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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?

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    Why the downvotes? – Math_Freak Feb 16 at 15:19
  • Don't worry about down votes. People do what they do. It could be as simple as a single word. I can't guess at any of the downvotes on the question or the answers here. Some voters are kind enough to explain. Others not. – Buffy Feb 16 at 15:42
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    How shall I address the Editor and let him/her know that I have obtained the same results but using much easier techniques? — I don't understand the question. Surely the editor will read the abstract of your paper. Why would you need to explain anything to them separately? – JeffE Feb 16 at 15:43
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    I think that the question is asked in the wrong way, probably that is why it was downvoted. If you find a new mathematical proof for a theorem, which is shorter or more elementary, that is many times novel enough to publish. But you need to remember that if the original result was published in a High Impact Factor, it was primarly because it was new. Do not expect to publish a new proof of the same result in the same high impact journal, aim lower. You do not need to address the editor in any way, you simply write a paper and emphasize that this is a simpler proof of – Nick S Feb 16 at 19:14
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    I don't think I've submitted a formal cover letter with a journal submission in two decades, but when I did, they read, in full: "Dear Editor, Please accept the attached paper for submission to journal X. Sincerely, The Authors." You're overthinking. The editor will read the abstract. As for the title, I recommend something direct like "A simple proof of Theorem Z". – JeffE Feb 17 at 6:58
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"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.

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  • How will I address the Editor? Shall I send the paper for peer review to the same journal where the original article was published – Math_Freak Feb 16 at 15:17
  • @Math_Freak Write the paper, send it to a journal. You can try the same journal, but especially if it is a good journal, expect it not to be accepted. New proofs to old results are typically valued lower than new theorems. – Nick S Feb 16 at 19:22
  • Please explain downvotes, to help improving the answer or for me to remove it if it is counterproductive. – Captain Emacs Feb 16 at 19:39
  • I am worried about the "cover letter" and how to choose the title – Math_Freak Feb 17 at 4:18
  • What's to worry? You explain that you shortened or simplified the known proof of a theorem. The editor can choose to find this interesting or not. In any case, if the simplification or shortening is considerable, it is definitively a contribution, even if not necessarily in the top journals. For instance, a proof that leaves out certain techniques necessary in the original, is also interesting. – Captain Emacs Feb 17 at 9:29
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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!

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  • I am worried about the "cover letter" and how to choose the title? – Math_Freak Feb 17 at 4:17
  • @Math_Freak what did your advisor say when you consulted them about those things? – Dan Romik Feb 17 at 4:19
  • He says " I am busy with my son's birthday party". My advisor is not concerned about my project at all – Math_Freak Feb 17 at 4:20
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    @Math_Freak well, I’m busy with lots of things myself too, and as I said in my answer one cannot give formulaic answers to such questions. You need to have someone with experience actually look at your paper and give you specific advice tailored to your situation. And maybe also work on developing good communication and trust with your advisor, and some patience to wait for him to get back to you when he’s back in the office, those things are probably much more instrumental to your success in research than the question about how to choose a paper title. – Dan Romik Feb 17 at 4:28
  • I understand but since its not possible to develop trust with my advisor anymore , my question is " How will you choose a good title in this case" , just give me your take – Math_Freak Feb 17 at 4:30
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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.

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  • How will I address the Editor? Shall I send the paper for peer review to the same journal where the original article was published – Math_Freak Feb 16 at 15:18
  • It could be the same journal or another. Consider, even, a higher ranked journal if that seems reasonable. It depends on what you have done, of course. – Buffy Feb 16 at 15:40
  • I am worried about the "cover letter" and how to choose the title – Math_Freak Feb 17 at 4:19
  • @Math_Freak Maybe you need to explain to us why specifically you worry about the cover letter / title. You are almost certainly worrying about the wrong things, but it's difficult to provide a convincing argument if you don't say what your worries are. – xLeitix Feb 17 at 10:59
  • Thank you very much for the answer – Math_Freak Feb 18 at 3:07

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