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Let's say I solved a million dollar problem [for instance P = NP] and wrote a paper describing my proof. Let's assume the conclusion starts like this:

Proposed algorithm, as far as our analysis goes, achieves polynomial time on an NP-Complete problem, showing that P = NP.

Should I add a sentence like this to the conclusion?

All the proofs in this article need to be checked by experts, to make sure that they don’t contain any logical flaws.

Given that no one can be sure about a lengthy proof, and given the importance of the P = NP problem, I feel like it should be added. But it may also weaken the conclusion. What do you think?

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    One presumes that you have checked the proofs. And, one presumes that you are an expert. So, no, don't include that wishy-washy sentence.
    – Jon Custer
    Commented Apr 10, 2017 at 19:00
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    I'm not a mathematician, and I haven't read a single mathematics paper in my life. But I would assume that every proof that is published will need to be checked by experts, starting with the reviewers. So, my concern would not be that it weakens the conclusion -- pointing out potential flaws in a paper is a question of scientific sincerity, so that's good. My concern would be that you might be stating the obvious, which might even sound a bit patronizing to some of your readers.
    – Schmuddi
    Commented Apr 10, 2017 at 19:00
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    @Schmuddi, IMHO it does weaken the conclusion. Of course it will be reviewed. Any paper that included that sentence though would be casting so much self-doubt on it that I can't imagine it not making any reviewer think twice even if they'd thought it was OK.
    – Fred Douglis
    Commented Apr 10, 2017 at 19:24

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No, leave it out.

  • It's redundant, because obviously any paper that claims to solve a major open problem should not be accepted by the community unless it has been carefully checked. You don't have to tell people that.

  • It's arrogant, because it's not up to you to tell experts what to do. They will decide for themselves if the paper has enough merit to be worth their time to check carefully. The vast majority of such papers are actually just garbage, and they do not need to be checked by experts.

  • It makes even less sense in a manuscript being submitted for publication. Just by submitting it, you are asking for it to be checked by reviewers; and when it is published, it will have been checked (though the community may still expect further checking before they really believe it).

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