publications - I (independently) solved a fellow student's research problem. I want to publish it. What should I do?

A fellow student and I are part of the same graduate student research group (in applied mathematics), under the same PhD supervisor. The (relatively new) student came to the group with an idea for a thesis, and we helped him come up with a different research idea that more suits our research interests, but still ties to his original goal.

The current formulation of his research problem is mostly due to input from me and our mutual supervisor. As in the model is based on our suggestions across multiple meetings.

Being interested in this student's research problem as well (or at least my formulation of it), some months ago I offered that we collaborate on it. Not much came out of it, mostly, I think, because this student is still very inexperienced, and his mathematical maturity is not so high.

Some time ago I came up with a different partial solution for the aforementioned research problem. As part of our (failed) collaboration I asked him several times to update his simulations to consider this solution, but he seemed to be against the idea, believing that the original formulation is better. Our meetings mostly consisted of arguing about which model is better and me trying to teach him some mathematical concepts he can use to analyze his work.

A few days ago I have (independently of the student or our supervisor) come up with a solution which is better, and completely different from what the student has been trying to analyze. The solution invalidates a lot of the student's work up until now (he has been working on this problem for a few months), since it is simpler and more effective.

I want to write up this solution in a paper and publish it. I already have basically all of the results written down (except one lower bound which I am still working on), and a nearly complete first draft.

Here's the problem. Do I include this student as a co-author? I am conflicted, because this paper really is my own original work. However, it is based on the research problem which our group "handed over" to this student. I do not wish to put him in the unfortunate situation of having months' worth of work invalidated, and everyone in our group views the problem I have solved as "his" problem. However, it is also true that this paper consists entirely of my own research.

Ideally in this case I would approach the student and ask him to collaborate with me on the paper, as in, refine some of the results, or simplify some of the proofs. However, based on many conversations with him, I believe that the student is too inexperienced to do this, and is not familiar with the main mathematical tools I have used to prove the paper's result.

How should I proceed?

Some more details: I should mention that I have no personal qualms about sharing authorship. I am mostly worried about two things:

1. 
   

   whether it is the most ethical thing to do;

   
   


2. 
   

   I feel that if I include him as a co-author, he will want to make a contribution to the paper. But I want to have complete creative control on the paper, and feel that sharing creative control with him is going to slow me down.

   
   

Answer

Welcome to the wonderful world of academia! I appreciate your consideration of your fellow Ph.D. student. I would suggest to invite the student to do some work on the paper, and then have him as second author. Perhaps the student can work on that lower bound? Or write down why the other approach does not work? Or more simulations? You can probably come up with something. If he refuses, you can publish on your own. Either way, if the results are good you get a first author paper, and the other student gets something for his work.

I would run this by your advisor, he might have further advice.