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I am a co-author on a mathematics paper, and we have submitted it to a journal. It will take a long while before we hear back from them, and I wanted to share my paper with friends and family.

If you share a paper before it has been submitted, it is theoretically possible that other people could steal your work, etc, before you submit it. What about after you have submitted your paper?

This might be similar to Can I publish research as "working paper" after journal submission? but I am curious about the mathematics world of academia. Also, what about other fields?

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I strongly recommend that you share your paper, not only with your friends and family but also with the entire academic community. Upload your paper as a preprint to arXiv. This is the major way for papers to be shared before publication (and after), so that other researchers can learn about your results without waiting for the peer review process (which in mathematics is particularly slow).

(Of course, you'll need to make sure your co-authors agree before you do this.)

See Why upload to academic preprint sites like arXiv?

You may want to double-check that your intended journal will still publish papers when their preprints are on arXiv, but I've never heard of any reputable publisher in mathematics having a problem with this.

If you share a paper before it has been submitted, it is theoretically possible that other people could steal your work, etc, before you submit it. What about after you have submitted your paper?

I would not worry about it. The journal has a record that you submitted it, which would be powerful evidence in case of a priority dispute. Posting to arXiv is an even stronger form of evidence, since it's automatically visible to the public.

In most cases, "stealing work" is a minimal risk, compared to the much larger risk of not getting sufficient attention for your work. It's usually best to err to the side of sharing.

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  • Is uploading to arXiv not considered "publishing" somehow? Why does the following from the AMS worry me about this advice: "No paper that has been previously published, or is being considered for publication elsewhere, should be submitted to the American Mathematical Society, nor may a paper that is under consideration by the American Mathematical Society be submitted elsewhere." – Buffy Aug 11 '18 at 22:18
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    @Buffy: No, arXiv uploads are not considered "publishing" for purposes of duplicate publication / submission. Additionally, you can see at ams.org/publications/authors/ctp that arXiv uploads are explicitly authorized, and the formal agreement at ams.org/authors/ctp.pdf asks the authors to certify that the work has not been previously published except as a preprint. – Nate Eldredge Aug 11 '18 at 22:21
  • (Note that my previous comment is applicable in mathematics, and all mathematics publishers I know have similar policies. It is not necessarily applicable in other fields; in particular I have heard that many publishers in chemistry will consider a preprint to be prior publication.) – Nate Eldredge Aug 11 '18 at 22:29
  • It would be good if you put all the information in these comments into your actual answer to make sure they get preserved. Links and all. Comments can get removed. – Buffy Aug 11 '18 at 23:15
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    @Buffy Posting a preprint to arXiv is not considered “publishing” in any field that actively uses arXiv, in particular, physics, math, and CS. – JeffE Aug 12 '18 at 3:14
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Friends and family should never be an issue. Presumably you trust them to honor a request not pass the paper on.

In general, you can't stop plagiarism. You can only watch for it to occur and object when it does. The evil-doers will evil-do.

But after you submit your paper others (editors and reviewers) have seen it and know that as of a certain date, the work came from you. There are other ways to establish priority, but that is pretty good.

The question you cite gives good advice. Publishers differ. But until you relinquish copyright the paper is yours, even if submitted. Some publishers will want to be the ones to give the first-views of a paper. But most will tolerate a small amount of sharing just to keep good relations with authors. But a separately published (even if informally) version will upset some of them if you do it after submission. It is hard to call it a work in progress at that time.

For mathematics, look at the editorial policies of the various publications of the AMS.

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