Who should the authors of a corrigendum be if I am correcting someone else's mistake?

Question

My project was based on a famous paper, which, unfortunately, contains a major mistake, discovered by me. Since I already spent a huge amount of time on this direction, I submitted my "correction result" and presented it as a new paper. I made this decision due my advisor's advices and this site.

However, the editors just made a decision that my paper is only publishable if I rewrite it as a concise corrigendum with less than 1500 words.

While I have no problem in serving the community by writing a corrigendum, I am a bit confused, because:

1. For a correction note, the authors are usually the original team (but not always).
2. For publication of comment or correction note made by others, the original authors are usually contacted by the note authors first (I have not done this).

Does the current situation sound normal?

Answer 1

Contact the original authors

Unless you have very good reasons for not doing so, I'd urge you to contact the original authors of the mistaken paper. If your work gets published then they will hear of it -- better that they hear of it from you first!

Assuming your work is correct, they are likely (if not certain) to be gracious. They might give you useful advice, or even publicize your work for you. (Here is an example of a mathematician calling attention to an error in their own paper, with credit to the person who found it.)

If it happens that your own work is incorrect, then they are likely to catch and point out the mistake.

Depending on the circumstances, the result might become known as the Them-You theorem, which would very likely be good for your career. Here is a prominent example, where the correction paper was published in the Annals of Mathematics! So don't sell your work short, and consider submitting to a different journal, especially if you contact the original authors and they are encouraging.

Answer 2

If you have a proof that the original paper has a serious flaw, such as using a counterexample to show that a stated theorem is actually false, and you also provide a correct theorem and its (correct) proof, then this feels to me like it is sufficient for a new paper, not just a correction. This seems (to me) to be especially true for an important paper. I'm not the one judging, of course, but it seems like grounds for a discussion with the editor.

Moreover, since you make an intellectual contribution to the field, you should get authorship status on whatever is published. The "normal" action may not be appropriate.

Another option is to withdraw the work from this publisher and submit it elsewhere. If your new proof is novel in some way, then I think you have both an argument to present to the current journal and grounds for publication elsewhere.

But, as with most things, novelty is an important consideration and the editors/reviewers may have decided that what you have lacks that element.

Answer 3

Without knowing the details and reading your paper, it is hard to tell. In any case, it is your paper with you as the author, even if it is called a correction.

Mathematics editors are notorious in asking for shorter versions. You need to decide whether you can comply with the editor's limit or not. If the theorem is famous, you will have made your mark. You should feel free to submit to another journal. You can also use the 1500 words to prove the theorem wrong and then publish elsewhere your version of the theorem.