I'd like to ask other mathematicians about how they write papers. I love doing math for its own beauty and writing papers simply to communicate with the community what has been discovered. I am also a bit concerned about this because I am an "early-career mathematician" and if I don't want to be a "short-career academic mathematician" I need to get some articles out.
I'm working on several projects and each is in a different stage.
One: I wrote some, collaborators wrote some, we have something paper-like which needs major revisions. Collaborators are very-early-career mathematicians so don't know how to write mathematics. But I barely know how to write mathematics well and certainly have no training in guiding beginners through writing for publication, so this is a learning experience for all!
Two: We keep thinking we've got it, almost -- just need to write it up. Have some written notes. I feel far from having a complete paper. Why?
Three: Just started so have such an amorphous pile of small results that it is hard to imagine yet how to put it together.
In post-dissertation-land, I don't generally start with a paper in mind. I start with a problem I want to answer. I work and work on research and reading and throwing away scratch work. I write expository notes to myself and others (students, collaborators). I try to write a fair bit for myself, but haven't channeled most of this material into articles.
Once I have some results that I think are worthy of an article I put them together, with proofs, and start writing the introduction. That's a paper! Time to revise about 17 times.
How do you shepherd projects toward papers? Do you start with a paper in mind or with a problem in mind or with a person you'd like to work with? How intentional are you about keeping that goal of publication in mind?