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Let's say in a paper when I am talking about a theorem someone else proved, I state the result in the exact same way, word for word, as in their paper. Is this considered plagiarism? I would still give credit and citation to the result, just that I don't paraphrase the statement.

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    It is plagiarism only if you state it without reference, implicitly claiming that it is your own discovery. If you say: "The well-known Mean Value Theorem" and then state it, you are OK, even if your statement is word-for-word identical to the version in some book. When stating something not as well known as that, provide a reference (to help the reader, more than to avoid accusations of plagiarism).
    – GEdgar
    May 20, 2021 at 11:41
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    Does this answer your question? Is copying equations plagiarism?
    – Louic
    May 20, 2021 at 11:59
  • @Louic I think copying an equation is fine, but not paraphrasing seems like I am stealing people's hard work.
    – k99731
    May 20, 2021 at 15:57
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    @k99731 Academically it isn’t, as long as you give them credit. May 20, 2021 at 17:53
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    @kosmos in sensible systems, that flag would go a human marker (academic or TA) would would spot the citation and context and not worry. Not all systems are sensible; I've heard recently of students being auto-failed for plagiarism scores on turnitin, and I've also seen scores reach over 20% just from the bibliography and a few short common phrases.
    – Chris H
    May 21, 2021 at 12:10

3 Answers 3

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In mathematics, often there are highly optimized/perfected statements of theorems. It would be silly to alter them (introducing damage?!) just for the sake of avoiding exact quoting. Cite, that's all.

That is, unless you have something to add to their idea, there's scant point to changing the wording... apart from the risk of mis-stating them!... just to meet a sort of fake goal. Cite and acknowledge. Be honest. With citation, what could possibly be the objection to quoting a perfected assertion of a good theorem?

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    'unless you have something to add to their idea, there's scant point to changing the wording' Unless, for example, you're an undergraduate and one of the learning outcomes you're supposed to demonstrate that you've achieved is something equivalent to "students will be able to review and rewrite key theorems". Learning outcomes or items in marking rubrics that involve the word "understand" often are equivalent to that. May 20, 2021 at 7:39
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    I believe there is one subtle issue. Copying a theorem is not plagiarism, provided that the source is cited. In fact, even copying ten theorems from a single source is not plagiarism, provided that the source is cited. However, from the perspective of the copyright holder (often a corporate entity) the latter may appear as a breach of copyright. Whether something like fair dealing/fair use exists and is applicable (and to what extent) depends on the jurisdictions involved. Thus, if one has an intention to "copy" a significant part of a scientific work, it may be safer to paraphrase. May 20, 2021 at 8:11
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    @user9716869, I strongly agree. Copyright must also be considered. It is a separate issue from plagiarism. But also note that there is a rule (usually included in copyright laws) that you can't copyright something that can be said in only one way. Some math falls under this rule.
    – Buffy
    May 20, 2021 at 11:07
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    @user9716869 math.meta.stackexchange.com/a/1854/152317 Basically it depends on how much "idea" vs "expression" the theorem is. If it is the mathematical equivalent of simple language then it may not be copyrightable at all...even if the idea is quite complex, because ideas aren't copyrightable. May 20, 2021 at 14:23
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    I'd say "the well-known Mean Value Theorem" doesn't need a citation because (a) it is well known, and (b) calling it well-known tells us that you didn't invent it, even if I personally didn't know it.
    – gnasher729
    May 21, 2021 at 9:27
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The first sentence on the wikipedia article for plagiarism reads:

Plagiarism is the representation of another author's language, thoughts, ideas, or expressions as one's own original work.

If you state a result or definition that someone else came up with, (in your own words or theirs), and say that you came up with it, then that's plagiarism.

If you state a result or definition that someone else came up with, (in your own words or theirs), and properly attribute it to the original author, then that's not plagiarism.

Things are a bit different when talking about "classical" results, if I would have need to state, say, the fundamental theorem of calculus, I would either:

  1. state the theorem in my own words and give no attribution,
  2. copy the theorem from e.g. a textbook and give proper attribution.

The point here is that in this case there is no risk of me giving the impression that I'm trying to pass off the result itself as my own. Further, in the case of 1, I am actually using my own words, so there is no risk of plagiarism. In the case of 2, I am using someone else's words, and thus give proper attribution.

It should be noted that plagiarism is distinct from, but related to, copyright infringement. If you directly copy a passage of text (or piece of music, etc.), no amount of correct attribution can absolve you of copyright infringement. However, this does not mean that you can never copy text directly. Doing so might be considered fair use, or you could have permission from the copyright holder, or the work might be exempt from copyright in the first place.

In general, you should make sure that you commit neither plagiarism, nor copyright infringement. (In the above example, I would feel confident that copying a single theorem from a textbook, and using it in a longer work would not be copyright infringement, but I am not a lawyer, and this is not legal advice.)

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    +1 For explaining what plagiarism is. Plagiarism isn't about exact wording, so paraphrasing is irrelevant.
    – jamesdlin
    May 21, 2021 at 0:56
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It is not plagiarism if it is cited and credited correctly.

What would make it plagiarism is obscuring or hiding the citation or referring to the work of others in a misleading manner.

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