# Is it okay to include a simplified and easy version of a result already proved?

I am preparing to write an article. For that, I got an easier proof of the already published result. My result is very simple to prove. Is it ethical to include this result in my article after citing the other author's work that we are improving their result? Kindly help. Thanks a lot.

• I find your question unclear. Do you have a simpler proof of the full theorem or of some special case? (You write "easy version of a result".) Is your new proof a main result of the article that you are preparing, or is this an application of another new result, a proof of a result that you need in the article, or something else? Jun 25, 2018 at 11:32
• It is extremely common, and has been so for over a hundred years. It isn't clear why you think that it has an ethical dimension to it. Jun 25, 2018 at 12:18
• It's fine to do this, but don't say in the paper that you're improving the result if you're only improving the proof.
– user37208
Jun 25, 2018 at 14:46

Yes.

New proofs are always good and of scientific value, and may be of significant use and interest in their own right. In some cases they are even worthy of a paper of their own. As an example, just recently on MathOverflow I saw Zhi-Wei sun mention that a result of his currently has 6 proofs from 6 different papers and sets of authors (including his own and himself).

• I may be wrong on this, but it would seem the ability to prove the same thing from different approaches is the easiest way to bridge the gaps between multiple fields. I've heard of many problems that are solved by saying "well if we convert this problem into that problem, and solve it in that space, and convert it back, we can solve our original problem" - and things like this are the building blocks for beginning those transitions. Again, I'm not a mathematician, but it seems reasonable to me! Jun 25, 2018 at 14:36

It's better than ok, it's usually a Good Thing to do, since:

1. It helps readers understand what the more complex result means, or what its significance is, by considering a simpler-to-perceive case.
2. The simpler result is often powerful enough to be used itself - even if not for the specific use the original prover of the complex result had in mind.
3. The simpler result can sometimes be established with a different, simpler proof, which may be of independent interest. Alternatively, if the proof is similar, the simpler result's proof helps understand the more complicated proof of the more complex result.
4. Simpler results are often simpler to keep in mind.

Of course there's the question of your submission page limit - devoting space to a simpler results means condensing or removing other parts of the text, but that's something to decide based on the specifics of your article.

I agree with the two previous answers that publishing your simplified proof is good. Simplified proofs often lead to improved results; some of my own papers began with the idea that I can simplify a known proof but then developed into applications of the simplification, yielding new results. You might want to check whether your simplified proof can be easily extended to yield more than the original result.