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?
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8$\begingroup$ I think the abstract is supposed to summarize, not advertise the paper. $\endgroup$– GH from MOCommented Jun 28, 2015 at 16:22
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2$\begingroup$ "The key to writing a good abstract is in formulating your theorems." --- impan.pl/EN/PubHouse/writing.pdf $\endgroup$– Carlo BeenakkerCommented Jun 28, 2015 at 16:41
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2$\begingroup$ Step #1: write a math paper. $\endgroup$– Gerry MyersonCommented Jun 28, 2015 at 23:58
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6$\begingroup$ 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. $\endgroup$– HalbortCommented Jun 29, 2015 at 1:27
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$\begingroup$ See discussion on meta: meta.mathoverflow.net/questions/2337 $\endgroup$– user25199Commented Jun 29, 2015 at 10:00
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3 Answers
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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.
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1$\begingroup$ Bozhe moi! (and yes, this is a good answer) $\endgroup$ Commented Jun 28, 2015 at 23:51
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1$\begingroup$ @ToddTrimble I saw what you did there! $\endgroup$– David Roberts ♦Commented Jun 29, 2015 at 4:09
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1$\begingroup$ @DavidRoberts You didn't see me plagiarize! $\endgroup$ Commented Jun 29, 2015 at 4:29
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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 ...".
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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 $x^3-y^2=17xy$".