funny. yesterday i was trying to explain to my friend, a physics grad student like myself, why i wanted to study algebraic geometry. i said, it's because physic

funny. yesterday i was trying to explain to my friend, a physics grad student like myself, why i wanted to study algebraic geometry. i said, it's because physicists only know about groups, because everything seems to be groups. but rings have more structure than groups and fields have more structure than rings and that's what algebraic geometry is about. this comment is probably too late. you are right that most things turn out to be a group, but not "just a group".