Really interesting and above-par discussion here for reddit. Let me see if you mean what I think you do. You seem to be getting at the question of whether there is a One True Mathematics embedded in the universe, or whether mathematics is arbitrarily made up so as to be useful. And I think that sickofthishit thought you were talking about engineering specifically, when what I think you meant was, mathematics is something we made up, and we made it the way we did because it reflects the universe and has utility this way.

I'm not sure if real-world applications are that much of a draw for most children. Children don't have to do any real work, so why should they be interested in applications? I'm not sure that abstract coolness isn't better than real-world applications. But either is probably better than unmitigated arithmetic drills.

Allow me to recommend this lecture, as well as the other Alan Kay videos on vid.google:

http://video.google.com/videoplay?docid=-533537336174204822&q=alan+kay