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My research answered a very specific question. But the hypothesis I was testing will also likely have very broad application. I want to make sure to convey that importance in my paper. Is the first line of the introduction an acceptable place to do that?

I am thinking the first line of the introduction might be something like:

For decades our knowledge of myTopic has been insufficient to answer questions like A, B, and C. I considered scenario C₁ to test my hypothesis, which now shown to be correct in this case, will likely play a key role in answering these other questions going forward. Some background on scenario C₁ is...

Or should the introduction only mention background info which is directly relevant to the scenario I actually investigated? And then I can suggest the larger importance of this discovery elsewhere in the paper?

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    Depends on the journal where you want to submit your manuscript. Some want you to be short and specific, others want you to tell a long story, starting broad and then zooming in. – Mark Jan 9 '18 at 1:09
  • I would pull it off the other way round: Basically you have solved c1, but the implications of it make a huge impact on whole yourTopic. But, as Mark said, it depends on the venue. – Oleg Lobachev Jan 9 '18 at 8:36
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The answer to your question entirely depends on your field and the venue to which you will submit your paper. Software Engineering papers, for example, tend to have much longer and broader introductions than Math papers. Papers at smaller and more focused conferences and journals have shorter and more focused introductions that those at broad venues, since they address a more specific readership.

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Within the field of mathematics research, there is a bit of a tradition (almost a competition really) to create useful but extremely short papers, with minimal context. In some cases the introduction is non-existent and the reader is expected to put the result in context through the statement in the title of the paper, and their own knowledge of the field. This is somewhat tongue-in-cheek, and is a way of demonstrating that valuable results can be given without padding them out with literature.

For example, there is a famous mathematical paper that refuted Euler's sum-of-powers conjecture by providing a short counter-example. This paper states its objective in the title, and then presents the counter-example in two sentences, without any further context. This is regarded as a useful paper that establishes the falsity of a major mathematical conjecture.

Another mathematical paper (dubbed the shortest ever) states its question as a single sentence, and then has an answer that consists of two words and two diagrams. In this latter case, the authors refused to add an introduction to their paper despite requests by the reviewers, since they wanted it to be as short as possible. (Although this has been dubbed the shortest paper ever, my view is that it is effectively longer than the above paper, since it includes two large diagrams. Also, the article describing the article is inconsistent with how it was actually published; the editors put the title sentence into the body and gave it a simpiler title.)

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    For what it's worth, I've noticed a general tendency in mathematics papers published in the last 20 years or so to have much longer introductions about previous and related work that had been the case for the several decades before this. My guess is that this is due to the availability of digital searches using Mathematical Reviews (used to be you had to go to the library and flip through the yearly indexes), JSTOR, google scholar, etc. The effect is cumulative also, in the sense that after one paper digs up lots of background stuff, later papers can build on it. – Dave L Renfro Mar 8 '18 at 13:52

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