It's a process. There is little utility to be gained from specifying mathematics, the title and abstract should explain why a general audience might care, but the meat is often for your advisor. If you think that more people will care then expand it out, use your school standards, even more? sure you can check out some knuth books on mathematical writing or use this grammar, but have you considered programming? It's by far the most inclusive and effective way to tell other people what you actually mean. Maybe popular languages aren't optimal for this try a specification language.
I'm in no way saying you should DO mathematics in a programming language, rather translate it for a wider audience. At a sufficiently high level even little kids could understand your argument before drilling down into specifics, and since the spec never actually has to run it can be as high level as you want limited only by verification time