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Is it a bad idea to mention in a paper that I plan to address some of the questions it rises in a future paper?

Background: While discussing some results from a recent preprint with other people, we came to the conclusion that with similar methods we can prove a much more general statement. In fact, we are working on it now, and already have some preliminary results (not quite as general as we hope to get though). Now, while revising the original preprint, which I hope to send to a journal soon, I am faced with a dillema: Should I mention that we are currently working on the more general problem, and hope to publish its solution in an upcoming paper? It is a very natural generalisation, so I certainly should mention the problem itself as a possible future direction.

Positives: The positive aspects of mentioning the future project are, I think, quite self-evident. For us, it gives marginally more peace of mind (people are less likely to try and obtain our future result if they know we are working on it), and marginally more publicity (possibly someone will be interested in the problem after reading the first paper and will look up the upcoming one later). For the public, it gives a fair warning (so less chance someone will start working on this problem and be disappointed we did it first) and a reference for where future results might be found.

Negatives: There are also several reasons why mentioning the future project may be counterproductive, and/or/hence put us in bad light. I'm not sure how valid the following concerns are.

  1. I'm claiming rights to something that's not mine. Until we have a proof of the new result, we have no special rights to it; while here I am, claiming the problem as ours. This may especially irritate people who would also like to work on the problem, but now feel compelled not to.

  2. I'm obstructing future progress. Perhaps someone would have produced a better solution to our problem if we didn't deter them. This is especially important if at some point we discover that our project was overly optimistic and that we do not have a solution in the end.

  3. I'm putting irrelevant things in the paper. Someone might argue that the purpose of a mathematics paper is to communicate mathematics. References to past papers serve to give credit where credit is due and to enable the reader to look them up. Conjectures and divagations about future directions are also fair game, as they are ultimately about mathematics. But writing about our future directions is about as relevant as saying that I'll be working on the problem while listening to classical music and doodling on a piece of white paper with a green pen.

(If relevant - my field is pure mathematics. Perspectives from other disciplines are very welcome.)

Edit to clarify: My impression is that for questions like that, there is a clear-cut (but often unwritten) set of rules which say what you can and cannot do in a paper. If this is a border-line case where the decision is genuinely opinion-based, then I would be very eager to learn this as well.

  • I want to flag this as "will attract opinion based answers" as this is asking if people think this is a bad idea........But I won't I will just leave my observation as a comment..... – NZKshatriya Jan 27 '17 at 3:59
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    @NZKshatriya Fair enough, thank you for pointing this out. I am not sure if this makes the question inherently more likely to "attract opinion based answers". My impression is that there are some fairly clear-cut but unwritten rules about what you should and should not put in a paper. If there is no community consensus, then the answer to my question would be that the decision is opinion-based, i.e. that it's permissible but not obviously OK. – Jakub Konieczny Jan 27 '17 at 4:12
  • I like @DanRomik's answer and wanted to add: Even if someone else works on the general case, either because you didn't warn them off, or they ignored your warning -- they might not end up going exactly where you're going with it. So, this may be one of those cases where perhaps the best way to help is not to "help." – aparente001 Jan 27 '17 at 6:38
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    Just a note that the correct answer will be field-specific. In my field (in computer science), it's normal to have a section called "Future Work", or at least a paragraph about potential future work. A reviewer even once asked me to mention a particular idea in this section. – lighthouse keeper Jan 27 '17 at 6:55
  • Work on the new result. Don't mention the new result in the preprint nor subsequent journal submission. Add a citation to the journal submission whilst making corrections. – user2768 Jan 27 '17 at 9:30
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This is a great question, but I think it's slightly misformulated. What you are thinking of doing is neither "bad manners", nor can it really be considered "marking your territory" in all but an extremely weak (so weak as to be essentially meaningless in my opinion) sense. The correct question is the one you ask in the body of the question: is it a good idea? And specifically, is it a good way to build a solid reputation for yourself and to maximize the impact of your work?

The principle at work here is that in general it's a bad idea to brag about achievements you haven't yet attained. You might think that by doing so you are "marking your territory", but that's simply not the case: in reality it is fair game for anyone to publish a proof to a claim that you say you plan to prove in a future paper (and if they publish a proof using a different technique than the one you use, as you suggested, then that is even more legitimate and there is even less concern that they will be deterred by your "territory-marking", to the extent that such a concern exists at all). On the other hand, by trying to lay claim to results of which you do not currently have a written proof you undermine your own credibility: no one knows whether you will follow through on your promises, and everyone has seen cases of people making such claims and never following through, and would therefore be quite likely to be very skeptical of your claims (both the present claims and any claims by you they will encounter in future papers). So, by and large, bragging about as-of-yet-unattained achievements is not a winning strategy, and I'd advise against it in all but a handful of circumstances.

So when is it appropriate to advertise planned future follow-up work at the end of a math paper? I can think of two situations where it may not be a bad idea:

  • You have a 90%-complete manuscript of the future work and have a very high degree of confidence that you can complete it in a very short period of time, and you believe that advertising the future work helps make your current paper seem more attractive. (But be very careful: predictions of this sort tend to be wildly optimistic. I am speaking from personal experience, which I'm guessing is shared by almost everyone who has been publishing in pure math for more than a few years...)

  • Your intent is not to advertise the future work in a selfish, territory-marking sort of way, but rather to advertise directions for follow-up work that you believe are of interest to the community in an altruistic sort of way that makes it clear that anyone is free to pursue those directions. It's still perfectly fine to imply that you plan to do so yourself, just don't expect that this gives you any special rights that prevent others from beating you to the punch. For example, you can write something like:

    To conclude, an interesting open problem is whether a non-Riemannian hypersquare exists. We believe the techniques of the current paper can be used to show that the answer is positive, and plan to address this in future work.

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    I agree that the final paragraph you wrote IS appropriate, but I also think it IS territory marking to some extent. Certainly reading such a statement would make me much less likely to suggest the problem to an average graduate student (without checking with you first), and if I had also noticed your technique might be applicable to this open problem but didn't know your technique well already, such a statement would certainly deter me from learning your technique for the purpose of working on this open problem unless I had other reasons for learning your technique. – Alexander Woo Jan 27 '17 at 6:09
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    @AlexanderWoo ok, fair enough. I think much depends on the credibility of the researcher making the claim. Some people have built enough of a reputation that if they say they intend to publish something then it's almost certain they will follow through, but with an unknown researcher making a similar claim I personally would not be inclined to pay this much attention. – Dan Romik Jan 27 '17 at 6:28
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    I agree that the described statements do not lay any real claim on anything. However, I somewhat disagree because I fail to see how it is bragging to announce future work. In general (though this might be field-specific), future work remarks illustrate how the described work is not a "dead-end", corroborate the usefulness of the results, and show that the authors think about the topic beyond the point of just "churning out another paper". Whether they write "someone can do ..." or "we're planning to do ..." is, realistically, just an insignificant variation in wording. Most readers will be ... – O. R. Mapper Jan 27 '17 at 8:37
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    ... aware of how unplannable availability of researchers, publication opportunities, and time for specific ideas often are. Thus, at best, "we're going to ..." means "if you want to see these results, feel free to team up with us and drive this endeavour because we're really interested in this topic and will at least provide some advice". It is certainly not a promise or even a guarantee of any sort. – O. R. Mapper Jan 27 '17 at 8:40
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A "moral high ground" answer:

  • It's not "your territory", it's everyone's. That is, scientific discoveries should not be seen as owned in any way by individuals or groups, but as common treasures of human civilization.
  • It's good to let your fellow researchers know what you're working on, because:
    • This prevents redundant parallel work (although of course sometimes parallel work on the same problem with different perspectives can be a good thing; it's just that you want to know whether that's the case or not).
    • It increases the chances of collaboration with other researchers interested in the same problem.
  • Papers should not reasonably be limited from the addition of a few short paragraphs indicating future research directions; and even if such a restriction is in place for some reason, such intentions can be published on a research group / individual researcher website or blog.

Thus if we ignore things like squabbles over credit, I believe the answer is pretty clear.

PS - I would always tone down what's expected, to avoid the deterring effect you mentioned and not to have to retract what I claimed. So "We're working on the problem" is preferable to "We believe we've obtained a solution" as long as it's not 100% sure-fire in-the-bag.

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    It's good to let your fellow researchers know what you're working on. This prevents redundant parallel work. FYI, I'm working on proving the Riemann Hypothesis. And on P vs NP. And the other Millenium Prize problems. Consider yourself warned :-) – Dan Romik Jan 27 '17 at 15:17
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    @DanRomik: Oh, really? That's good to know. Then I'll get to work on the low-hanging fruit that follows from your last paper on frobnicating bars, since you won't be doing so. Thanks :-) – einpoklum - reinstate Monica Jan 27 '17 at 15:25
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    No, I'm working on that problem as well. I'm very good at working on many things st the same time. Please don't work on that problem, it will only be a redundant duplication of efforts. – Dan Romik Jan 27 '17 at 15:32
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    @DanRomik: I haven't told you what problem I was thinking of yet... :-\ – einpoklum - reinstate Monica Jan 27 '17 at 18:08
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I think it is both expected and acceptable to let people know in a paper both what the conjectures and open questions are, and to let people know whether you are working on them, whether you hope to solve them and whether you intend to publish something on them.

However there is a subset of behavior which I think is bad manners when I've encountered it:

  1. Author(s) X publishes paper A.
  2. They cite by name currently unpublished paper B, by the same authors.
  3. In a particularly annoying case, some of the results in paper A depend on other results in paper B. Sometimes it's not even clear what the statement of these results is, just that if you knew what it was, you would believe the claims made in A.
  4. Researcher Y reads paper A.
  5. They unsuccessfully search for paper B which they expect has now been published.
  6. They contact X and request a preprint.
  7. X informs them that paper B is not quite ready to send out preprints since they are in the process of adding some even more exciting results.
  8. X promises to send out paper B when it is ready.
  9. <crickets>
  10. Y doesn't know whether to believe in the results in B, whether to work on their own proof of these results, whether the results in A are still correct, whether or how to cite the 'ghost paper' B in their own work.
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    It's not bad manners, it's just a bad paper, and your story ends with: 11. Paper gets rejected from any respectable journal it is submitted to. – Dan Romik Jan 27 '17 at 15:14
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    @DanRomik Both the story and my experience include paper A getting published in serious journals. It would be annoying if no-one could ever publish something that referred to just-about-to-be-published results which for whatever reason belong in a different paper. – jwg Jan 27 '17 at 15:57
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Why not mention the work being done?

I do not know how reproducibility and repeatability are treated in pure mathematics. But in many fields they are important. So, even if others publish your upcoming solution first, repeated work is important for reproducibility and repeatability (at least in some fields). And no one can deny that you were on the right track (try to ignore the publish or perish mindset).

On top of that, if others know what you are working on and that you are close to publishing it (I would avoid claiming that though, see example below), chances are that they may go to develop alternative solutions, that can, later, be compared with yours. A model may have a shortcoming in a particular situation, but may be the best in another (I see this a lot in engineering).

An example

In a paper of 1969, it is stated in a section just before the conclusion:

Work is in progress at BPA to incorporate the frequency dependence approximately into the method of characteristics; (...) The weights would have to be chosen to match the frequency spectrum derived from Carson's formula (...)

And then in the conclusion:

(...) Further work is necessary to find a satisfactory way to represent frequency dependence of line parameters.

It certainly marked the territory by acknowledging that future work is needed, it is in progress, and it was pointed out what a possible solution would be.

As far as I know, a widely used/accepted solution just came to be in 1982 by a PhD student being advised by the author of the first paper. It took more than ten years to arrive at a milestone. Of course, even today, there still is research being done about this particular topic...

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