Digression: This uncertainty about dates does not improve; in fact it gets worse. Because we know the date of Archimedes' death and can deduce something about the logical connections between his work and Euclid's, we are reasonably certain to within a few dozen years about when Euclid lived. But for the later mathematician Diophantus the period of uncertainty is much more extensive. Estiamtes range up to a span of 500 years! The problem is discussed in an interesting article on Diophantos by Norbert Schappacher. This is quoted by the Wikipedia article on Diophantus, but Schappacher's message is ignored. People believe what they want to believe.

It is often asserted that Archimedes was born in 287 B. C., but (as mentioned timidly in one of the Wikipedia articles) this is based on an assertion made without further explanation in Byzantium 1400 years after his death that he was 75 years old when he died.