# Solving open problem with elementary method, is this publishable

I believe I solved an open problem in my field, but the method I used is elementary, is the result still publishable?

To make it more specific, I found a problem and solved it. The method I used is neither advanced nor new. It seems that no one is trying to solve it, except one famous person in my field mentioning that it is an open question. Under this situation, will my result be worth publishing?

• Does that famous person live? If so, is there a reason not to ask them? After all, they might be interested in the problem. Jun 3, 2021 at 12:01
• You could ask his university department? Jun 3, 2021 at 12:34
• There are lots and lots of open problems, an infinity of the beasts. Whether the community finds any specific one interesting, well that's something else altogether. But one must follow one's dreams and callings. So yes, proofs by elementary means can be interesting (in mathematics see "Proofs from the Book") though not to everyone. Have fun, good luck! Jun 3, 2021 at 17:11
• In mathematics (at least), a simpler proof is more interesting/important/publishable than a complicated proof. Jun 4, 2021 at 7:55
• On a first read I thought the question was "Is this punishable?" and I was going to answer: Rather! Jun 6, 2021 at 8:06

Yes, it's publishable.

• This paper solves a problem of Euler, so it’s not exactly a typical illustration of OP’s situation. Jun 3, 2021 at 17:01
• I think the question is not "was there ever a paper that was like this and was publishable" but rather whether "generally speaking, is a paper like this publishable". In that case, the example you have posted proves little. Jun 4, 2021 at 8:22
• Random remark: an even shorter version of that paper was published. Jun 4, 2021 at 21:06
• @JimmyK4542: Gotta love the brute-force approach to problems! Jun 5, 2021 at 23:09

It is; I just published a paper like that myself. The criterion for publishing is simply that people want to read it. If it's a known open problem, especially one with a pedigree and a famous name attached to it, it's probably of interest to a fair number of people. For that matter, the fact that the proof is elementary may be an advantage. There was interest for a while in an elementary proof (i.e., without complex analysis and results like Tauberian theorems) of the prime number theorem, for example, well after the result itself was established.

What is publishable is up to the publisher with advice from a few of their reviewers. But if they don't see it, they can't publish it. So, you should consider submitting it to an appropriate journal.

However, it is probably worth the effort of getting some local advice. Things may have changed since the report that it was open. Some open questions are very important and a proof would be interesting. Perhaps especially interesting if it uses elementary methods. But the reviewers and the editor will be the judge.

The editor might, however, suggest that you publish it as a "letter" rather than a full paper, so be prepared for that.

• Thank you for the answer. I am still new to publication process, what is a "letter"? Jun 3, 2021 at 12:21
• A "letter" is a very short paper - maybe a couple of pages. There are some journals that specialize in such short publications. Some others will include them also. Jun 3, 2021 at 12:33
• AIUI, in some disciplines, a letter (e.g. in Phys. Rev. Lett.) is more prestigious than a normal paper (e.g. in Phys. Rev. B). I'm not sure if this makes any difference to the answer. Jun 4, 2021 at 8:54
• @DanielHatton thanks for mentioning this. PRL papers ("letters") are typically 4-5 pages which is by no means "very short". I'd also not refer to them as a "normal paper" and a "letter", as well as "normal" and " very short" papers. Those are just two different formats of publishing, and the difference is much more structural than just length. Jun 4, 2021 at 13:05

Yes, it is definitely publishable. One prominent example from recent times is the resolution of the sensitivity conjecture in discrete mathematics/theoretical computer science.

It is sometimes the case that a conjecture is considered important not just because it has been open for a long time, but instead because experts believe that a resolution to the conjecture will use new methods or techniques that will prove fruitful in solving other related problems. So, while it's great that you've managed to settle an open problem in your field, moreover one that has been publicized by an expert in the area, this alone may not be enough to have it published at a top journal in your field when your solution is elementary.

However, that does not mean it is not publishable anywhere. It would be best if you can contact a senior researcher in this field, say in your department, who can evaluate your work and suggest which journals have a high probability of accepting your submission.