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?

7$\begingroup$ I think the abstract is supposed to summarize, not advertise the paper. $\endgroup$ – GH from MO Jun 28 '15 at 16:22

2$\begingroup$ "The key to writing a good abstract is in formulating your theorems."  impan.pl/EN/PubHouse/writing.pdf $\endgroup$ – Carlo Beenakker Jun 28 '15 at 16:41

1$\begingroup$ Step #1: write a math paper. $\endgroup$ – Gerry Myerson Jun 28 '15 at 23:58

5$\begingroup$ Why is my question on hold as off topic? Similar questions such as [mathoverflow.net/questions/1243/howtowritemathwell?rq=1] on mathematical writing have been asked. $\endgroup$ – Halbort Jun 29 '15 at 1:27

$\begingroup$ See discussion on meta: meta.mathoverflow.net/questions/2337 $\endgroup$ – user25199 Jun 29 '15 at 10:00
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 leftbifurcled rectangles. He conjectured no such rectangles exist when the number of bifurcles $n$ is odd."
State your results, in nontechnical language, if possible. "In this paper we show the existence of leftbifurcled 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.

1$\begingroup$ Bozhe moi! (and yes, this is a good answer) $\endgroup$ – Todd Trimble♦ Jun 28 '15 at 23:51

1

1$\begingroup$ @DavidRoberts You didn't see me plagiarize! $\endgroup$ – Todd Trimble♦ Jun 29 '15 at 4:29
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 easilyunderstood interestpiquing corollary of the main result "As a special case of our results, we demonstrate the existence of infinitely many integer solutions to the equation $x^3y^2=17xy$".