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I was working(in maths) for some months on a paper. After I got the results, I found out that some of those were already obtained in another paper that was not very related to my topic. In fact, in that paper, the result is stated as of 'minor' importance because the main purpose of the paper was quite different. It is the technique that he used to prove this, the one that I rediscovered and used in my paper to prove this result and others in the same domain. Due to this, I didn't have a reason to search there in the first place. Although I have other results in my paper, this one was one of the main ones. Of course, I want to cite the old paper. Hence my questions:

  1. Is it worth publishing this with a proof?
  2. Assume now that I do publish it with proof. Is a phrase like: "Although we arrive at this result independently, it turns out that this was already obtained in [Ref]" acceptable in the paper?
  3. Is there a more correct way than the phrase above to cite the old paper?
  • To be clear, is your proof essentially the same as the proof in the old paper? – user37208 Feb 13 '18 at 15:06
  • @user37208 Yes it is – jhndoe Feb 13 '18 at 15:10
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Since your proof is essentially the same as the proof in the literature, you have to state a good reason for including it anyway. Something like "although this argument has already appeared in [citation], we include a proof to demonstrate its connection with our other results, and also for completeness." But the longer the proof is compared to the length of your paper, the less valid a justification like this will be. If this proof takes up more than say 25% of your paper*, I recommend removing it, and simply mentioning the relationship between that theorem and your other results. There's nothing wrong with short papers, if the results are good.

Either way, understand that your paper will be judged on what's new in it, and write your introduction accordingly.

*People may disagree with this number in either direction, but it gives you a rough idea. Certainly 50% would be too much, and 10% is probably fine.

  • thanks for the answer. What about question 2? – jhndoe Feb 13 '18 at 16:08
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    @jhndoe: I think that is answered indirectly through #3: use user37208's suggested wording instead. (Another phrase commonly seen is "for the reader's convenience".) Emphasizing that you proved it "independently" just gives the impression that you did a sloppy literature search and thus ended up doing a bunch of redundant work proving something that was already known. – Nate Eldredge Feb 13 '18 at 16:32
  • It's fine to talk about having done something independently when you did it simultaneously with the other authors and could not reasonably have known about their results. At the least, you should have made substantial progress on your work before theirs was published. But in the case of a much older paper, this doesn't apply. – Nate Eldredge Feb 13 '18 at 16:34
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I would suggest submitting your paper.

An appropriate title could be «A proof of [result X] using [technique Y]» or «A study of [Result X] and associated corollaries».

The abstract introduction should start with «[Result X] has been first proved by Mel Doe in XYZ. This paper presents a novel proof of this result, achieved applying [technique Y]. In addition, this paper presents a series of corollaries proved using the same technique: [list of other minor results]

Is it worth publishing this with a proof?

Ask the editors of the journal, underlining the use of the technique you used.

  • 1
    Thanks for the answer. However, I should have been more clear(I will edit the question): the author indeed proved the result. The technique is what I am constantly using in my paper, either to prove this result or others on the same domain. Since he is focused on another topic, in that paper this result is stated as of 'minor' importance. – jhndoe Feb 13 '18 at 10:58
  • I updated the answer. I still think it is worth publishing such a paper. In-depth studies focused on a single problem (however minor) are often useful to students and newcomers of a field. And, IIUC, it will be a nice way to present the use of this technique. – gioele Feb 13 '18 at 11:11
  • As clarified in comments above, the proof is not novel. – Nate Eldredge Feb 13 '18 at 15:36

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