Is it worth publishing a paper rephrasing what past papers did with a different mathematical framework?

Question

I work industry (I'm an engineer with a decent background in math) and for work I often read through papers and I attend conferences to keep up with the state of the art.

I've noticed there're few papers (not very recent but not very old either) whose methods can be derived in a more elegant way using other mathematical frameworks.

I was wondering if it make any sense to re-work all the math these papers did and publish them somewhere. It wouldn't be potentially having new results from these papers but just reformulating them, maybe a new reformulation might highlight new properties worth experimenting.

My question is:

1. Is this kind of work worth some paper submission somewhere?
2. If no new experiments are produced that would yield different results I wouldn't really say they are worth engineering wise (I might be wrong though), so for sake of mathematical interest is there some Journal of applied mathematics of some kind that could fit for this purpose?
3. I struggle to find similar work somewhere but I'm not really good with looking up math papers / applied math papers do you have any suggestion of something I can look up?

Answer 1

Here is my opinion and suggestion (I claim no authority).

1. Elegant derivations are of indisputable value, even if they are mathematically equivalent to existing results. Think of postgraduate students reading your paper and having an "aha" moment, for example. By contributing elegant results, you are promoting your sub-field, which could be appreciated by other researchers.
2. I won't be able to suggest a journal, unless we work in the same area. I doubt it is possible at all without knowing the details. There probably exists an applied mathematics / engineering journal dedicated to your topic, which leans towards mathematical aspects and has many non-experimental papers. If you want to submit a concise paper, perhaps, look for the word "communications".
3. If searching by keywords in Google Scholar or similar doesn't yield what I want, I try the following. Crawling citations from the most relevant papers or books / volumes / series / conferences. Checking publication lists of the most relevant researchers / labs. Reading theoretical chapters of doctoral theses, which can be a good source of carefully chosen references.

Answer 2

This isn't exactly my field, so you will have to judge whether any of these suggestions apply to you.

In pure math and some other theoretical fields, the theorems aren't actually the most important thing. They are, in a way, signposts, that indicate where we are. More important in many cases are the proofs that lead to the theorems as they can give insight into why things are true and that insight can lead to additional advances of the art. So, here, a new proof of an existing theorem would be welcome, provided that it leads to a new insight.

In computational work, say CS, the efficiency of an algorithm on a particular class of problems can be all important. But a given algorithm that is good for one kind of problem may be inappropriate for another. Here, a new algorithm that is more efficient on some important class of problems, or even one that is no worse on a larger class might be welcome. Insight might also be important here, as well, if a new algorithm gives new insights into some class of problems.

In some fields, I think, that if you have a lot of scattered results, developed from different ideas and techniques, but you can unify them into a cohesive whole would, again, have value, though it might be harder to recognized in a Balkanized world. But, again, if the unification leads to insight it would be worth publishing.

There are other situations as well, I'm sure, in which such publication would matter, provided that it is recognized. You might have to point it out, of course.

And note that, in some sense, such a paper would be an advance in a somewhat meta sense. The problems are already "solved", but the improvement is in the way we think about those problems that forms the advance.