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I agree that the question would be an entirely appropriate CW question: it is an important question on the practice of mathematics which is of interest to research mathematicians, many of whom find themselves in this situation and have no idea what to do.
I also think the wording is already pretty good. Maybe make more clear the level of generality of your question: do you want good advice in general or are you looking for an answer to a specific situation? If the latter, the more detail you can put in without coming close to identifying the specific paper and author would be helpful. For instance, do many other papers cite this paper? In such a way so as to invalidate subsequent results? Do the experts in the field know about the mistake? (In a previous situation of this kind, I found myself surprised by the extent to which some cognoscenti were absolutely unfooled, and conveyed this information to their colleagues and students but did not make any move towards public correction.)
Finally, and this is more by way of answer -- I have absolutely never seen a corrigendum/erratum to a math paper written by the person who found the mistake (when different from the author of the original paper). This is quite standard in other fields but it simply doesn't seem to be our way.
I think one point about mathematics is that it is both a much stronger statement to say that you think someone's paper is wrong, and one about which the author and finder are much less likely to disagree. There are lots of other fields (most humanities, for example) where reasonable people simply disagree over the interpretation of the facts, and it's considered normal and healthy to point out why you think other people are wrong. In mathematics, it's a different matter, since usually if you are pointing out other people are wrong, you will have come up with a sufficiently convincing argument to convince the author as well.
The whole Daniel Biss story is quite remarkable; I think it is a slightly different matter when the paper in question is in the Annals. The remarkable thing is that he is now a politician and advisor to the governor of Illinois.
Not for nothing, but I think that failure to correct small technical points is a pretty annoying problem. While established people in field X probably won't have a tough time making the fixes themselves, graduate (and undergraduate) students reading those papers in order to learn the material often will (or may trust that the author is right and try to fill in the details of a broken argument).
Of course filling in details and fixing errors "builds character", but it takes a very small amount of time to put a list of errata up on the arXiv (or your personal webpage). In the olden times, I'm sure it was much more difficult to do so (since I assume it required publishing a correction in a journal), but nowadays, I can't see it taking a significant amount of time at all (assuming one has come up with a correct proof, but it seems like most conscientious mathematicians would (try to?) come up with one of these as soon as they find out about an error anyhow).
This was really a response to Kevin, though. I hope it's not too impudent of me to voice my opinion in such senior company ;).
Edit: Upon rereading my post, it seems like I'm calling you old, Kevin (olden days, senior company). This was not my intention, but I figured I should indemnify myself now rather than explain myself later =)!
http://arxiv.org/abs/0911.2441 could be an interesting instance.
@Jonas: as a mathematician, when I make an assertion with a universal quantitifer, I am implicitly asking if my listeners know any counterexamples. :)
I do not regard the arxiv paper by Mnev as a counterexample. Looking back at what I wrote, I should have been more clear: what I have not seen is a published erratum (presumably in the same journal; to do otherwise seems simply strange) by someone other than the original author. In a way the Mnev/Biss incident is a close to extreme case which serves to reinforce my point: mathematician A publishes a paper claiming a fantastic result in the top journal in our subject. Mathematician B discovers an error in A's paper. Over a period of years, B does everything he can to get the word out, eventually putting an "A's paper is wrong" preprint on the arxiv. Of course "everything he can" does NOT include having the leading journal publish B's erratum, so B has to wait until A writes up his own erratum (essentially, "Yes, I admit that B is right and I can't fix it"), which takes several more years! I think that a sociologist studying our tribe would find this weird -- why can't the journal simply publish B's erratum to A's paper?
Anyway, as the other comments indicate, this is a delicate issue. Note that no one is weighing in on the appropriateness of the question -- we're already trying to answer it. It seems to me that GRP should go ahead and ask the question on MO itself.
Thanks for the examples. I guess it's just that I've been reading through some things recently that make Lang's Algebra look like he did a pretty thorough job proofreading =D!
I've been reading this thread with interest, since I've had some experience with this sort of thing.
Years ago, when I was in my first postdoc, I came across a published paper which claimed that there was an error in one of my earlier papers. As it turned out, the problem was that the authors of the paper had not properly understood something. I wished then that they had gotten in touch with me before publishing their paper so that we could have come to some agreement. I wrote them a letter (or email, I forgot) explaining the situation. They never replied, nor published an erratum. I found this behaviour in very poor taste. After all, they were established researchers and I a lowly postdoc and since in my field (hep-th and related areas) people are perhaps not as critical as they should be, relying less on the content than on the authors of the paper, and their claim could have hurt me. (For all I know it has!) The lesson I derived from this incident is to try, by all means, to contact the authors of paper in which you think you've found a mistake.
I am presently at the other end of a similar situation. An eprint appeared recently which contradicted (although not explicitly) a paper of mine with a postdoc. We worked through the eprint with great care and found a technical error which, when properly corrected, reconciles their work with ours. We sent our analysis to the authors and although the situation is still fluid, they've at least engaged with us. Of course, it's not clear what will happen in the end. Perhaps if time passes and the eprint is not corrected/withdrawn we might be forced to send a "Comments on..." to the arXiv, but I really would like to avoid this if at all possible.