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Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. In the Sand-Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. A biography of Archimedes was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited Alexandria, Egypt, during his youth. Nonetheless, from his works, it is clear that he maintained collegiate relations with many scholars based there, including his friend Conon of Samos and Eratosthenes of Cyrene.

The standard versions of the life of Archimedes were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in The Histories by Polybius (c. 200-118 BC), written about seventy years after his death. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city from the Romans. Polybius remarks how, during the Second Punic War, Syracuse switched allegiances from Rome to Carthage, resulting in a military campaign to take the city under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher, which lasted from 213 to 212 BC. He notes that the Romans underestimated Syracuse’s defenses, and mentions several machines designed by Archimedes, including improved catapults, crane-like machines that could swung around in an arc, and stone-throwers. Although the Romans ultimately captured the city, they suffered considerable loses, in no small part due to the inventiveness of Archimedes.

Cicero (106-43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero presumably found Archimedes’ tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up and was able to see the carving and read some of the verses that had been added as an inscription. The tomb carried a sculpture illustrating Archimedes’ favorite mathematical proof, that the volume and surface area of the sphere are two-thirds that of the cylinder including its bases. He also mentions that Marcellus brought to Rome two planetariums built by Archimedes. Later, the Roman historian Livy (59 BC-17 AD) essentially retells Polybius’ story regarding the capture of Syracuse and Archimedes’ role in it.

Plutarch (45-119 AD) wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. He also provides at least two accounts on how Archimedes died after the city was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. The soldier was enraged by this and killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he must not be harmed. Marcellus called Archimedes "a geometrical Briareus." The account of his last words, "Do not disturb my circles" (Latin, Noli turbare circulos meos; Katharevousa Greek, μὴ μου τοὺς κύκλους τάραττε), is based on the work of Valerius Maximus (fl. 30 AD) and is likewise late.