If the main idea of an article is simple enough to be meaningfully exposed in the abstract, should that be done?

Question

I'm trying to decide between two kinds of abstracts for an article I prepare.

• One mentions by name, goal and principle the well-studied, often taught, and commonly used theoretical construction I start from; tells I propose dual smurfs (one large, one small) rather than the usual single smurf, and that I get the benefits of both large and small smurf, with practical applications.
• The other eats like 180 words (out of the recommended 150--250) to introduce some notation¹, then my dual smurfs, an extra variable, two new formulas describing the modified relations. I hope it could trigger a "that could work!" feeling in the target readership. But I have to severely trim the rest.

I fail to find a middle ground: it's either deferring meaningful explanation of the how to the body of the article, or spending most of the limited space/attention span for a basic exposition.

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Some context: I'm an engineer using cryptography professionally, not an academic. I only previously wrote one article as a single author², back in 1999. I now have a quite different idea, hopefully improving a well-studied, often taught, and commonly used theoretical construction. I plan to first post my article on a specialized preprint website, with three goals:

1. Raise interest of academics in the field to either get a summary refutation, or find a coauthor mastering more advanced proof techniques than I do, to get more precise security reduction.
2. Make a disclosure that prevents others from filing patent (I won't). That goal complicates privately circulating the article, since the few academics I know in the field tend to have ties to the industry.
3. If possible get published in a top conference.

The abstract matters to 1; less for 3, as I can change the abstract when I submit; not for 2.

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¹ Four variables known to the target audience but under a plethora of notations and often two names, the usual smurf, one short formula on how the smurf relates to the variables.

² The attempt went well. LaTeX didn't kill me. I got published in a top-4 conference with peer-reviewed proceedings, then invited by academics to merge my material into an article in the reference journal of the field, sort of an obituary to the signature standard we had broken in significantly different ways.

Answer 1

In my field(s) [statistics, economics, finance], it's generally bad practice to introduce notation in an abstract, unless the journal is highly specialized. My suggestion is to go with the first abstract and then get right into things using your second abstract during the introduction. I really like papers that have a well-written abstract and start laying notation almost immediately - big time saver as a reader and helps me avoid missing a useful paper.

Here are some helpful tips for abstract writing.

Answer 2

This is a personal view, I suppose, and others might disagree, but the purpose of an abstract is to permit a reader to get a complete picture of the work, not an introduction or background. Those can be separate sections of a paper. But a fairly knowledgeable reader should be able to read the abstract and know what the paper's results are. If they are concerned with the details or question those results they read further, but there isn't a need if the abstract is accurate and doesn't raise questions in the mind of a reader.

In particular, the abstract's purpose is not to tickle the reader into reading further, nor to provide definitions of terms that only make sense later.

In a math paper, not so far removed from what you are doing perhaps, the abstract would contain a statement of the main theorem proved, though perhaps not in technical form. If a reader wants to see how that was arrived at then they read further. Often the proof is more interesting than the statement itself, but unless I'm very interested in that particular question I may not need to personally vet the proof. But, I need to know the paper's conclusion for the abstract to be valuable at all.

Answer 3

You should think of how the end users will read your abstract. In any field, there are too many papers that come out every day to read every paper in detail. The main purpose of the abstract is therefore to quickly convey to a reader who is scanning a few dozen abstracts over coffee what are the main results and conclusions of your paper, so that the reader can make a quick decision about whether or not they want to come back and look at your paper in more detail. Often (whether consciously or not) these judgments occur on both a textual level -- are your results plausible and interesting -- and a metatextual level -- does this abstract read like it was written by someone who knows what they are doing. Even if someone doesn't actually read your paper, you would like them to come away with a clear takeaway message, so they are aware of the results of your work.

Going into enough detail that you have to define non-standard notation is almost certainly a mistake. Your reader's attention and time is a resource; getting someone to follow your notation is a use of that resource that probably could be spent focusing on the main result. The abstract will necessarily be terse and of course will not contain all the evidence that supports your claims. It should provide some very brief context (this lets people decide whether your paper is even in the ballpark of what they are interested in), describe at a very high level what methods were used, and in particular what novel approaches you used (this lets people judge whether your methods are powerful enough that you can plausibly show what you are claiming to show), and explain the main results and conclusions (that's the good stuff -- what did we learn?). On a meta level, an abstract that gets too far into the weeds technically will typically signal inexperience in writing papers. At least, it will put a roadblock between your busy readers and the good stuff you want to tell them.

Answer 4

Think of the sequence title -> abstract -> introduction as a funnel or inverted pyramid. As we go down, the word limit increases. As we go down, the specificity increases. Finally, by the end of the introduction, the complete concept of the paper and its context should be clear. Each step in the sequence is convincing the reader to precede to the next step. I should say, convincing the right reader, because it is also acting as a filter, informing potential readers that "no, this paper is not quite what you're looking for". You could also imagine a sequence of filters of increasing fineness, filtering out your potential audience until you're left with only those who are precisely interested in reading your paper. This is to everyone's interest. It makes your work more visible in the literature and it saves precious time and attention for potential readers.

With this concept in mind, you can see that disrupting the order can cause problems. What happens if the abstract is too specific, say by jumping straight into technical notation? You will lose the audience who are not already familiar with the notation. You will lose the audience who think "oh so they're just doing xyz, it must be pretty obvious and basic if they can neatly present it in the abstract" because you haven't laid out the context. You haven't explained why this approach is important/interesting/novel.

It follows logically, then, that you should prefer option one.

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I would also add that some journals (perhaps many) will not allow you to include mathematical notation in your abstract because of various issues related to indexing, rendering within databases and so-on.

Answer 5

It is hard to be sure without knowing the details. But the first way sounds better.

The only advantage of the second way seems to be that it could trigger a "that could work!" feeling. In other words, if I understand correctly, you are worried about readers losing interest without bothering to read past the abstract (your goal 1).

Just try to pique their interest in the abstract, and show that you know what you are talking about, then in the main text present the whole of the main idea as soon as possible.