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I am writing a mathematical paper where I (re-)state a well-known theorem, followed by several corollaries. One of these corollaries is my main result and, naturally, it is somewhat lost in the text, while I would like it to stand out to the readers without them reading through all the running text (where it is described as the main result). What is the best way to highlight it? Putting a box around it or make a gray background/shading seems like an overkill, but maybe this is the way to go? Any suggestions?

(Sometimes, stating the main result in the very beginning as a theorem is the best way to go, but in this specific paper I would like keep the order of the statements, since I like the corollaries coming after the theorem they are based upon and they also build on one another.)

Remark: I first posted this question on Tex Stackexchange, where it was off-topic. I am not sure whether it is on-topic here (I did check the help center, where I would argue that it fits the "academic writing and publishing" topic). If I am wrong, please tell me nicely and suggest an alternative. :-)

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    I think it's on topic here, and is in the same spirit as this question. That said, you may be interested in the question Main statement as theorem or corollary on MathOverflow.
    – Anyon
    Commented Mar 13, 2023 at 13:09
  • @Anyon Thanks, this helps a lot, especially the second link! Commented Mar 13, 2023 at 13:18
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    When it comes to visual highlighting like box or shading, you need to know the journal's information for authors, style and formatting guidelines etc. Most journals I know wouldn't be happy to have special highlighting for a specific corollary. They would want to have same formatting for all of them, and surely not more than for a theorem. Better use explanations as in @Buffy's answer to convey your message. Commented Mar 13, 2023 at 13:26
  • I've once read a paper whose main contribution was restating a theorem from someone else's paper. The theorem in the original paper was extremely abstract and likely to be overlooked, because it was so hard to see its implications and applications. The second paper applied the theorem to a particular problem, and restated the theorem in that context, and that was brilliant.
    – Stef
    Commented Mar 14, 2023 at 10:00
  • If it's your main result, don't forget to mention it in the abstract and if possible in the title too. Many people only read those.
    – Joooeey
    Commented Mar 14, 2023 at 16:21

4 Answers 4

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If I understand your situation correctly, your paper has a well-known theorem (proved by other people) and a number of corollaries which are your results. One of these corollaries is your main result and you would like to highlight it more.

A simple solution would be to just rename the main corollary a theorem. Then your paper would have two theorems, one in the introduction and credited to other people and one in the main part which is your main result. A result doesn't need to have a difficult proof to be considered a theorem instead of a corollary. If it is important in itself that makes it a theorem.

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    Thanks for your suggestion! While the other answers were really helpful as well, I think I will go for this simple solution. I think adding a name to the theorem, say, "Theorem 4 (main result):" or "Theorem 4 (sharp bounds on ...):" can also prevent the readers from overlooking the main result. Commented Mar 14, 2023 at 8:06
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    One also has to wonder why if you proof one theorem in your paper that is not called theorem 1 (or 2 if you want to call the famous theorem theorem 1 but it probably already has a name if it is famous no?)
    – Kvothe
    Commented Mar 14, 2023 at 12:31
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You can use both the Introduction and the Conclusion to point out the significance of any part(s) of your paper. Since most mathematicians will automatically jump to the conclusion that if you call a thing a Theorem and another thing a Corollary that the former is more important. But, as you note, it ain't always so.

The Introduction can note that some "apparently" lesser thing is really the "big bang" and the Conclusion can give the consequences of that.

Actually those consequences can also be alluded to in the Intro.

Likewise, if you provide an abstract, while you mention the "main" Theorem, include words that point to the Corollary as more significant.

And, of course, you may be wrong. If the corollary "follows easily" from the Theorem, then it is more than possible that the Theorem has additional consequences that make it especially significant.

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    Hmm, I've hardly ever seen a paper in pure math that contains a "Conclusion" section. Maybe I misunderstand what you are referring to? Commented Mar 13, 2023 at 15:31
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    Ah ok, but now I see that OP works in a field which many people might rather count as applied math. Commented Mar 13, 2023 at 15:34
  • Thank you for your answer, this was really helpful! I mostly agree with your arguments, however, some readers might simply jump to the theorems and not even read the running text. Also, concerning your last point: Yes, the Theorem is most likely more significant, but as I wrote it is well-known and not my own result. I only state it to "set the stage", so the reader can easily follow my arguments. Naturally, I want to highlight my own result. :-) Commented Mar 14, 2023 at 8:11
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    @IljaKlebanov "some readers might simply jump to the theorems and not even read the running text" No I doubt that. Most people read as Buffy pointed out the abstract and the conclusion. Most readers might stop reading after that, as they understood your paper is not interesting to help with their problem.
    – usr1234567
    Commented Mar 14, 2023 at 13:42
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I don't recommend using visual formatting to accomplish this (other than the normal formatting that applies to all the theorems and corollaries). I also don't recommend delaying the highlighting of your result until the introduction is finished, as another answer suggests. Instead, use words to explicitly communicate the structure and story of the paper to the reader. For example, at the very start of the paper, something like:

"The Lasser Theorem, proved in the seminal paper [1] and stated as Theorem 1.1 below, is known to have many significant applications in this field. Many of its corollaries are stated below, including the important Corollary 1.8 about the non-semisimple Noetherian case. The purpose of this paper is to provide a (new/shorter/more insightful/less dependent on deep theorems) proof of Corollary 1.8."

Then right before stating Corollary 1.8: "As mentioned earlier, the following corollary also follows from Theorem 1.1; in this paper we provide a new proof of the corollary using (model theory/numerical differential equations/similar triangles)."

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  • Thank you for your answer! I agree with you and will certainly include such discussions early on in the text. However, I am afraid that some readers might jump to the theorems and skip most of the running text. This is why I chose to accept another answer. Commented Mar 14, 2023 at 8:13
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If I'm understanding correctly. I think moving the 'well known theorem' part to a section called 'background' would solve your issue, As it removes the extra background stuff from your results. This will mean your actual new/interesting results are by themselves and not 'lost in the text'. Also it just makes sense, since it's well-known it is (nearly by definition) background and your paper is building upon this theorem.

Though with your ordering requirement, I would admit that it may be slightly strange to have a background section immediately preceding the results section. I would just put it in its usual spot though, you can reference back to it if you think it makes sense.

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