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I am writing a mathematical paper, and I have been able to complete 2/3 of the paper’s main proof. However, I have been stuck with the last third for more weeks than I can count, and I am getting to the realisation that I won’t solve it by myself. Right now, I can either store the draft in the drawer of papers I will never complete, or I can try to find a co-author who can complete the missing third of the proof. I understand that depending on how the proof ends, the final result may be a bit different than it currently is, but I am quite confident it won’t be too different from its current version. Given the amount of time and effort I have put into this draft, I’d much rather find a co-author than archive the paper. The problem is that I seem unable to find anyone who wants to actively work on this with me. So,

What are the best ways to find a co-author who can help me finish the paper?

EDIT: I thought of contacting the researcher who wrote the main paper my work builds upon, but this person is now retired.

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    I would look for authors who have worked on a similar project, especially grad students. Apr 23 at 18:21
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    Try to change the title and so forth so that you only are setting out to do what you've already accomplished. You could even put in a paragraph about the remaining proof (1/3) as "for future investigation" etc.... Apr 23 at 18:26
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    If you don't have the proof, then you also don't know that it is 2/3 done. It could be entirely the wrong approach, and lead nowhere for all you know. Apr 23 at 18:45
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    Why do you doubt it? You're stuck here, so presumably you've come to a difficult step that either takes far more effort to get around than what you've put in or may indicate you're on the wrong path. Why are those things unlikely and you've concluded that you just need to find another person?
    – Bryan Krause
    Apr 23 at 19:41
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    What is your academic status ? Is there nobody in your current department to whom you might refer the matter ? If not, can you compile a list of mathematicians who are likely to be capable with this type of proof and then pare this list down to the best 4. Then explore these individuals' work in detail before choosing the best one to approach.
    – Trunk
    Apr 24 at 12:35

3 Answers 3

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I thought of contacting the researcher who wrote the main paper my work builds upon, but this person is now retired.

Absolutely reach out to that person. Lots of academics continue working in retirement, and actually have more time for research now they have to do less teaching and administrative jobs. And even if they are not interested in collaborating with you, they may have already thought about the problem you are struggling with and might be willing to share notes. Or they may be able to point you towards students of theirs, or other people they know are working in this area, and might be willing to introduce you - an introduction from an established researcher, even retired, might well be more successful than a cold email.

If that person is not responsive, or you can't reach them, look at other people whose work you are citing. And all of their grad students. These people are already adjacent to and probably interested in your area of work, and your common interest is a good hook for contacting them.

Depending on your time frame, you could attend conferences or similar and see who is working in your area and looks approachable. (Someone once attended a conference in my area and introduced themselves to me in exactly this kind of situation, with a half-finished book. We then worked together to finalize it.)

Cast your net wide, be succinct in your emails, and don't be disappointed if most people have other ongoing projects that do not leave them time to work on your project. Good luck!

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    Also include people who cited the same work(s) as you.
    – jcaron
    Apr 24 at 8:13
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There's no other real way to answer this aside from building connections with other like-minded researchers with whom you've common interests. I'm a... 4th, year PHD student at Georgia State. I am not at all shy about reaching out to other PHD students (at my school, or otherwise) or professors researchers who I am in the field of.

In turn, this has resulted in me developing contacts in various departments. So, if there's a part of a paper I can't do myself, I can ask those I know to see if they're interested. But, that usually involves an email that begins something like

"Hi ____, I'm Jared. I'm a PHD student of public policy at Georgia State..." and then I get to talking with them about my work and how it relates to theirs. Forming relationships is a key skill in life, and academia is no exception to this.

So, you'll need to do your equivalent of this.

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but this person is now retired.

This makes even more worthwhile to reach out to them (unless they retired 30 years ago...). They may be open to get you in touch with people that shared the research interest with them, or even they may be interested themselves.

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