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38

I only hope that computer-aided proof checking saves mathematics before it collapses under the weight of decades of irresponsible publishing. Of all disciplines, peer review in mathematics should serve to guarantee nearly absolute confidence in the validity of published results. Many subjects have grown so complex that one can't reasonably expect new ...


20

I regard it as part of my job as a referee. But the amount of time I spend checking proofs really depends on whether the point of the paper is to prove something I already believed but didn't know how to prove (in which case I spend a lot of time) or to tell me something new, in which case I might spend very little time on the proofs and rather focus on ...


18

I agree with everyone else -- you should disclose, and I see no problem with this. Let me raise a subtler issue: A few years ago, I had the experience of being repeatedly sent a paper where the result was correct but, in my opinion, not close to significant enough to appear in the journals where the authors were sending it. I sent a report to this effect ...


11

I agree with David: I think that my job as a referee consists mainly in checking that the proofs are correct. However, checking that the proof is correct can in practice not be done by line-by-line checking. Referees are not computers, nor are the writers of the articles. Rather I have a kind of critical, "falsificationist" approach. I try to see what are ...


11

I more or less agree with Sheikraisinrollbank, but for the sake of argument... I've always found it slightly hard to fully separate "Is this paper interesting" from "Is this paper correct". It seems like mathematics (especially towards the pure end) is full of interesting, plausible "facts" we don't have proofs of. Isn't part of the point of maths to find ...


11

I have done this as a reviewer, and have had it done to me as an author. I have no problem with it. I do think you should disclose to the editor that you've reviewed the paper before. (This can create the awkward situation of having to say "I reviewed this for journal A, and didn't think the theorem was interesting enough, but it fits just fine in your ...


3

I am waiting for a time when high ranked journals will require besides mathematical proofs written for human also alternative proofs that can be checked by computers (written in special language like Coq or Mizar). In this case referee will not have the obligation to check the validity of the proofs (this will be done automatically at the submission stage) ...


2

If the author finds a mistake (or someone finds and tells to the author) s/he usually publishes a correction in the same journal. If the journal is reviewed by Mathscinet or Zbl, they usually review the correction as well, so you can find it. Papers posted on arxiv are usually corrected, before or after publication. Be sure that you read the latest posted ...


2

I've been in this situation with a paper that had significant problems and was submitted to a second journal without addressing any of the comments that I made in my first review. I explained this to the editor of the second journal and gave him a copy of the first report that I'd written.



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