Mathematics has its own particular conventions and rules when it comes to writing. There have been several attempts to write them down. The most famous is Halmos’s excellent essay “How to write mathematics”. Other good sources of advice are the following two books:
(I reviewed these two books in the Australian and New Zealand Journal of Statistics a few years ago.)
But if you just want a quick summary, I recommend Dave Richeson’s blog entry “The nuts and bolts of writing mathematics”.
- Using personal pronouns in research writing
- Why Word is a bad choice for academic writing
- Writing responses to referee reports
- What you wish you knew before you started a PhD
- Your name is your brand