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I am a PhD student in mathematics. Recently, I could extend some old result to higher dimensional. I want to make a paper. But I doubt that is a good result or not, because most part of my proof is the same as the proof in the orginal version. In fact, what I did: I try to understand which part of the proof does not work for higher dimensional. So, I replace them by higher dimentioanl theorems. Do I neglect my result and do not make a paper? Or I have to do it?

I checked that no one did it before me.

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    What does your advisor say? – Buffy Aug 1 at 13:36
  • @Buffy : He is not familar with my work. – R R Aug 1 at 13:43
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    @RR if your advisor is not familiar with your work, they cannot advise you. You probably need to work together to rectify this. – Flyto Aug 1 at 14:50
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    Do you know anyone working in this field? E.g. the original authors? – user111388 Aug 1 at 15:08
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    @user111388 : I'm going to meet a guy who is best this area. I will ask him about my result. I asked orginal authors about their result in higher dimention, they mentioned they have not thought about it, but they believe it works. – R R Aug 1 at 15:15
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Normally extensions to existing work are valuable. I suggest that you take advice from your advisor if there is any to give.

But you can also write it up and submit it to a journal. Let the editors and reviewers decide whether it is worth publication. It would be a mistake to just assume that it isn't without feedback from other mathematicians - such as reviewers.

This is true since, as you say, the original proof doesn't work for higher dimensions and the original authors may not have contemplated the extension.

  • :Thank you. I gave it to my advisor. I add two new thoerems to it, but they are not long( around of half page). Do you know if there are something new in a paper, then it won't have been rejected any problem?or reviewers can still does not accept my paper. – R R Aug 2 at 17:36
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Ask your advisor.

  • He's the one most likely to know what you're doing.
  • Even if he doesn't know what you're doing (a bad sign), he's the one most likely to have the motivation to figure out what you're doing.
  • Part of his job is to help you figure your way around in academia. That includes figuring out what's worth publishing and what isn't.
  • Writing a paper takes time. If it's not worth publishing, that's not good use of your time. Your advisor should care and stop you.

In principle, extending already-known results to higher dimensions is publishable; however if the extension is trivial and leads to unsurprising results, it might not be. Publishing two separate papers then becomes salami slicing and can be pretty aggravating. I once handled a paper where the reviewer wrote a harsh review accusing the authors of writing almost-the-same papers by varying the system being studied by a small amount (clearly other journals had asked him to review papers by the authors too). Enlist your advisor's aid to avoid situations like this.

  • Thank you. I gave it to my advisor. I add two new thoerems to it, but they are not long( around of half page). As i said . i replaced those parts which does not work with some theorem that works. I do not know that means trivial or not.Do you know if there are something new in a paper, then it won't be any problem?or reviewers can still does not accept my paper. – R R Aug 2 at 17:40
  • @RR some new content might not be enough - there needs to be enough new results for acceptance. – Allure Aug 3 at 1:00
  • I proved something that is important but my proofs are not long. I don't know that is enough or not. – R R Aug 3 at 11:19

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