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I've recently submitted a paper for review for a reputed math journal. The main paper is just 2 pages (everything else being in appendix), where I setup a new problem, and the central result I had left unproven. (I said the proof is yet to be done). I did not send this paper in a hurry, I had spent a good amount of time and best of my abilities to prove it, but couldn't. The paper cleared editorial screening (after being there for a few weeks) and went to "Under Review". What could be the reason to go to "under review", when there is no proof that has to be reviewed. I'd like to understand, what are all the things that are "reviewed" for a math paper that is "under review"?

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    Does the journal have a web page "instructions for reviewers" or similar? If so, that will tell you what reviewers are supposed to evaluate. – Patricia Shanahan Oct 9 at 3:30
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    If the journal is “reputed”, it will want to evaluate your paper not just for being correct (which seems a nonissue in your particular case) but also for being novel, interesting, and related to the topic of the journal. So a reviewer is assigned and the paper will undergo review just like any other math paper. – Dan Romik Oct 9 at 5:35
  • Are you sure it is a reputable journal and not one that is essentially a pay for publication scam? – user2705196 Oct 10 at 12:06
  • @user2705196 : Yes. – user102868 Oct 10 at 12:14
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There's a good chance the journal is getting confirmation that it is indeed a new problem. The fact that it's new to you does not mean it's actually new - perhaps you've simply not seen the paper(s) that stated and maybe even solved the problem.

The journal could also be confirming if the problem is actually interesting. It's not so difficult to come up with a new problem, but coming up with an interesting new problem would be something else.

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    And +1 for the second point. – Buffy Oct 9 at 10:38
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    @Buffy : Last sentence is true only for number theory and combinatorics. Not in areas like Analysis. – user102868 Oct 9 at 12:00
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    @user102868, Sorry, no. My dissertation was in analysis. All mathematics should be interesting. There is no point otherwise. I once worked on a problem (prior to dissertation) that turned out to be too easy. I could generate new theorems every day. That was boring. Trivial is boring. Later I found something interesting. – Buffy Oct 9 at 12:11
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    @user102868 write down a random function, compute its derivative, and destroy the paper where you wrote the original function. The indefinite integral of the result exists, and can be expressed in terms of elementary functions, but the techniques necessary to find it out may or may not be applicable to less capricious cases. – Davidmh Oct 9 at 12:36
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    @user102868 how about : here's a small modification of a well-known PDE, prove existence and unicity of solutions in some class of regularity, and find an efficient numerical scheme. it seems to be a big industry. – glougloubarbaki Oct 9 at 13:24
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Why woudln't they review your paper? All reputable journals review all papers that they consider publishing..

The fact that there's no proof to check doesn't mean there's nothing to check. Arguably, in a mathematics paper, it means there's more to check: why should they accept your paper that doesn't prove anything? The fact that you put everything in an appendix doesn't mean it doesn't get reviewed. The journal will be publishing that appendix, so they want to know that it's OK. (Otherwise, everybody's next paper would be "Abstract: [blah blah] Introduction: See appendix." and publishing just got a whole lot easier.)

  • I am not saying it should be accepted without checking. If you see the last line of my question "what are all the things that are "reviewed" for a math paper that is "under review"?", so I am asking what are things other than "correctness of result" that will be reviewed. If you see the title of my question, before the edit (chnged by David Ketcheson), I was asking "what are all the things that are reviewed for a math paper". The title proposed by David Ketcheson might have slightly misled you to think that I am arguing for accept without reviewing, but thats not the case.(contnued... – user102868 Oct 10 at 11:13
  • ...I think my question is completely answered by the answer by Allure and the comment by Dan Romik. – user102868 Oct 10 at 11:14
  • @user102868: In the initial version of your question, you asked "What could be the reason to go to 'under review', when there is no proof that has to be reviewed", which makes it sound like you expected to bypass review this way. So it's no coincidence that David Ketcheson edited the title that way, and David Richerby's answer works just as well for the original version of the question as it does for the current version. – ruakh Oct 10 at 17:16
  • @user102868 What do you feel that I've assumed? You asked, "What could be the reason to go to "under review", when there is no proof that has to be reviewed[?]" and I answered that question. If the journal publishes your paper, then their name becomes associated with it. They want to make sure it's of appropriate quality. – David Richerby Oct 11 at 7:19
  • @DavidRicherby : No worries, the rhetoric style made me think like that. I got your message : the fact that they review is more of a common sense thing to any journal, and no different for a math journal. – user102868 Oct 11 at 8:36

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