Archimedes was a native of Syracuse, a Greek city in Sicily. Archimedes' father was Phidias, an astronomer. We know nothing else about Phidias other than this one fact and we only know this since Archimedes gives us this information in one of his works.It is reported by some authors that he visited Egypt and there invented a device now known as Archimedes' screw. This is a pump, still used in many parts of the world.

In the preface to "On spirals" Archimedes relates an amusing story regarding his friends in Alexandria. He tells us that he was in the habit of sending them statements of his latest theorems, but without giving proofs. Apparently some of the mathematicians there had claimed the results as their own so Archimedes says that on the last occasion when he sent them theorems he included two which were false "... so that those who claim to discover everything, but produce no proofs of the same, may be confuted as having pretended to discover the impossible." There are, in fact, quite a number of references to Archimedes in the writings of the time for he had gained a reputation in his own time which few other mathematicians of this period achieved. The reason for this was not a widespread interest in new mathematical ideas but rather that Archimedes had invented many machines which were used as engines of war. These were particularly effective in the defence of Syracuse when it was attacked by the Romans under the command of Marcellus.

Plutarch writes in his work on Marcellus, the Roman commander, about how Archimedes' engines of war were used against the Romans in the siege of 212 BC:

"... when Archimedes began to ply his engines, he at once shot against the land forces all sorts of missile weapons, and immense masses of stone that came down with incredible noise and violence; against which no man could stand; for they knocked down those upon whom they fell in heaps, breaking all their ranks and files. In the meantime huge poles thrust out from the walls over the ships and sunk some by great weights which they let down from on high upon them; others they lifted up into the air by an iron hand or beak like a crane's beak and, when they had drawn them up by the prow, and set them on end upon the poop, they plunged them to the bottom of the sea; or else the ships, drawn by engines within, and whirled about, were dashed against steep rocks that stood jutting out under the walls, with great destruction of the soldiers that were aboard hem. A ship was frequently lifted up to a great height in the air (a dreadful thing to behold), and was rolled to and fro, and kept swinging, until the mariners were all thrown out, when at length it was dashed against the rocks, or let fall."

Archimedes once said "Give me a place to stand and I will move the earth". Other inventions of Archimedes such as the compound pulley also brought him great fame among his contemporaries yet Archimedes, although he achieved fame by his mechanical inventions, believed that pure mathematics was the only worthy pursuit.

The achievements of Archimedes are quite outstanding. He is considered by most historians of mathematics as one of the greatest mathematicians of all time. He perfected a methods of integration which allowed him to find areas, volumes and surface areas of many bodies. Archimedes was able to apply the method of exhaustion, which is the early form of integration, to obtain a whole range of important results and we mention some of these in the descriptions of his works below. Archimedes also gave an accurate approximation to "p" and showed that he could approximate square roots accurately. He invented a system for expressing large numbers. In mechanics Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and solids. His most famous theorem gives the weight of a body immersed in a liquid, called Archimedes' principal (remember the 'Eureka" story?).

Archimedes was killed in 212 BC during the capture of Syracuse by the Romans in the Second Punic War after all his efforts to keep the Romans at bay with his machines of war had failed. One of Plutarch's versions of the story of his killing which had come down to him is the following:

... a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was then at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him.

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