# Could giving an alternative approach to proving an established result be worthy of publication? [duplicate]

(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 "can" be published. But the feedback you get will be valuable in any case.

• "The reason that such insight is important is that it can often lead to solving additional, unsolved, problems." I agree completely, but let's say for argument sake that it is not yet known whether my approach could definitely do that. Would journals still accept a paper purely on the basis of it being different and (debatably) more elegant? – MathsGuy Mar 6 at 23:53
• That is up to them, of course. I can't predict. But "different" probably isn't enough. If the technique you use is standard for similar problems then probably not. But you need to submit it to get the feedback. – Buffy Mar 6 at 23:55
• What do you mean by "if the technique you use is standard for similar problems" ? – MathsGuy Mar 6 at 23:56
• A theorem might have two fairly straightforward proofs. Neither is more interesting than the other and neither is particularly interesting in itself. In such a case it isn't the proof that is interesting, so one is plenty. "New insight" is the operative concept here, not "different". – Buffy Mar 7 at 0:02

Presumably you'll do the work anyway, so you might as well attempt to get it published. The opinionated majority (tongue in cheek) may find it "unworthy", sure. Yet there may well be someone who'll get inspired by your work, or find the little insight they needed to keep moving in their work on another problem. I'd say that you may wish to keep at it until the publishing pursuits clearly won't be resolving in a constructive manner anymore - that is if the idea gets rejected without any feedback that you could use it to improve it. When it comes to such a dead-end, you can just stick it on your personal website as a "white paper", push it to arxiv, etc. But perhaps don't do that until you're sure that all avenues of pursuit available to get it published in mainstream journals get exhausted.