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Is it legal to include another person's result in my research paper?

For instance:

Theorem (Name of the author): Statement

Proof. The proof of this appeared in [1].

  • Does the publisher to whom you want to submit this paper offer a style guide? That may have the information you're looking for. But what you're really asking about is if it is legal to quote someone else's result. The answer is "yes, it's legal, so long as you give the other person the appropriate credit." – aeismail Feb 25 '15 at 1:08
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Isaac Newton said, "If I have seen further, it is by standing on the shoulders of giants." Research would grind to a halt if each scientist had to start from "scratch."

So the question becomes, "How should I use the work of others?"

The answer: By citing their published work. Since the number of times a publication has been cited is often used to measure its impact, this is both fair and ethical.

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  • Thanks @NickVence, does my format seems okay? And citing is also applicable even if the result is an unpublished work say the result is located at question and answer site such as stackexchange. Am I correct? Thanks again. – Jr Antalan Feb 25 '15 at 0:59
  • Assuming you are a grad student, your job is to give your advisor a great first draft. He will make the ultimate wording decision. However, consider the following wording: According to Bob's theorem [1], given x, y follows. – Nick Vence Feb 25 '15 at 1:12
  • If the work is unpublished, I would contact the author. Perhaps he is writing a publication right now. If not, would he like to be a coauthor? If not, cite the idea as private communications or unpublished work. Ultimately, this will be your advisor's call. – Nick Vence Feb 25 '15 at 1:17
  • That was a nice suggestion. I know now what to do. Thanks for your help. – Jr Antalan Feb 25 '15 at 2:41
  • "Assuming you are a grad student, your job is to give your advisor a great first draft. He will make the ultimate wording decision." Assuming that the advisor is not a coauthor on the paper -- and in mathematics is it more common that she will not be -- in fact it is the OP who makes all the ultimate decisions on the paper. What he can get from his advisor is very good advice. – Pete L. Clark Feb 25 '15 at 3:00
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Not only is this completely "legal", but -- up to issues of formatting and style that are up to you to decide -- it is a practice that occurs in the vast majority of contemporary mathematical papers.

If you are unsure about how to word things, consulting your advisor (I sure hope you have one, since mathematics is a difficult profession to break into unaided, intellectual issues aside) and consulting many published math papers are both good ideas.

Let me address the style issue a bit: this occurs in your choice to either set off Prof. A's result as a theorem in its own right versus just citing it when needed in the proof of a result in your paper. There are good reasons to do both. I'll start you off with one sample paper to look at and try to get some feel for when each is done. Then look at a few dozen others. Anyway, it's really up to you. One tip: the reader should not be confused, even for a second, as to whether the result she is reading is due to you or is a recalled result of someone else. So please choose a style/formatting that makes this immediately clear.

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  • Note that definitions are often copied in exactly the same way. Students who've been carefully trained to always use quotation marks around direct quotations are often confused by this convention in mathematical writing- in most disciplines you'd be expected to use quote marks around the material that is copied verbatim. Plagiarism detection software often raises red flags about this kind of copying, so be prepared to defend what you've done. – Brian Borchers Feb 25 '15 at 5:11

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