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I am a PhD student in mathematics and have an idea for a general theory, which in a sense is an intermediate case between two opposite ends of well-understood theories. This intermediate case has gained little attention in the literature.

I came up with this idea for a more general theory by studying an explicit example in this intermediate case. The theory includes the two well-understood opposite ends in a trivial way.

I have checked with my supervisor, and he said it was a good idea and "I should write up the details". I have done so, but it has been sitting like this for almost two years. It's very tangential to the research of my supervisor and, as far as I can tell from trying to get his input, he is more interested in this particular example and not in the theory that should be built around it.

I read in "How to protect your unpublished ideas?" that the best thing would be to put this idea on the arXiv and try to submit it as a paper.

I obviously can't ask you here whether my idea is really good. But other than my supervisor, there is no faculty with this area of expertise at my university. I also don't know any other professors well enough to simply write an email asking for an opinion.

Developing the theory in all generality would be time consuming. So I'm wondering which of the three options would be best:

  1. Submit a paper now, co-authored with my supervisor, using just my example and hinting at the more general theory.

  2. Working out the details for some other cases and try to publish alone.

  3. Wait until I have more time to focus on this project (after my PhD).

  4. Put a preliminary version on the arXiv, running the risk that it contains some errors (errors on the order of magnitude of forgetting additional hypotheses, I know it works in a few examples).

In any case, I would confer with my supervisor to see whether it would be okay for me to try to publish something by myself.

I should also say that, for my taste, I'm a little short on papers (I have two short papers in B-grade journals) and I'm looking for a PostDoc soon.

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    You don't submit ideas. You submit results. – JeffE Oct 6 '15 at 16:30
  • @JeffE I meant "working out the details of what up to now is only an idea with a few motivating examples and submitting the results" but it was too long for the title. (I changed the title now.) – Earthliŋ Oct 6 '15 at 16:38
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    Sounds like a great project to pull forward from a back burner to help you deal with the anticlimax you will very likely find yourself dealing with after completing the PhD! If there is no great danger of someone scooping your idea -- wait. – aparente001 Oct 15 '15 at 23:22
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I can not give you a fully fledged answer at all, but some things to take into consideration:

Where do you want to place your article? This determines the amount of time you will have to spend on it. This has to be in-line with your idea about being short on papers (because it might not help the issue if noone reads the journal). I personally would find it a tad rude to publish alone, if the idea has spawned from something connected to your work for your insitute (and might also not be allowed depending on your contract). If you are not pleased with option 1 with respect to your ideas about the paper's benefit for you I would go with 3. You could also think about finding a PostDoc position which includes the work on this subject. If you do this intelligently, you could also use this as a selling point for yourself. Ideally this also would be the general idea of a perfect PostDoc position, allowing to develop your own ideas and research. You could try doing so with a research stipend while going abroad.

  • Thank you for your thoughts, especially with respect to the social/ethical aspect. As I said, (1) this is completely tangential/unrelated to my research, (2) I had the idea by doing calculations independently, and (3) I wouldn't consider publishing alone without talking to my supervisor. Are you saying it would be rude to ask? – Earthliŋ Oct 6 '15 at 13:31
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    In my book asking is almost never rude, if you ask considerately. This however depends solely on the person you're asking. What I usually do is: Imagining to be the person you're about to ask and trying to figure out his goals and thoughts about the topic (publishing, author lists, hierachy, in this case). It helps me to find out about possible directions to proceed in and also the direction of approach to the person (i.e. the specific way to formulate the question). He is your supervisor, so if he acts to your best benefits, I would ask him and let him advise myself. – kamuro Oct 6 '15 at 13:40
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    I personally would find it a tad rude to publish alone — Unless you acrually did the work alone, in which case publishing alone is not merely not rude but mandatory. – JeffE Oct 6 '15 at 15:36
  • @JeffE Could you explain why you say "mandatory"? – Earthliŋ Oct 6 '15 at 18:03
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    @Earthliŋ, the usual mantra for academic publishing is that only people that contributed substantially to the work of producing the results described in the article or to the production of the article itself should appear in the author list. Some communities have agreed to try to follow the Vancouver Protocol which is stricter than what I just said. Different communities have different standards, but you should not put people on the author list who did no work on the article. – Bill Barth Oct 6 '15 at 22:37

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