How to write an abstract for a math paper? [closed]

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?

• I think the abstract is supposed to summarize, not advertise the paper. Jun 28, 2015 at 16:22
• "The key to writing a good abstract is in formulating your theorems." --- impan.pl/EN/PubHouse/writing.pdf Jun 28, 2015 at 16:41
• Step #1: write a math paper. Jun 28, 2015 at 23:58
• Why is my question on hold as off topic? Similar questions such as [mathoverflow.net/questions/1243/how-to-write-math-well?rq=1] on mathematical writing have been asked. Jun 29, 2015 at 1:27
• See discussion on meta: meta.mathoverflow.net/questions/2337
– user25199
Jun 29, 2015 at 10:00

1. Avoid notation if possible. Notation makes it really hard to search electronically.

2. 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."

3. State your results, in non-technical language, if possible. "In this paper we show the existence of left-bifurcled rectangles for all prime $n$."

4. 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".

5. Never, ever, ever, cite papers in the bibliography by giving citation numbers; the abstract is an independent entity that should stand on its own.

• Bozhe moi! (and yes, this is a good answer) Jun 28, 2015 at 23:51
• @ToddTrimble I saw what you did there! Jun 29, 2015 at 4:09
• @DavidRoberts You didn't see me plagiarize! Jun 29, 2015 at 4:29

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