Should I point out a flaw in a paper, which will likely result in withdrawal and resubmission, before I start to write the review?

Let me suggest that you do a proper review and somewhere, it doesn't really matter where, note that part of this is already settled and needs at least a citation of prior work. Since the work is old it may just be an oversight on the part of the authors as you suggest yourself.

However, in mathematics, the reasoning behind a statement, the proof, is almost always more important than the final statement itself, especially if the proof is novel in any way. This is because proofs offer insight in to how to approach problems that simple statements do not.

The fact that an old result emerges simply as a corollary to a new result isn't especially surprising, actually. It is an interesting fact that might, in itself give some insight into problems related to the old result.

If all questions in mathematics could be answered by the same set of techniques, then it would be a pretty boring field.

And, as you say, Theorem A seems on the face of it to be independently valuable. Do your best job and don't neglect to point out problems and omissions along the way, as you normally would.


If I understand your question, you're saying that Corollary B has already been proved half a century ago, but the authors are apparently unaware of it.

If that's the case, you should point it out now, before you start reviewing. As you point out, the authors will probably have a lot to rewrite, which could make swathes of your review irrelevant.

I would tell the editor the issue and suggest pointing it out to the authors (i.e. option 3), but also say that you can review the paper anyway if they prefer. You can potentially save a lot of time this way. If they say you should review regardless, you probably don't lose much time, either.


I think you take too much responsibility for other persons' (presumed) actions. I'd say write in your review what you know (that the problem was settled before) and what you think (namely that Theorem A merits publication in its own right). Be as comprehensive as you like; certainly you help the author and maybe editor by providing some more detail, this mainly depends on the time you can spend on this.

It is the job of the editor, not yours, to decide about rejection of the paper. Don't base your behaviour on the assumption that the editor might do something, in their own responsibility, that you wouldn't agree with. Neither base your behaviour on assumptions of what the author will do with their own work if you write this-or-that and whether this may or may not be good in your opinion. It is up to them to decide that. So give them open and proper information on the standard way (i.e., in your review) and leave their job to them. Note by the way that if the editor decides to reject, there are many other journals, and maybe the author will in their next attempt to submit just cite the original paper and state clearly what is original about their own approach. As an expert in the field, you may even be asked to review that update.