I wish to be a successful mathematician. I want my papers to be read, enjoyed, even eagerly anticipated. I struggle, however, to write well.
Most of my posts are stream of consciousness. They are my thoughts, with only a little reflection thrown in. This I don't mind. My blog isn't to advertise myself, allow inclusion into a community or to make money (though those things would be nice). Each post is a reminder to myself of my thoughts on some research topic. Each post is here for me to refer to later: I will save time by having easy access. I also post them online, since these thoughts are a product of my publicly funded research. Someone's tax paid for the time I spent reading a paper and as I am being paid for my thoughts, why not post the unpublishable in a public place.
The same is not true of my publications. Each research paper is not only a collection of proofs on some topic, it is also how I communicate with my peers. It is a conversation, a phone call, an email. Indeed it is my principle form of communication. Many of my peers will only know me through my papers. When I apply for a job my papers will be my CV. They will represent who I am and what I do. They are my envoy to the mathematics world.
I cannot afford, therefore, to publish poorly written papers. I must aim for each paper to be a jewel of exposition. Of course, the content must be there, but my papers must readable, accessible, understandable. Otherwise the content will be hidden, I will be asking too much of the reader. Ideally they should also illuminate and inspire. I will fail to achieve this lofty goal, but by aiming for it, my writing will improve.
I am currently writing paper with Adam Rennie. His attention of structure, form and the intended audience shows how feeble my previous attempts have been. In an effort to improve I'm reading Halmos' essay on writing mathematics. Since I often read something, understand it then forget all, I'll post a summary of the the essay soon.