recognise him while he was drawing figures in the dust; Plutarch gives several versions, including Marcellus' order to spare him. In 75 BCE Cicero, as quaestor in Sicily, found a presumed tomb with a sphere and a cylinder.

Surviving works must be separated from legends. Reliable ones include On the Sphere and Cylinder, The Sand Reckoner and the Method. 'Eureka' in the bath (Vitruvius, about two centuries later), the burning mirrors (not in Polybius, Livy or Plutarch; mentioned only in the second century CE) and 'Do not disturb my circles' (not in ancient sources) are legendary or unconfirmed.

His work was translated into Arabic in the ninth century and into Latin in the twelfth; the first printed edition appeared in Basel in 1544. Galileo called him 'my master'. In 1906 Heiberg recognised his texts beneath a medieval prayer book, the Archimedes Palimpsest, which contains the only known copy of the Method.

The painting by Domenico Fetti with this dossier dates from 1620; it is an imagined likeness, since no reliable contemporary portrait of Archimedes is known. His image has appeared on the Fields Medal, one of the highest honours in mathematics, since the twentieth century.