Writing math papers is more like technical writing than writing essays, but general advice on technical writing only gets you so far.  For more advanced advice, Igor Pak offers his opinionated thoughts.  I especially recommend his tips on how to create a productive Final Remarks section.

(Real beginners at writing math papers make a standard suite of mistakes, most of which have clear analogies with the problems described in Mark Twain’s Fenimore Cooper’s Literary Offences.)