why did archimedes of syracuse go to alexandria to study and not near home
because his father felt it was better to send his son away from the warfare being waged around Syracuse
Alexandia had better campus :) (the biggest library in the world). Archimedes' teacher in Alexandria was Euclid (the guy who codified classical geometry), so their staff also outclassed Syracuse. It seems that at the time being Alexandria was the place to be when it comes to education. Syracuse was hellenic city, so was Alexandria under greek (Macedonian) rule.