Knowledge of the lives of ancient philosophers like Archimedes is not prevalent. We know from his writings that he grew up and spent much of his life in Syracuse, a Sicilian port on the Ionian Sea. His life spanned (approximately) the years 287 B.C. to 212 B.C. His father was the astronomer Phidias and he also mentioned his friend and possibly kinsman, King Hieron II (ruler of Sicily from about 270 B.C.). According to other authors, Archimedes traveled to Egypt and there invented the device known as "Archimedes’ screw," a pump that is still used widely around the world.

There are many references to Archimedes in writings of his time period. His fame then was not due to an interest in his mathematical ideas—it was in his inventions. Plutarch wrote about Archimedes’ "engines of war" being used against the Romans in the siege of 212 B.C. Apparently Archimedes was persuaded by King Hieron to devote some of his mental ability toward that purpose.

It is interesting that despite the fame he achieved because of his mechanical inventions, he believed that pure mathematics was the more worthwhile pursuit. Plutarch describes his attitude:

Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, of the precision and cogency of the methods and means of proof, most deserve our admiration.