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The title says it all. Suppose you are refereeing a paper where the author A makes strong statements about other papers by a different author B, like: the proof of Theorem 1 in paper [B] is wrong and we provide an alternate proof.

One possibility would be to diligently read the other paper, compare the results, and decide. This doubles (or triples) the refereeing effort, and puts the referee in a more difficult position, opposing both author B and the authority of the other journal and its referees, in case he decides to support A's claim. I am not sure this is the proper course of action, especially when the disputed result is not of such importance to deserve an exceptional attention.

Another possibility would be to ask the managing editor to involve (also) the other author B in the refereeing process, asking his opinion. The potential dangers in following this way are clear I think.

What do you do in such situations?

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    $\begingroup$ Why not simply ask the author to write in his paper specifically what is wrong with the proof in [B]? This would certainly make it better and easier for both the referee and the readers. $\endgroup$ – Andrei Smolensky Jul 17 '14 at 10:32
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    $\begingroup$ Good question. Does A carefully point out the error in B's proof? Is A's proof of B's theorem sufficiently different and interesting to warrant publication even if B's proof turns out to be correct or easy to repair? $\endgroup$ – alvarezpaiva Jul 17 '14 at 10:32
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    $\begingroup$ Point out the potentially troubling and unsupported statements and recommend their removal or weakening. If the author provides data supporting the alternate proof, good. No support behind B's proof being wrong? Don't say it. It would be like asserting Andrew Wiles' proof missed covering the exponent being the sixth Fermat prime. (We have only found five so far.) $\endgroup$ – The Masked Avenger Jul 17 '14 at 10:47
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    $\begingroup$ I think, as the comments indicate, this is a difficult question to answer in the abstract. What to do depends too much on the specific circumstances. It's worth noting that Voevodsky discusses a real example of this in his talk on proof checking: math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/… $\endgroup$ – Deane Yang Jul 17 '14 at 15:33
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    $\begingroup$ This is a delicate situation since: (a) people are easily offended, and especially so when something non-flattering about them appears in print; (b) a general policy where mistakes in published papers can never be pointed out is obviously silly. Regarding your second paragraph, I personally have always subscribed to the theory that responsibility for the correctness of a paper rests solely with the author, not the referee (or editor or anyone else). $\endgroup$ – Christian Remling Jul 17 '14 at 17:27

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