In a mathematics thesis I am currently working on, I use a statement we proved in the exercise classes of a lecture I attended last year, but neither the exercises nor the lecture notes have been published. I am wondering whether it is still possible to cite the exercise, and if yes, in what format.
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Is it allowed/ possible to ask the thesis advisor?– user111388Commented Apr 20, 2020 at 6:24
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@user111388 My thesis advisor said that I shouldn't include the proof, but was also unsure how to proceed. He said I should first search for it in books and that we would see what to do if I couldn't find it. I didn't find it and we haven't talked since. I will ask him again, but I was wondering whether there was a somewhat generally accepted way to go about something like this.– Peter KoepernikCommented Apr 20, 2020 at 6:55
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Okay, thank you for the reponse! Is it possible for you to recreate the proof?– user111388Commented Apr 20, 2020 at 7:29
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why not add the statement & proof of exercise as an appendix?– OurCommented Apr 20, 2020 at 8:28
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3I suppose one possibility is to pose the exercise as a question in Mathematics Stack Exchange, perhaps giving the context, and if a suitable-for-your-purposes (well written, sufficient detail, etc.) answer doesn't show up after a few days, then post your own answer. Once this is done, cite the answer(s) in your thesis.– Dave L RenfroCommented Apr 20, 2020 at 9:38
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3 Answers
Things that you use, but didn't create, need to be cited. In this case, you can write "about" the exercise or, perhaps even including the statement of it in total (caveat below). But the citation would need to include the name of the source and preferably the date and location at which you were given it as an exercise. Even a rough date, as in March 2018.
The caveat is this. People who create things normally have an automatic copyright on it. It was "published" in some sense when it was given to you. So you also need to respect that. But the more serious issue here is that you can't "fairly" copy a "complete work". So, even a Limerick, which is only a few lines long, can't be quoted completely if copyrighted as it is, in some sense, a "complete work." There are some exceptions, depending on local law, for academic use of things, but they don't permit unlimited copying.
I recommend that you do two things. The first is to follow your advisor's advice and not publish a solution, since this makes the exercise potentially useless for the future, destroying its value (a consideration in copyright law). And second, that you contact the originator and ask for advice. I suspect that a reasonable person would have little problem with you publishing a statement of the exercise in a larger work, but might object, also, to the inclusion of the solution.
But for the citation of such a thing: name, place, date. Such things are also often tagged specifically with a notation such as "private communication", though that specific one doesn't apply here. "Classroom Exercise, used with permission" might work.
Note also that copyright law varies widely as does the definition of "fair use". But a bit of care can normally solve all issues.
You always cite your source as best as you can. If your best citation is “unpublished solution to a lecture exercise”, then that is what you should cite. If you can find a better citation, fine. If not, cite it this way.
Since you don’t want to rely on something unproven, you should include the proof. One reason to have a citation is to allow others to verify the result, so the proof should be somewhere where I can read it. If there’s no other place than your paper, that’s where it should be.
And to avoid accusations of self-plagiarism you should probably mention how the proof was created.
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I don't think the charge of self-plagiarism can occur here. The OP isn't referencing their own published work. But ordinary plagiarism is a possibility if the impression is given that the OP developed the exercise themself. And including the proof seems to go against the wishes of the advisor who may have been the originator of the exercise.– BuffyCommented Apr 20, 2020 at 14:57
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The advisor is not the original source, but a colleague. He said he thought it was unnecessary to include a proof that I would just copy from somewhere, but also wasn't sure whether or how to cite the exercise. So if I do include the proof, would I just put a line like "This proof is taken from the exercise classes of lecture X that was given in year Y by lecturer Z" in the beginning? Commented Apr 20, 2020 at 15:43
In mathematical research, one cites statements, proofs, hypotheses, arguments, etc., for 2 reasons:
To avoid taking credit for that which is not your own discovery.
To build on the shoulders of others and not recreate the wheel.
It happens not infrequently that part of your argument is not yours, i.e. is either directly taken from elsewhere or at least strongly inspired by it, but there is not an easily accessible source for it. Quite often the point is something insightful someone scribbled on a blackboard somewhere after a talk or seminar, or even "folk wisdom" that everyone is some subfield knows but somehow turns out to have never been written down.
It is quite acceptable to do one of the following (and I have at various times done all 3):
Articulate the argument, but make it clear you are not claiming ownership. This tends to be best for "folk wisdom"-type results.
State the result, citing who made it (or introduced you to it), with the best possible citation. This tends to be best when there is significant IP in the result or proof; you don't want to scoop someone on something they could/should publish themselves.
Write your own argument, adapted/simpified for your use case, inspired by what you have seen elsewhere. You should then note/cite that this was inspired by such-and-such. This tends to be best where your application is in a pretty special case compared to greater generality in the argument that you have seen elsewhere.
In the case of an exercise in a previous course, where you were encouraged to Socratically "rediscover" the answer yourself as a student, it seems unlikely that the 2nd approach is necessary. So I'd choose either the 1st or the 3rd, based on whether you're using the exercise in full generality or not.
You could also check with the instructor in that course, since a lot in a course is not original thinking. He/she may be able to tell you where it came from and you could then cite and refer to the actual original source.
