Leif Erikson's Vinland anyone? The way i understand it is that there is no solid proof the Chinese made it past Africa and that the rest is just speculation, please correct me if i am wrong. The Vikings are the earliest with any actual solid archaeological evidence to back it up, though i did hear something about some Irish monks, not sure if there is any proof or information on that.
But anyway, yes, Africa was the Old World (in theory the oldest seeing how many scientists agree that is when humans originated) and America was the last place to be discovered by the Europeans so is the New World.