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.
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?
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:
- state the theorem in my own words and give no attribution,
- 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.)