What is the status of questions of the form:
I came up with this idea. But I don't think its original. Please show me how this idea is unoriginal.
On one hand it could be seen as spam - advertisement for research. On the other hand, it can be done in good faith by people who come up with lots of ideas but don't want to get too sidetracked from their studies, and want to be helped by more experienced mathematicians.
"Is this original?" is not a good mathematical question on its own. The answers to that are "Yes" and "No" and neither one of them furthers anyone's mathematical knowledge.
That said, I don't think this is really what an genuine asker wants to know anyways. Perhaps, one of the following is true:
You touched upon an instance of some unfamiliar, but interesting structure. Tell us where it came from, and maybe we can point you towards some helpful literature:
While trying to prove $X$, I found it convenient to define structure $Y$ by properties $Z$. Does $Y$ have a name? Are there papers shedding light on the possible structures of $Y$s?
Maybe you'll end up learning about something cool like near-rings or quandles and this will aid your understanding of $Y$ and therefore $X$.
You found an interesting way to solve problems, perhaps by an abuse of notation, or some other informal thing, but which seems to work.
While solving various problems, I noticed that one can usually treat the $X$'s as $Y$'s and get the right answer. For instance, (example). This yields the correct answer. Is there a way to formalize this? Is this common?
Maybe we can tell you about how infinitesimal aren't evil or funny symbolic things yield correct answers.
You reduced a famous conjecture to another intractable, but different looking problem.
I noticed that one can represent conjecture $X$ as asking about whether $Y$ satisfies $Z$. Does this reduction yield any insight?
Maybe we can tell you that this is a common technique, and perhaps what interesting connections it represents, but also why it doesn't make a solution more likely.
In general, my point is that you should make the origin of your ideas clear, as well as ask with a particular purpose. Moreover, we should not be having to follow you through a long path to get to the idea - the more specialized such a question is, the less likely it is to get an answer. The best questions of this form I've seen tend to be from students noticing larger patterns behind common exercises and being answered by explications of fields of mathematics based upon those observation, but I can imagine good questions of the form at any level, so long as the author does believe a good answer exists and does what they can to focus their question towards it.
(I primarily intend this advice towards amateur mathematicians asking such questions; I would expect mathematical researchers to have a reasonable sense of what sort of questions are productive and which aren't - though MathOverflow will likely serve them better)
