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I am a PhD student and I started studying a recent article of my advisor. During the study, I realized that some of the reasonings and results used in the article could be considerably improved. Moreover, the result of the main theorem of the paper could have been much more general. My advisor agrees on this.

Thus, the changes are significant. The problem is that the novelty of the idea belongs to the previous paper and that my changes, although significant, would be 4 or 5 pages of length (the original article is 10 pages length).

My question is whether significant but brief improvements of papers in the field of Mathematics can be published in some journals. Should I forget about this idea? Should I send the improved version to the same journal than the previous paper? Are there special journals for papers dealing with significant but brief improvements of extant articles?

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    As a general rule, yes, “significant but brief” improvements are very publishable in math, and a 5 page paper can still be excellent. If you have a shorter proof, a different proof, a more insightful proof, and/or a stronger/more general result, then by definition you have made a novel contribution. Thus, I think your determination that “the novelty of the idea belongs to the previous paper” sounds dubious to me, and you should definitely try to publish the idea. – Dan Romik Jun 8 '18 at 16:59
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    "The main theorem of the paper could have been much more general" - this itself looks like a reason good enough for publication. That's how progress in science is done - by making things better (well, in general). And while indeed most papers are longer, significant contributions only a few pages long are not that rare; and the significance of ones work is judged by its quality, not by its length. – user68958 Jun 8 '18 at 18:34
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    Write it and send it to arXiv first, worry about the journal later. – Sylvain Ribault Jun 9 '18 at 8:44
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    I was in a similar situation and I agree with @corey979 that the length doesn't matter. Yet, if it is "too easy" to generalize the original paper then your result might not be so novel. It is possible that the authors knew about this generalization but didn't thought it's worth writing down. Anyway this looks like something you should discuss with your adviser (which is also the author of the paper). – Yanko Jun 9 '18 at 10:31
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    I don't like the wording "significant but brief" because it suggests that brevity is a fault. I think of it as a virtue. Although I've written some long papers (over 100 pages), one of my best papers is 3 pages long. – Andreas Blass Jun 9 '18 at 21:27
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Mathematics is about solving problems, not extensive writing!

The briefer the better, the significance is even better.

There are lots of publications of novel proofs of the same theorem, just of the sake of development!

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