I'm publishing my first paper soon with three collaborators. We made a conjecture towards the end of the paper and intended to publish with the question still open. Another mathematician heard of the problem and found a solution to the conjecture. Now we have two options:
publish our current paper on our own, with the conjecture open, after which our friend would publish their solution as a separate paper, or
include their work at the end of our paper and make them a co-author.
Though our paper is pretty good already, the new work is strong and would make a nice addition, so the first option seems nice. On the other hand, I'm an undergraduate senior (entering graduate school this Fall) and so are two of the other collaborators. Thus it seems like adding another professor as a co-author may make my contributions (which I have worked very hard on) appear less substantial. Also in favor of option 2: if the other professor publishes separately, the citation may make our paper look good.
What do you think?