Are there journals out there that publish work by serious amateurs (but not at the level of academic researcher). I think that MAA journal American Mathematical Monthly is a good example (I could be mistaken).
I have an idea for an article that I think is interesting and potentially useful, but doesn't involve any really crazy advanced theory (e.g., only basic measure theory and calculus of variations with constraints). I would classify my article as probability theory at the advanced undergraduate/early graduate level (in terms of mathematical difficulty).
I found one called College Mathematics that appears promising.