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I managed to improve the techniques of a year-old paper to get a significantly stronger result. I used original ideas, but a large part relies upon results of the original paper. (to the point that half the paper may be recapping the lemmas of the past paper)

Q1) Is it acceptable to ask the author of the original paper if they would like to collaborate?

I have heard that Paul Erdos would do this, which is something I highly admire. However, I am an undergraduate, so I fear my invitations would not be appreciated.

Q2) If it is acceptable, how do I make sure to make my invitation not pushy or expectant?

I'm thinking of writing something like:

I was wondering if anyone else had already achieved this result, and if it would be fit for publishing. If yes, while I fear it may be rude to invite you to collaborate, please let me know if you are at all interested in getting involved.

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    $\begingroup$ If you've already proved the result, what would be left for the collaborator to do? $\endgroup$
    – Nate Eldredge
    Commented Jun 12, 2020 at 22:22
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    $\begingroup$ An option is to start a discussion on the subject, for instance sending a draft, and not evoke a suggestion of collaboration at the first email, but rather insist on mathematical questions. If the person you're asking gets involved in the discussion, at some point you could suggest a join project. $\endgroup$
    – YCor
    Commented Jun 12, 2020 at 22:25
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    $\begingroup$ This could also be appropriate for Academia.SE. $\endgroup$
    – Nate Eldredge
    Commented Jun 12, 2020 at 22:26
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    $\begingroup$ I am currently on roughly the other end of this question. I was flattered to be asked, but said that I hadn't contributed anything beyond the original paper, and so didn't merit co-author status. The asker wasn't a student, but a colleague; so, when he insisted, I relented. Had he been a student, I would almost certainly have insisted that he take sole authorship. $\endgroup$
    – LSpice
    Commented Jun 12, 2020 at 22:33
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    $\begingroup$ As others have said: you should certainly get in touch with the author and send a draft, if for no other reason than feedback. Also, FWIW, I have had the experience of feeling "I can prove the results, but the writing would be improved if I coauthored with Person X". $\endgroup$
    – Theo Johnson-Freyd
    Commented Jun 12, 2020 at 23:26

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I think a preliminary step is to talk to an advisor or someone near you who can read your paper. The intention you state is good, but I think it could be phrased more artfully. Here is what I recommend.

  1. Line up one or two people at your institution (people who taught one of your classes, or someone in your department who might have contact with the professor whose work you have used). Get their opinion on the advisability of reaching out and making your request. Ask them for how they might word your request.

  2. If possible, contact a student or coauthor of this professor and relate your concerns. As I understand it, your first concern is to get your work published and your second is not to step on any toes, especially those of the person whose work you have extended. If this student or coauthor is in the relevant fields, ask them for a sense of how publishable your result is.

  3. Based on this feedback, choose to approach the professor with the intention of announcing your work to him and ask if he (pronoun presumption on my part) is interested in reading it. Then let him make the next move.

In all of this, pick someone to tell of your process. There should be no reason for anything horribly wrong to happen. If and when it does happen, it helps to have someone who already knows your side of the story.

Gerhard "Plans To Backup His Backups" Paseman, 2020.06.12.

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