Archimedes was most famous in his time as the inventor of various mechanical devices, some of which were part of the Syracusans' defense. The details of these machines that come down to us do not warrant a serious investigation about them (contrary to the looooooooong and very silly discussion in the English article).

But Archimedes' major legacy lies in the contents of a number of articles and letters of a technical mathematical nature, most of them recording more or less the exact words he himself wrote (dictated?). The letters are essentially the only source we have that tells us something more than just the dry mathematics involved - we might deduce from them that Archimedes was a bit sour, or maybe just impish.