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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.

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  • $\begingroup$ I guess part of the issue is that professional or aspiring mathematicians are often motivated by economics, and it would seem exploitative to use this Q&A to further one's economic standing at 0 cost. But on the other hand, if it is taken as simple free inquiry,there seems nothing bad about asking this kind of question, except maybe it produces more clutter on the site. $\endgroup$ – 123 Jul 2 '15 at 17:50
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    $\begingroup$ In principle I think this sort of question is fine, but be sure to include more than "Here's a definition. Has this been studied?" Anyone can probably throw up together random definitions on the spot (like "the class of number whose number of digits contains the letter 'u' when spelled in English"), but this isn't interesting to anyone. Include motivation, what inspired you to come up with this idea, similar things that exist and that have been studied... (In a word: context) And make sure that it's focused, too: don't link a 10 page paper and ask if there's a new idea in it. $\endgroup$ – Najib Idrissi Jul 2 '15 at 17:53
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    $\begingroup$ @NajibIdrissi Is a "random definition" a random variable over the space of 1st order predicates? That is brilliant, I never thought of that! $\endgroup$ – 123 Jul 2 '15 at 19:01
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    $\begingroup$ As a matter of style, writing things like "Please show me how this idea is unoriginal" never strikes me well - it looks awful disingenuous to have a phrase which seems to only exist to give the impression of, "I'm not a crank who would be gulled into thinking my ideas are original" while simultaneously asking, "...but are my ideas original?" $\endgroup$ – Milo Brandt Jul 2 '15 at 23:40
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    $\begingroup$ I have had decent success with questions like this on MO. Both in the form of "is this result known?" (mathoverflow.net/questions/33770/…) and in the form "has this been studied" (mathoverflow.net/questions/136381/… which resulted in an email from a researcher who had begun doing research on the topic). $\endgroup$ – Tobias Kildetoft Jul 3 '15 at 6:59
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"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)

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  • $\begingroup$ see new meta.math.stackexchange.com/questions/20921/… $\endgroup$ – Will Jagy Jul 3 '15 at 17:53
  • $\begingroup$ All this is good, but very naive. Not comfortable thoughts and ideas often block. Why people come to tell the idea to the forum? Because it is not possible to publish it. When you tell her then try and the forum block. Many have good ideas, but often cannot even be discussed. $\endgroup$ – individ Jul 10 '15 at 6:59
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    $\begingroup$ @individ: It's not a "forum" :) $\endgroup$ – Lightness Races in Orbit Jul 13 '15 at 21:27

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