Evidence indicates that cats were first tamed in Egypt. The Egyptians stored grain, which attracted rodents, which attracted cats. (No evidence that such a thing happened with the Mayans, though a number of wild cats are native to the area.) I don't think this is accurate. It is certainly not the whole story. Cats didn't start as mousers. Weasels and snakes and dogs are more efficient as rodent-control agents. I postulate that cats started as psychic companions, as Familiars, and have never deviated from this function.