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My problem is regarding How to find collaborator who is interested in my ideas and complete the research paper. How to find someone like this. In paper , have completed statement of every theorem and most of there proofs. Some of work reminds.

I have completed some work on polynomial representation in terms of other polynomials this gives consequences many results, it also connected with waring's problem and sum of Power series ( Faulhaber's Formula), we can express any number in decimal whose digits are cubes, one piece of work recently i have asked here on mathoverflow https://mathoverflow.net/q/461431/149083 .

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    This is a very big question and depends a lot on your context - what kind of institution do you work for, how much research track record do you have, etc. There are some good suggestions here academia.stackexchange.com/a/68134/88659 but if you want genuine help, you need to provide much more context, e.g. what's your situation (e.g. grad student), what have you tried already, why do you need a collaborator specifically, ....
    – Felix U
    Commented Jan 4 at 14:28
  • Why can't you finish it on your own?
    – Christian Hennig
    Commented Jan 5 at 14:25

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What you are asking for is generally very difficult unless you are associated with a large university. That gives you the opportunity to discuss ideas with several people, a few of whom might have interest, depending on the topic.

An alternative is to attend (many) conferences and use the time between talks and in the evenings to speak with people in the field.

You could also write to authors who have published closely related papers and ask if there is interest in your ideas. You may or may not get answers, however.

But all that is difficult since math specialties can be very narrow along with interest in such topics.

You may be faced with doing the work on your own and then getting feedback only from reviewers of submitted papers.

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    I have also found that it is very easy to find collaborators when you are ready to talk about/work on the problems that interest them and next to impossible when you want to get someone to work on something that interests you (unless miraculously the interests coincide, which doesn't happen often). So, I always start the new contact with trying to solve the other person's problem and only after that do I nudge them gently in the direction I want to go.
    – fedja
    Commented Jan 5 at 12:38

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