I am planning to submit an article to a mathematically-oriented journal (namely: Archive for Rational Mechanics and Analysis).

I have quite a lot of results so I wrote a section "Main Results".

Question 1 In this section, the results are given as theorems, and each proof is given in another section. However, there is one simple theorem whose proof is only a few lines long. Can I provide the proof in the "Main Results" section, or is it not customary to include any proofs there?

Question 2 I am used to adding conclusions to my articles, but all the articles I read in this journal do not have any. Should I do the same and not add any conclusion (note that nothing is mentionned about this in the guidelines)?

  • I would think hard about whether the simple theorem belongs in the main results section. The whole point of a section like that is to emphasize the most important theorems in your paper. I'd only state it if the full statement is necessary to understand what comes next. Otherwise, you can give an informal statement followed by (see Theorem 3.1), or leave it out of the results section entirely.
    – user37208
    Jan 29, 2016 at 23:34

3 Answers 3


Can I provide the proof in the "Main Results" section, or is it not customary to include any proofs there?

It is fine to include a proof of a few lines in a section titled Main Results, if you feel that that helps your narrative, if it adds some insight that is useful at this point in the paper, or if the proof is extremely elegant or interesting. It is also fine not to do so. Good writing cannot be summarized in a few rules, one needs to always think about what makes sense for the particular context one is thinking about.

Should I do the same and not add any conclusion?

Pure math papers almost never have a Conclusion section. If the reader reads the introduction, the results and the proofs and still doesn't know what conclusions are to be drawn from the work, it is a bad paper and no final section will save it. For this reason, many if not most math papers simply end after the end of the last proof. Others will have a final section titled something like "Additional remarks", "Final remarks" or "Open problems". This section will usually be short and forward-looking, addressing possible extensions of the work, or containing some half-baked thoughts about aspects of the work or related questions that the authors still don't understand well.


I don't have any. :-)

  • 1
    This answer contains exactly what I would have said. (So: +1, of course.) Jan 31, 2016 at 17:40

Concerning Q1: Generally, people do not give proofs in the first section and state only main results in the introduction provided that the paper is written in the style that you described. However, if you think that the proof of a theorem should be included in the first section, it is completely OK. See for example the following paper : http://arxiv.org/abs/1505.02604

Q2: I did not write anything with a conclusion section until now but there are many papers having a conclusion section. If you want to include some open problems and conjectures (may depend on numerical experiments) or some open-ended discussion it is appropriate to add a conclusion section in your paper. Otherwise, the conclusion section (as the title of a section) may not reflect the content of the associated part of the paper.


Question 1. I have seen both cases. I will include proof of the simple theorem in main results.

Question 2. In math, your conclusions are your main theorems. It is typically not needed to include a Conclusions section.

  • 2
    -1 for disparaging another discipline.
    – Bill Barth
    Jan 29, 2016 at 23:37
  • Conclusions are essential in engineering, precisely because the result can usually not be as clear as a theorem. But, +1 because you answered and I am not sure it was intended scorn...
    – anderstood
    Jan 29, 2016 at 23:41
  • @anderstood If it wasn't intended, it was highly negligent. Jan 30, 2016 at 8:03
  • OK, I edited answer to Question 2.
    – eli
    Jan 31, 2016 at 8:31

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