Never assume mathematicians can see past their little definition/lemma/theorem games to solve actual problems where those definitions/lemmas/theorems are "obvio

Never assume mathematicians can see past their little definition/lemma/theorem games to solve actual problems where those definitions/lemmas/theorems are "obviously" applicable. Some can, but a surprising number can't. I think this is due to a destructive meme that has crippled the minds of many mathematicians, causing them to instinctively equate applying their definition/lemma/theorem games to actual problems with low status.