Professor proposes a question she would be extremely happy to get solved and I solved do I have to write a paper solo or with her? My professor once came to my office and she proposed to me a well-posed research question: it was a theorem to prove that she was extremely happy to see and that would be a nice research question. After some months I went to her office claiming I solved it. She read it and highlighted some points that were not clear to her. I made the proof clean and neat, even generalizing it more than what she wanted. At the very end, she said: &quot;well, I see you solve it. Nice!&quot; and all ended up like this.
My question is: I basically did everything on that problem and my advisor &quot;just&quot; (even if I am grateful for this) made me aware of the research topic and basically read the first draft pointing out some things to explain a bit more. Now she seems not to be interested in publishing the paper, while it is for sure worth of publication since this is what she told me at the beginning. Hence, I am willing to do the job on my own. The question is: should I write it as a solo author, just with some thanks in the intro page or is it more polite to put her as co-author (even if, honestly, she did no more than what I told above)?
You owe her an acknowledgement in the paper, but nothing more. If she wasn't involved in the solution or otherwise in the paper, then she is really not a co-author and most would agree.
In some fields, advisors are regularly given authorship when they really shouldn't be, but that is more due to things like funding a lab and providing general support that makes research possible. But nothing you describe suggests that she is an author. Editing a bit and cleaning up the presentation isn't authorship.
But put a thank you in the paper for suggesting the problem.