How to address an Editor if I have new proof techniques of old results?

Question

I read an article published in a High Impact Factor journal and on reading I find that almost all of the proofs could have been done in an easy way.

I devised easy techniques myself and I find that the results obtained in that paper match mine.

Shall I publish my easy techniques stating in my paper that I have found easy proof techniques for the paper already published? Is it publishable?

How shall I address the Editor and let him/her know that I have obtained the same results but using much easier techniques?

How should I give a title for my manuscript?

Answer 1

"A direct proof of Cockatoo's equation."

"An elementary approach to Shrokensveny and Ljubovitch's inequalities"

"Deriving the circumferent super-Galois hyperextension of Williamson spaces from basic topological axioms"

Simplified proofs are amongst the most valuables contributions to mathematics if they convey either new perspectives, or clarity or simply insight into the problem. Just make clear that it is a simplification of known results and make sure your proof is solid.

I have myself witnessed the process of an important theorem reduced from a full book length of theory development to effectively one page of comparatively elementary mathematics. It is a perfectly legitimate contribution.

Answer 2

What makes this question challenging to answer is that it’s addressing the wrong level of generality: you’re asking about a very specific situation (publishing a simpler proof of a known result) but your questions suggest you’re missing basic facts about publishing of math research in general (how to “address an editor”, how to select a journal to send your paper to, and how to know if your research is even publishable) that have little to do with the specific situation you’re describing.

In terms of answering these questions, only one strikes me as answerable with the information you’ve provided: in math you don’t “address an editor” in any special way, you simply send in your paper using the process described on the journal’s website. If this involves an email to the editor, this need not contain anything more than a factual statement that you are submitting your paper to the journal. There is no need to “address” the contents of your paper or attempt to support the paper’s case for publication in the email - that’s the job of the paper itself.

For the other questions, I think you’ll have to find a knowledgeable person to actually look at your paper and give you advice about whether the results are publishable and what journal they will be a good fit for, how to choose a good title, etc. Those are all important questions but they would depend on much more detailed information than the mere fact that you’ve found new proofs of known results - papers meeting such a description can range anywhere from near-worthless to something that belongs in a top journal. Anyway, good luck!

Answer 3

New proofs are valued in mathematics if they open new doors. But the proof probably needs to be something that has value in its own right, though there are exceptions. A short proof of the four color theorem that doesn't rely on computers would be interesting, even without the "new doors" aspects. (I hope that is still the case. I haven't looked at it in a while.)

But new proofs of old things often give other mathematicians ideas about other ways to exploit the technique. Such proofs are interesting primarily if they offer new insight into the problem itself or, better, into some class of problems.

But if you just write the introduction/abstract of the paper correctly, then the editor doesn't need a special heads up. A quick glance will let them know what you are up to.

I can't give much advice on the title unless one of the key theorems is named and well known (Four Color Theorem, for example). It needs to be specific. A New Proof of an Old Theorem works for a college student project, but probably not so much for a publication.