How to write an abstract for a math paper? 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?
 A: *

*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.
A: 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 ...".  
A: 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 $x^3-y^2=17xy$".
