Archimedes and his #$%*^@ towers are in a scenario of one of the campaigns. Only thing I remember is that they're on Syracuse. And Sean, you are right. Reflected sun rays with mirrors to set ablaze approaching ships.
As for what Archimedes does, he simply is annoying. He does nothing but follow your units (no attacks, no conversions, no nothing). The problem is you must not kill him so you have to check your army at all time or they'll kill him and you'll lose.
When you see him, let him where he is and do not free him. Keep him for the last thing you must do.
In this scenariio, it is wiser to find the backdoor then trying to sail between Mirror Towers. Omnivac