How would you go about writing an abstract for a Math paper? I know that an abstract is supposed to "advertise" the paper. However, I do not really know how to get started. Could someone tell me how they go about writing an abstract?
Avoid notation if possible. Notation makes it really hard to search electronically.
Put the subject in context, e.g., "In a recent paper, T. Lehrer introduced the concept of left-bifurcled rectangles. He conjectured no such rectangles exist when the number of bifurcles $n$ is odd."
State your results, in non-technical language, if possible. "In this paper we show the existence of left-bifurcled rectangles for all prime $n$."
Mention a technique, if there is a new one: "Our methods involve analytic and algebraic topology of locally euclidean metrizations of infinitely differentiable Riemannian manifolds".
Never, ever, ever, cite papers in the bibliography by giving citation numbers; the abstract is an independent entity that should stand on its own.
Jeffrey has made a good list. I'll add one:
A major purpose of an abstract is to help interested people find your paper when they search for a topic. To that end, if there are multiple names in use for the concepts in the paper, I recommend that you try to mention them all, even if you have to write "also known as ...".
One thing that I have been taught to do in the body of a paper, but which may also make sense in an abstract is to state an easily-understood interest-piquing corollary of the main result "As a special case of our results, we demonstrate the existence of infinitely many integer solutions to the equation $x^3-y^2=17xy$".