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I often find myself writing summaries of the same sub-(sub)-branches of mathematics in the background sections of my papers. With time, this grows somewhat tedious, since there are only so many ways to state the same definition, and the exercise is not particularly intellectually stimulating. It would be convenient to cite a relevant "canonical" reference and follow the notation therein, but unfortunately in some cases there is no such reference - this is especially the case for relatively modern subjects, where the proper notation and set-up are something of a moving target.

Would it be considered self-plagiarism (or otherwise objectionable) to copy-paste the relevant section from a previous paper and edit it to add any details that are necessary for the current application (and remove the ones that are irrelevant)? It does not seem to me that this approach causes any loss to the scientific community, but I would also not be surprised if automated plagiarism checkers might notice the overlap and complain.

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    Do you hold copyright on the previous papers? If not, are there few publishers of your work, or many?
    – Buffy
    Commented Feb 27 at 17:44
  • 1
    Are these math papers or science papers with a math section? Standards are different. Commented Feb 28 at 17:17

3 Answers 3

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I'm not a mathematician and don't publish in math, but I do read some math-adjacent and applied math papers and so I'm somewhat familiar with these issues and I can tell you what is useful to me as a reader.

For definitions, notation, etc, I would quote yourself (copy) and cite. Make yourself the canonical reference for your purposes if it's something you've already done. Be explicit about what exactly you are copying, for example you might refer separately to the source for the original mathematics and the source for the notation you are using. If others use a different notation you can mention that when you cite them if you think it is relevant.

I would not repeat long sections of a paper; take only the most necessary parts and quote briefly. Let your reader know where they would find additional detail.

For repetitive introduction beyond that, I would think hard about what is actually necessary. Each paper should not be a review of the field, and there should be enough difference between papers to emphasize what is actually necessary to begin to understand the paper.

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Actually, plagiarism and self plagiarism are easier to deal with than copyright, assuming that you have given that up in publication. You can avoid all forms of plagiarism with citation of the earlier work. You are giving proper attribution (covering plagiarism) and providing complete context of your current work rooted in the earlier (self plagiarism).

Plagiarism checkers aren't your real issue here, provided that they don't lead to rejection by an automaton. An editor can simply let you know of the similarities to your earlier work. It isn't like a professor grading an essay.

If you don't hold copyright and don't have a rather permissive license from the copyright holder, then you are limited in how much you can copy-paste and even, to some extent, how much you can paraphrase the earlier work. A solution in such cases is to ask the earlier editor if they will give you a more permissive license. They might do that, especially if you are submitting to the same journal. It might be essential to do this if you are extending the earlier work.

But, note one thing more. For things that can be expressed in only one way, copyright is hard, maybe impossible, to enforce. If you need to restate a definition or formula from an earlier paper, even if it is by someone else, the "length limitations and quoting requirements" don't apply to the same extent as in prose. Axioms are hard to restate differently from the original as is the formula defining the derivative. While those are very important and may have been very creative, if you want to extend the ideas, as you are always permitted to do, the original formulations need to be kept or chaos will ensue. This is especially the case for a lot of mathematics. Editors will understand that. Copyright is about expression and reuse can be limited. But ideas, themselves, can't be copyrighted or owned. When idea merges completely into expression, things are different. You still need to cite as appropriate, of course.

So, cite earlier work as you should always do. Seek assistance from editors, especially if they note too much similarity, and try to avoid being too pedantic, which can easily occur when overusing copy-paste.


It is probably too strong to say that copyright can't be applied to things that can be stated in only one way, though IANAL.

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As you pointed out, if you copy-paste with a little edit you probably will be detected by the automatic plagiarism checkers. Unfortunately, the real problem is not the ethical or the productive one but the similarity percentage your paper could trigger. Editorials often run plagiarism checks with no context of the sections of the actual text detected as "plagiarism". Commonly, the paragraphs or sections that are detected with the most overlap in a paper are the background or preliminaries section which mostly contain definitions of the theoretical background for the paper.

You have two options.

  1. Write the definitions again. Yes, your original problem. Change them enough just to not obtain a 100% similarity score.
  2. Cite yourself indicating which parts of the text are used in the new paper.

I understand why you think that self-copy-paste is not a big deal but consider the lack of context the editors, reviewers, and automatic tools have when determining something as plagiarism. The current copyright practices in scientific publications also don't help.

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  • In math, your #1 is counterproductive and unnecessary for some things. It can lead to chaos. For example, restating definitions in different words can lead to different interpretations. The point is precision, for which the essence of the statement is its form. Moreover, in the broader, beyond math, context, paraphrasing doesn't guard against plagiarism, though your #2 does.
    – Buffy
    Commented Feb 27 at 20:14

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