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Are questions of the form "Is this a known result?" and "Is this an interesting result?" legitimate for MO?

I have sometimes found myself staring at results that were new to me and unsure whether they were genuinely new and/or of interest to others. For example, I recently found some very interesting results about polynomial functions on $\mathbb{Z} / n \mathbb{Z}$ that seem like they might be publication-worthy, but at the same time it strikes me as likely that they are old news to most algebraists. On the other hand Google hasn't turned up anything related to these results. Because my connection to research mathematics is somewhat attenuated (I was trained as a research mathematician but have spent the past decade working in Math Education) I don't have the kind of insider's perspective that I think would enable me to make such judgments for myself. It would be really helpful to be able to ask them here. On the other hand I don't know if this is the appropriate place for them, or if there is somewhere more suitable.

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    $\begingroup$ Quick reaction: I think it's likely that a question of the form "is this a known result?", tagged perhaps with a reference request, would be welcomed, particularly if you have exercised due diligence in searching this yourself. "Is this interesting?", like many questions which ask for an evaluation of research, is likely to get a less enthusiastic response. I would hope that an expert who is in a position to say, "no, I haven't seen this written down explicitly anywhere" might also add (if appropriate) something like, "but it's easily seen, because..." which might answer "is it interesting?" $\endgroup$
    – Todd Trimble Mod
    Commented Mar 31, 2014 at 0:38

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I recommend doing a search on meta.mathoverflow.net for "reference request". When I do it I get among the results Reference Requests: Good Ways and Bad Ways , Appropriate Reaction to a Failed Reference Request on MO , Should this site be "a shortcut to substitute for literature searches"? , and Getting Experts Opinions on Mathematical Results .

When you read these questions and others, you will find that there are good ways and poor ways to do this, as suggested by Todd Trimble in a comment above. Further, I have the sense that the community is not fully sure what the good ways are. However, if you make it absolutely crystal clear that you have put in some work, and just need a "bit of luck" (hopefully an expert will remember something that becomes a crucial pointer) that requires little or no work on the part of the responder, I think that sort of question would be well received. Also, you might check math.stackexchange, as the audience there might have the person you want. (Avoid simultaneous cross-posting, and do include references in delayed cross-posting.)

In order that the question be perceived as crystal clear, not only do I suggest following all the advice the FAQ and "How To Ask" pages offer, I also recommend the following structure for this type of question:

  • Brief statement of specific request. As an example "Is X (stated below) present in the literature for algorithm-complexity?" (NOT "Is this in the literature somewhere?")

  • Background/Motivation of result. "In working on a group theory problem, I came up with this numerical relation that I decided to tackle using approximation methods I learned in my PDE course..."

  • Inclusion of definitions and other material to make sure X can be understood by (relatively) nonexperts. "Using the notation of this on-line encyclopedia entry, Z is this graded structure, double counting orbits of this action on the nth grade leads to relation R_n, which suggests this dynamic approach Q to solve..."

  • Clear statement "X: the relations R_n are approximated (using metric M) to within delta by solutions f_n to the differential system Q, using verifier algorithm A which computes delta."

  • Recap, as well as acceptable alternatives. "Is this in the algorithmic complexity literature? I am also interested in connections to number theory or statistics, even if a minor variation of X (without algorithm A) is used instead."

  • Show a hint of your work. "I've checked what I know of computational group theory, including X, as well as basic texts Y and Z in discrete dynamical systems. I have a snippet from Knuth about Algorithm A, but not in relation to Q or f_n or R_n."

By going through the process of arranging your question this way, ideally additional search terms will be suggested to you that allow you to find it on your own (and report back your findings). Even if it is not suggestive to you, it might trigger the desired "bit of luck" in someone else. However, you don't want to overwhelm the reader: present just what you need to ask the question, and keep extra detail to the minimum and off to the side, perhaps in the section of showing some of your work. Again avoid generalities (we know you would be happy for any reference) and do what you can to support that expert who might be able to help.

Gerhard "Wants A Bit Of Luck" Paseman, 2014.03.31

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    $\begingroup$ Fantastic advice. Thanks so much Gerhard. $\endgroup$
    – mweiss
    Commented Mar 31, 2014 at 18:12

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