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I am a math postdoc. I have recently finished a good paper, but I want to make sure about it before I put on arXiv. That is why I have sent it to some good and great mathematicians to know their opinions.

Right now, I am a bit worried that they might steal my ideas as they have not answered my emails yet. On the other hand, I want to make sure that my paper is correct and good, which means I want to hear other opinions on it.

My question: Should I put my paper on arXiv or I should wait for their answers?

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    May I ask what precisely is your concern about your manuscript? As a postdoc in math, you certainly don't need "good and great mathematicians" to check your paper for correctness, since you have learned methods to ensure yourself that your arguments are rigorous (at least with very high probability). Is your concern whether your result is really as relevant as you suspect? Whether it's presented sufficiently well in the manuscript? Whether you missed relevant literature?
    – Jochen Glueck
    Dec 8, 2021 at 13:26
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    I would say that a good way to help ensure your work is correct is to give talks about it to experts and make sure you can answer all their questions. Experts are more willing to listen to a talk than read a paper.
    – Kimball
    Dec 8, 2021 at 20:52
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    Would it be possible to submit to a journal, and wait to post on arXiv until you hear the first round of reviewer comments? This will effectively serve the same function
    – Superbee
    Dec 8, 2021 at 23:24
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    Wasn't one of the original reasons for putting a paper on arXiv to provide an opportunity for feedback before submitting for publication?
    – chepner
    Dec 9, 2021 at 1:02
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    Also, the arXiv allows for revisions (it keeps the old versions, defaults to newest). So if something can be presented better, or needs correction, you can always post revisions later. I guess the only "danger" is posting something egregiously bad and publicly get a bad reputation... but even in that case you could always post a revision saying: "The earlier version was flat-out wrong for X, Y, and Z reasons." Everyone makes mistakes (some people just don't feel comfortable admitting it, or letting others see or discover the mistakes).
    – TravisJ
    Dec 9, 2021 at 15:36

3 Answers 3

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There is nothing wrong with sending a new math paper to colleagues, including people you don’t know personally, and either before or after you put the paper on arXiv. I am on both the sending and receiving end of such messages on a somewhat regular basis.

However, it is unrealistic to think that the people you’re sending the paper to will immediately sit down and check its correctness, or that they will do so even within several months. That’s simply not going to happen unless there is something extraordinarily exciting about your results. People might respond with minor feedback, point out a missing reference or some typos, make some general comments about your approach etc. but “good and great” mathematicians are simply very busy people. You should not expect anyone to validate your work if they have not been assigned to do so as a referee on behalf of a journal.

Your dilemma is not so unusual, and has a standard solution, which is to carefully reread and check everything you did, and then share the paper publicly on arXiv, submit to a journal and let the normal process play its course.

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    Thank you very much for your advice. I was so scared when I saw tensors_are_4_engineers's answer as I didn't think people might steal the paper. that is why I wanted to put the paper on arXiv before I receive the opinions those that I sent my paper to them.
    – Adam
    Dec 8, 2021 at 17:46
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    I would not even count on the referee to validate the correctness of my work. I think that the author is the main responsible for the validation of his results.
    – Yanko
    Dec 9, 2021 at 13:47
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If you're a math postdoc, at this point you should probably have good relationships with other mathematicians. Those are the people you can & should talk to about your paper -- not because you should be afraid of plagiarism, but because unsolicited emails to review a paper will probably just get ignored by the faculty you sent them to. They're not going to be bothered to read it, let alone plagiarise it. "Good and great" mathematicians get these kinds of emails all the time, and they're usually from cranks and amateurs (because trained mathematicians know better than to cold email professors to review a paper). So they just ignore all such emails in general.

That is why they haven't answered, not because they're busy plagiarizing your work.

I think it's best if you can find someone in your circle, and failing that, in your institution. If no one you know does research in the relevant topic, it's much easier to approach people in your institution and get taken seriously than with total randoms. Again, plagiarism isn't something I'd be concerned about, rather you should worry about getting someone to pay attention to it at all.

But if you're really really worried about plagiarism, an alternative to posting on arXiv (which is permanent) is to post somewhere else, e.g, your personal website -- where there can still be a verifiable record of your work, but you can take it down if you find out something is garishly wrong with it.

Postscript: if you absolutely positively have to send it to someone not in your (extended) network, "good and great" should not be your criteria, rather it should be "highly relevant" -- someone in your subsubsubfield you know would be very interested in your work (for example, you're extending their results, solving an open problem they posed/have great interest in, etc.). You might still get ignored, however.

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  • Thank you very much for your advice. Unfortunately, there is no one in my group who is familiar with my research, but I explained my research to them and there was no problem. As they are not specialists, I can not be completely sure. I completely agree with you that I should find someone who pays attention to it, but I have not found such a guy; my friend who does research in my field read the paper carefully and it was fine, but as I said I want a specialist to read the paper.
    – Adam
    Dec 8, 2021 at 12:11
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    "Again, plagiarism isn't something I'd be concerned about, rather you should worry about getting someone to pay attention to it at all." Truer words have never been spoken.
    – xLeitix
    Dec 8, 2021 at 12:52
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    +1 for "They're not going to be bothered to read it, let alone plagiarise it.
    – Dave L Renfro
    Dec 8, 2021 at 14:20
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    @Adam Don't try to get a full peer review done on your own, that's what submitting to a conference/journal is for. Get a sanity check (which you say you already got) and go for it. The relevant specialists you're emailing may very well be asked by the journal to review your submission. Then you fix the mistakes they find.
    – CSSTUDENT
    Dec 8, 2021 at 19:51
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I would suggest you to post it on arXiv, which will address both of your issues —

  1. Unavailability of reviewers: Some experts might find your paper on arXiv and give feedback.

  2. Risk of stealing: The world will know that you are the first one to come up with these results using your method.

Best of luck!

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