How to write an abstract for a math paper?

Question

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. — GH from MO, Jun 28 '15 at 16:22
"The key to writing a good abstract is in formulating your theorems." --- http://www.impan.pl/EN/PubHouse/writing.pdf — Carlo Beenakker, Jun 28 '15 at 16:41
Why is my question on hold as off topic? Similar questions such as [http://mathoverflow.net/questions/1243/how-to-write-math-well?rq=1] on mathematical writing have been asked. — Halbort, Jun 29 '15 at 01:27
See discussion on meta: http://meta.mathoverflow.net/questions/2337 — , Jun 29 '15 at 10:00

Jeffrey Shallit · Accepted Answer · 2015-06-28T16:42:20.800

55

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.

edited Jun 28 '15 at 16:42

answered Jun 28 '15 at 16:15

Jeffrey Shallit

2,918

1

Bozhe moi! (and yes, this is a good answer) – Todd Trimble Jun 28 '15 at 23:51
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@ToddTrimble I saw what you did there! – David Roberts Jun 29 '15 at 04:09
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@DavidRoberts You didn't see me plagiarize! – Todd Trimble Jun 29 '15 at 04:29

score 18 · Answer 2 · answered Jun 28 '15 at 16:24

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 ...".

score 15 · Answer 3 · answered Jun 28 '15 at 16:59

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

How to write an abstract for a math paper?

3 Answers3