In the March Notices of the AMS, Cornell professor and award-winning author Steven Strogatz outlines the challenges he faced writing a series of math columns for the New York Times, offers "three routes to mathematical seduction," and acknowledges three expositors of science he tries to emulate when he writes about math.
Strogatz stresses the importance of capturing audience interest. Don't just state assumptions, state theorems, prove theorems, and stop, he says:
If you want someone to follow your mathematical disquisitions voluntarily—or better yet, happily—you have to help him or her love the questions you're asking.
Read the essay.