I spotted this interesting article in the Globe and Mail (you may have to register to view it) about a tribe in the Amazon who have no concept of numbering or counting. So, essentially, they can't count or perform simple arithmetic nor can they learn how. This tribe, the Piraha, are quite interesting in other ways as well. The Piraha have no distinct words for colours and no written language; they have a collective memory that only goes back more than two generations; and they don't sleep for more than two hours at a time (more details about the Piraha can be found in the article). To say they're "different" really misses the point.
The existence of this numberless tribe also has some interesting linguistic and psychological implications too. There's this theory, linguistic determinism, which proposes that language defines thought and the existence of this tribe would appear to partly support that. The gist of the theory is that if a language lacks words for certain concepts it would prevent the speakers of this language from understanding those concepts (this article from The New Scientist has the details). The theory's a bit controversial too and there isn't any consensus as to why the Piraha can't count. Professor Everett, as mentioned in the Globe article, believes that the reason why the Piraha are so different is because they want it that way. The Piraha see themselves as different and better than those around them: everything they do is a way to maintain this difference and their collectively perceived superiority.
Personally, I'm more freaked out by the fact that they only sleep for a couple hours at a time, that's just nutty. I wonder how they feel about coffee?