I want to discuss this question. It was closed, re-opened, then closed again. The close reason is "off-topic", and I want to ask if it really is off topic. The question itself basically asks Can we formalise the notion of "interesting" mathematics?
Two preliminary point: Firstly, I think that if you are going to participate in an open/close war then you should comment, or ensure that someone has commented for you (and if so upvote that comment to make it clear that you agree or something!). This has not happened here (10 users have voted to close, none commented). Secondly, I should make my stance clear: I believe that this is an interesting question, especially as I believe that "interesting" and "beautiful" are synonymous, and relevant to current trends (see, for example, here or this PhD thesis, and one can clearly see the benefits to the current trend of "automated theorem discovery" (this seems to do a reasonably survey, dated 2009)). The idea of explaining beauty in mathematics transfixes even the best of us. I do not know how to answer the question, nor do I know if it can be answered.
The case for it being "off-topic" seems to be the following.
There is no obvious answer. Specifically, a high-rep user said that they "don't see how this can be reasonably answered".
My interpretation of this argument is: "noone who has read the post knows how to answer it, and that includes a high-rep user!". I do not believe that this is a valid close reason.
An earlier meta discussion, here. (This is not really relevant to the discussion at hand, but does give background.)
My re-open request, here.