Could giving an alternative approach to proving an established result be worthy of publication? (I don't believe this is a duplicate to Can I publish a paper with new proof but the same result?, because not only am I using a different proof, but also an axiomatisation that could perhaps be seen as controversial)
I am a post graduate student of pure mathematics that hasn't published anything yet.
Hypothetically, let's say that there's an established result in mathematics that was stated and proven using a popular axiomatisation.
Let's say that if you state and prove the same result using a different (non-standard) axiomatisation, then the result becomes (perhaps debatably) more elegant.
Is it possible for paper like this to be worthy of publication?
If so, are there any specific journals that you think might be more likely to accept such a paper?
Slightly more detail:
The established result uses ZFC as axiomatisation, my approach uses ZFC + Atoms as axiomatisation. The result that I'm restating and reproving concerns general mathematical structures.
Often enough the proof of a theorem is more important than the statement of it. This is especially true when a new proof gives some insight into a problem that the original proof did not.
I don't know whether your new proof is different enough or interesting enough or gives new insight, but if it is, then it would be an important thing to publish.
An example of such a problem is the Four Color Theorem. When I was in school it was the Four Color Hypothesis and nearly everyone in my age cohort thought about it for a while I suspect. It was originally proved using computers to examine a very large number of special cases. But to a mathematician, this is a very unsatisfactory proof. One would love a short and insightful proof not depending on computation as it would be very likely to give insights into the nature of planar maps.
The reason that such insight is important is that it can often lead to solving additional, unsolved, problems.
So, you can certainly submit such a paper for publication, but it is editors and reviewers that will decide whether it &quot;can&quot; be published. But the feedback you get will be valuable in any case.