[danarmak]

Do applications motivate students? Personally I would expect examples like these to de-motivate, since they make clear that the subject does not, in fact, apply to the students' idea of real life.

If you teach abstract mathematics and make vague promises they will be really useful, some students may believe you. But if you try to demonstrate how they're useful, and the best examples you can come up with are estimating the number of piano tuners in Chicago or the number of air molecules in the room, things students know they won't ever need to do in their lives, they should become less interested.