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We (including my teacher) designed a new algorithm in computer science and my teacher proved that it is good enough about its time complexity, but I'm not sure about that and worry that the proof be wrong.

Could I submit it to a journal?

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    Two questions: (i) is your "worry that the proof be wrong" a concern about a specific part of the proof or just a general anxiety? (ii) Is your "teacher" an academic in CS with other publications in the field? If the answer to the latter is "yes," then you should direct questions about journal procedures to her: she will be well qualified to answer them. You should also discuss your concerns about the proof with her, provided they have any positive amount of grounding in fact. Collaborators need to discuss reservations with each other; that is a critical piece of quality control.
    – Pete L. Clark
    Dec 31, 2015 at 13:34
  • @PeteL.Clark (i) I have a general anxiety that our work have no useful thing to be expressed as paper. (ii) unfortunately, my teacher is not so professional and seems it does not have any paper in journals! but since this is my obligation to submit paper for project, I do.
    – Majid
    Dec 31, 2015 at 13:40
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    "unfortunately, my teacher...does not have any paper in journals!" I'm sorry to hear that. "[B]ut since this is my obligation to submit paper for project, I do." Wait, what?!? The course you are taking obligates you to submit work for publication?? That has been discussed on this site before, and the consensus was that this is a bad and possibly unethical requirement. Requiring students to submit a paper for publication -- coauthored with you! -- when you do not have any published papers seems especially fishy. These are two red flags that you are not in a good academic environment.
    – Pete L. Clark
    Dec 31, 2015 at 13:45
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    @majidR Here is a question from years ago that Pete might be referring to. It discusses whether it is acceptable for a professor to require students to submit papers in a course: Professor withholding course grade until submission of conference paper
    – Austin Henley
    Dec 31, 2015 at 17:33
  • @AustinHenley oh! it seems you was in my state too! but my grade now is given, but I should submit paper, otherwise it will be retracted!
    – Majid
    Dec 31, 2015 at 18:23

3 Answers 3

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It is your responsibility, not the referees', to make sure that a published proof is correct.

The reviewers should make sure that the results have some merit; some check proofs line-by-line, and some merely check that the result is plausible and that the proof methodology looks sound. Sometimes errors slip by. Nevertheless, if the result later turns out wrong, your reputation is at stake, not the one of the reviewers.

So speak with your advisor and make sure that your proof is correct before you submit. It might be the case that the proof is correct and you just haven't grasped all the details because you have less experience. Or it might be the case that there is a flaw to address and correct, in which case you should act before submission.

It is not a good research mentality to think "We only have to fool convince one or two referees", in my opinion.

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  • How my reputation would be at stake: (i) if I submit a paper with an error that I couldn't get it, but the referees get it and rejects paper?(ii) what about no one (me and the referees) got it? Is there something like black-list or what?
    – Majid
    Jan 1, 2016 at 17:55
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    If the referees find it and reject it, you get the reputation of a researcher who submit bad papers with them and the editor. There is no formal black list (as far as I know), but they are less likely to spend time on your manuscripts in future, since you put little care in producing them. If no one finds it at this stage, it is even worse: the paper gets published with an error, and you get the same reputation with everyone in the community. People will report your error in their findings and correct it when they cite you.
    – Federico Poloni
    Jan 1, 2016 at 18:54
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You should not submit if you are not confident the proof is right. Why not trying to boost that confidence instead? Two strategies I can think about to do that:

  • Give a talk in your department where you explain the proof to your peers and to more experienced researchers. It doesn't need to be anything formal, it could be a seminar, a research group meeting, or even a reading group.

  • Publish a preprint instead (for example on the arXiv), or write a blog post. If you are lucky, another researcher who is interested in the result will comment on it.

In general, I am suggesting that you discuss the result with other people before you publish it. It may be that you will catch the mistakes (if any) yourself, just by getting the chance of discussing it with other people.

EDIT: As pointed out in the comments, the second suggestion applies or not according to the OP's level of confidence. Of course, I didn't mean people should use the arXiv users as oracles that check the correctness of their proofs. It is nevertheless, at least in my opinion, an intermediary step before publishing to a journal. And anyway, arXiv was just an example, what I really suggested is to publish it somewhere online in order to give it more visibility.

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  • You are right, but I afraid that if my professor know that I'm not sure about its proof and asking others for correctness, become upset!
    – Majid
    Dec 31, 2015 at 18:06
  • @Alessandro Publish a preprint instead (for example on the arXiv). Could you explain why arXiv is a place to publish a preprint of a potential publication of which the author have doubts on the correctness of a proof?
    – Sathyam
    Dec 31, 2015 at 18:11
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    @Sathyam Obviously it depends on the level of confidence he has in the correctness of the proof. All things considered, I think the level of confidence required for a preprint is lower than the level of confidence required for a journal submission. With a preprint, you aren't asking editors and referees to spend time on your work; the process of correcting and submitting a revision is simple; and it's understood by readers that the work has not been peer reviewed and may be preliminary (he can even give an explicit warning in the text)
    – ff524
    Dec 31, 2015 at 18:21
  • @Sathyam also see I made a huge technical mistake in an arXiv paper... How bad is it?
    – ff524
    Dec 31, 2015 at 18:23
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    @ff524 Done! In general, my answer was meant to give more practical suggestions, instead of just saying "bang your head against the proof until you're confident."
    – Alessandro Cosentino
    Dec 31, 2015 at 19:15
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My first hypothesis is that all the authors have done their best to have correct proofs, and that the question was asked with honesty to get advice, in order to be published in a serious journal.

This being said, it is not uncommon "not to be sure", or "to be afraid proofs might be wrong". Indeed, the history of science is paved with significant published papers containing flawed proofs, sometimes quite small. This happens even in mathematics, as detailed in Widely accepted mathematical results that were later shown wrong?

If your proof is ok, great. If not, and the algorithm is interesting enough, options are:

  • a reviewer detects it, and rejects: you would work some more,
  • a reviewer detects it, and suggests corrections: you can publish or resubmit, possibly adding the reviewer to the author list (if the contribution is significant enough), or at least to the acknowledgement part,
  • nobody detects it, but you does afterward: submit a correction.

If you are aware that the proof is wrong, you ought to correct it before submitting it.

Meanwile, there exits a huge business of poorly reviewed conferences and journals, that would publish anything with some fees, and a huge amount of retracted papers recently. This undermines the work of honest scholars.

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    I strongly disagree with this cavalier attitude. Correctness is one of the minimum requirements for publication. Of course, people make mistakes, but why would you submit a paper that you don't believe to be correct?
    – David Ketcheson
    Dec 31, 2015 at 15:36
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    The algorithm isn't interesting if it is incorrect, or in this case has a worse than expected time complexity.
    – Pål GD
    Dec 31, 2015 at 15:41
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    @David Ketcheson When I wrote my answer, the OP said he was not sure, and was worry the proof could be wrong. I (still) believe this was a sound attitude. Now his comments have clarified the situation, but I believe the questions should be updated to reflect the actual situation. And I will update my answer, based on the hypothesis questions are asked with honesty
    – Laurent Duval
    Dec 31, 2015 at 16:18
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    I disagree with this answer. Referees are busy enough already. Do not waste their time with proofs that you yourself do not believe in (and which also are probably unreadable, or else the correctness or incorrectness would be clear to you).
    – darij grinberg
    Dec 31, 2015 at 16:24
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    I do not give advices I would not follow. To me, "have done their best to have correct proofs" is a correct requirement, and I feel it is coherent with your last sentence. Let us be specific: I do signal processing. Parts of the works is proofs, part is algorithms, part is experiments. Nearly everybody in the field measures errors using some instance of squared errors. Everybody knows such measures are irrelevant. Nobody checks on each data available. So nobody can be absolutely convinced the results are correct. Even in pure maths, full logical proofs are difficult and rare.
    – Laurent Duval
    Dec 31, 2015 at 19:34

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