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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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  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.

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    $\begingroup$ Bozhe moi! (and yes, this is a good answer) $\endgroup$ – Todd Trimble Jun 28 '15 at 23:51
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    $\begingroup$ @ToddTrimble I saw what you did there! $\endgroup$ – David Roberts Jun 29 '15 at 4:09
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    $\begingroup$ @DavidRoberts You didn't see me plagiarize! $\endgroup$ – Todd Trimble Jun 29 '15 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 $x^3-y^2=17xy$".

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