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My partner is a very bright theoretical CS student. Recently she proved a pretty significant result that she is aiming to submit for SODA. In addition, the paper was done completely without her advisor (who is a very well established tenured professor in the field).

She has shared with me that she is very worried about publishing the paper alone, in case the paper has a mistake. She wants to publish it with her advisor, so that he spends some time reading, verifying the result, and rewriting some rough patches in the paper. I've told her that publishing as a single author PhD student is very impressive in this field, and her advisor has encouraged her to publish it alone, if she so desires.

My question is, how big of a problem is it if she publishes it and there turns our to be a mistake? Is it very deterimental to her reputation? I've even tried to read the paper to help her, and I believe to the best of my knowledge that the results are correct, but then again, I'm not from the community so I cannot provide her with the assurance her advisor would otherwise give her that the results make sense and are correct. It also took me more than 3 weeks to verify the results (or roughly $30$ hours), so it is a big investment of time that her advisor would have to put in.

She obviously believes her results are correct, but is lacking on the confidence to let the paper out. What would be the sane thing to do here? Submit anonymously to SODA and see the reviews instead of posting on arxiv?

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    $\begingroup$ My experience of PhD students is that the ones who publish by themselves typically are much more likely to go to postdocs afterwards. $\endgroup$
    – Tom
    Commented Jun 18, 2023 at 19:49

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I would encourage her to publish by herself if there is no input from the advisor (in terms of problem, ideas, etc). The advisor may not be able to do a very careful reading but it is quite common for advisors to proof read without authorship - it is part of being an advisor/mentor and in some sense they are obliged to help unless they are too busy with other activities. She can request it for sure and see what they say. She can also try to get the help of her fellow students in the department. It is quite common for graduate students to help each other out with proof reading. Mistakes are not uncommon even when there are multiple authors and confidence comes with experience. One has to try submitting after a good faith effort on checking for correctness and hope for the best.

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    $\begingroup$ I would add that as the author is a PhD student, the advisor can carefully check the actual proof as part of the PhD work/ thesis of the author. This is independent of the particular write up of this proof that is going to appear in the paper. $\endgroup$
    – quarague
    Commented Jun 19, 2023 at 8:02
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If she did all the work, then she is the sole author. She need not be so worried about errors because the paper will go through a peer-review process, whose purpose is (also) to evaluate the correctness of the paper.

I would expect a decent advisor to offer some amount of feedback without asking automatically for co-authorship. Has she not asked the advisor about their opinion on what to do? That's why they're called "advisors", you know. I do hope she's not hiding the paper from the advisor, that could spell a great deal of trouble.

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    $\begingroup$ My interpretation of her advisor has encouraged her to publish it alone, if she so desires is that the advisor knows about the paper, and already offered some advice. $\endgroup$
    – Emil Jeřábek
    Commented Jun 18, 2023 at 15:12
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    $\begingroup$ Ah, sorry, I missed that part. Well then, it's obvious isn't it? She should publish, she just needs some assurance not to worry so much about errors. $\endgroup$
    – Andrej Bauer
    Commented Jun 18, 2023 at 18:18
  • $\begingroup$ I agree with that. $\endgroup$
    – Emil Jeřábek
    Commented Jun 18, 2023 at 19:27
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You might find this question of academia useful "When should a supervisor be an author?". As you can see from there, the standards vary greatly by field but in mathematics and cstheory, it is fine (and good) to publish without your supervisor. It shows independence.

It is also fine to ask your advisor (or anybody else) for their opinion on your paper without automatically including them as an author. If they spot (and fix) a big mistake then you can offer authorship.

Also, one shouldn't be afraid to ask their advisor for advice. It's their job!

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    $\begingroup$ +1. You commonly see in research papers at the end an acknowledgement to other researchers who carefully read a draft of the paper, contributed to discussion and such. I suspect that it also happens very often that this kind of contribution is not explicitly acknowledged, if that other researcher is the advisor, or, for example, a longterm collaborator. $\endgroup$
    – Hermann Gruber
    Commented Jul 7, 2023 at 14:01

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