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Is this question acceptable?: How do I fix someone's published error?

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  1.  
    • CommentAuthorgrp
    • CommentTimeJul 8th 2010
     
    I think this question is appropriate, but would like help on the wording so as to reap
    optimal or near-optimal community benefit. Also, there may be other issues in
    raising the question that should be considered here first.

    "Paper A is in the literature, and has been for more than a decade.
    An error is discovered in paper A and is substantial in that many
    details are affected, although certain fundamental properties
    claimed by the theorems are not. (As a poor analogue, it would be
    like showing that certain solutions to the Navier-Stokes equations
    had different local properties than what were claimed, but that the
    global properties were not affected. The error is not of the same caliber
    as Russell's correction of Frege's work in logic.)
    The author is notified, who kindly acknowledges the error in private.

    Now what?

    Should the remaining action lie fully on the author, or
    should the discoverer do more, such as contact the journal,
    or publish his own correction to paper? How long should one
    wait before suitable action is taken? And what would be
    suitable action if not done by the author? "

    I can make it a question with more focus, but I believe the
    latter questions help in eliciting answers with more focus.

    I welcome constructive suggestions on this.

    Gerhard "Ask Me About System Design" Paseman, 2010.07.08
  2.  

    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.

  3.  
    Pete, regarding your last point, you may find the following interesting:
    http://arxiv.org/abs/0709.1291
    The original author subsequently published an official erratum.
  4.  

    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.

  5.  
    I have seen this sort of thing occur several times. My experience is that 9 times out of 10 the situation is nothing like "the main result is wrong" but rather more like "the main result is right but the proof is a bit wrong but can be fixed but the fix isn't immediately obvious to everyone". More importantly, my experience is that the importance of this discovery is sometimes evaluated rather differently by the author (who might think that this is just a technical issue and it doesn't really matter) and the discoverer of the slip (who might have spent hours of their life trying to understand the incorrect argument and now feels either proud to have found a non-trivial slip in the paper, or annoyed at the author for making the slip).

    True story: In my life I have found *two* slips in two papers by two (distinct) people who are currently faculty at Harvard. Both times I notified the author by email, got an acknowledgement that there was a problem, and then, about a week later, got a big email containing a fix. Both times the fix would be 1/2 to 1 full journal page if expanded out. Both times the main theorem of the paper is correct but the proof is incomplete. Neither time was a correction forthcoming. As far as I know the emails to me are, in both occasions, the unique reference to the fix. But this doesn't bother me at all. These are technical oversights made by people who are very clever and whose basic ideas are sufficiently robust that all the main arguments are still going to be fine. If I had broken the main theorem I would expect the author to issue a retraction, but if it's just "technical errors" that can be fixed, then why do anything? The papers will be outdated by future work of the authors, in both cases, in a few years (in fact this has already happened with one of them) and who cares about these small technical points?
    • CommentAuthorHarry Gindi
    • CommentTimeJul 9th 2010 edited
     

    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 =)!

  7.  
    @Harry: the "younger me" absolutely agrees with you. But the 41-year-old me (i.e. me now) is less convinced. Let's take the particular case of paper X, which contains a proof of theorem Y which is incomplete because there is a non-trivial slip in Lemma Z, and in fact Lemma Z is false (I have a counterexample), but a messier slightly different statement Z' is true and the messier slightly different statement will suffice because in the two times in the paper that Lemma Z is invoked, if we modify the argument slightly then we can use Z' instead. If Theorem Y was a proof of Fermat's Last Theorem then this should be announced to the world. But if Theorem Y is an important-at-the-time but rather technical statement about modern number theory which has now been completely dwarfed by Theorem Y' which itself has a much more natural, conceptual and clear proof, then the author of the paper proving Theorem Y might well figure that it's not worth the bother of trying to fix it up because with age comes other time-consuming things like teaching and kids and working on your next paper, all of which somehow dwarf the idea of making some technical fix to some paper that you suspect no-one will ever read. [in fact the first sentence in the email reply I got from one of the authors in question was "whatever are you doing reading that old paper?"]
    • CommentAuthorNmbr
    • CommentTimeJul 9th 2010 edited
     

    http://arxiv.org/abs/0911.2441 could be an interesting instance.

  9.  
    @Nmbr: this is exactly an instance of what should _not_ happen. The paper you link to makes a massive deal out of a *typo* in a paper by Gun Murty and Rath. GMR prove a transcendence result but mis-state their result---they state that a certain number is always transcendental but in a few cases it's trivially 0 because they forgot to rule them out in the statement of the theorem. Their proof is fine; the statement of the theorem needs a tiny modification and the paper is fine. GMR fixed the slip, plus six other typos, in a ten-line corrigendum published in the same journal as the article. The ArXiv post you link to makes a mountain out of a molehill, in my opinion, and I don't think it possibly achieves anything at all other than making the original authors very angry and making a whole bunch of onlookers like myself shake their heads in disbelief.
  10.  

    @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.

    • CommentAuthorgrp
    • CommentTimeJul 9th 2010
     
    I appreciate the points that Pete L. Clark and others have brought up: the severity of the error does
    dictate the response required, as does the collective knowledge of the error.

    I will post a second version of the question in this forum in a few hours, to include a taxonomy of types
    of error and other considerations that might determine a response; if this version turns out to be potentially
    more productive in the opinion of this forum, then I will post it before another 24 hours has passed, otherwise
    I will go with a version similar to the one starting this discussion. In the meantime, I encourage more
    vetting of the original question in case there is some issue that I have overlooked.

    Gerhard "Ask Me About System Design" Paseman, 2010.07.09
    • CommentAuthorBCnrd
    • CommentTimeJul 9th 2010 edited
     
    Harry, I have an example even better than Kevin's. There is someone very well-known who wrote a paper several years ago on an important topic Y in number theory, and I think the paper is not going to be outdated for quite some time (since in a sense it develops the "right" way to do certain things). At a crucial place in the proof of one of their theorems is a technical gap which I only saw how to justify by using something subtle and not widely known from EGA. I wrote an email to the author with an argument to justify this point (it was more or less obvious what had to be done if one were familiar with that part of EGA, but was kind of long when written out), and asked if there's a simpler way.

    After some back and forth, the author said that probably one needed to do something like that (he hadn't noticed the issue previously, but upon being told knew exactly what had to be done), and I suggested putting something about it -- perhaps even just a reference to the relevant EGA result, if not the argument -- into the paper, since at the time *it hadn't been published yet*. But the author declined, on the grounds that the only people who would check that point would be the same ones who knew the relevant fact from EGA. (Probably he's right.) I happened to disagree with the author about not at least pointing readers to the required fact, but everyone has their own writing style. (It is not realistic to expect others to write in the way one thinks is best.)

    Just as the Internet makes it easy to post corrections, it has another advantage: anyone who is confused about something can email the author just as Kevin and I did, or more typically email a friend with relevant expertise. (It is important to not be in isolation.) In the case of the above example, perhaps the author will simply forward my old email. :)
  13.  

    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!

  14.  

    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.

    • CommentAuthorgrp
    • CommentTimeJul 10th 2010
     
    Here is version 2.

    -----BEGIN-----
    How do I fix someone's published error?


    Paper A is in the literature, and has been for more than a decade.
    An error is discovered in paper A and is substantial in that many
    details are affected,
    although certain fundamental properties claimed by the theorems are
    not. (As a poor analogue, it would be like showing that
    certain solutions to the Navier-Stokes equations had different
    local properties than what were claimed, but that the
    global properties were not affected. The error is not of the same caliber
    as Russell's correction of Frege's work in logic.)
    The author is notified, who kindly acknowledges the error.

    Now what?

    Should the remaining action lie fully on the author, or
    should the discoverer do more, such as contact the journal,
    or publish his own correction to paper? How long should one
    wait before suitable action is taken? And what would be
    suitable action if not done by the author?

    Based on remarks from those who previewed this question
    on meta.mathoverflow, I propose the following

    Taxonomy: There are various kinds of error
    that could be considered.

    typographical - An error where a change of a character or a
    word would render the portion of the paper correct. In some
    cases, the context will provide enough redundancy that the
    error can be easily fixed by the reader. Addressing these
    errors by errata lists and other means have their importance,
    but handling those properly is meant for another question.

    slip - (This version is slightly different from the
    source; cf the discussion on meta for the source
    http://tea.mathoverflow.net/discussion/493/how-do-i-fix-someones-published-error/ )

    This is an error in a proof which may be corrected, although
    not obviously so. In a slip, the claimed main theorem is either
    true or can be rescued with little cost. In my opinion, the degree
    of response is proportional to the amount of effort needed to fix it
    (which is often minor),
    but there may be slips major enough to warrant the questions above.

    miscalculation - Often a sign or quantity error. In some cases
    the results are minor, and lead to better or worse results
    depending on the calculation. I've included some miscalculations
    in some of my work to see if anyone would catch them. I've
    also prepared a response which shows the right calculation and
    still supports the main claims of the work.
    (The case that inspired this
    question falls into the category of a miscalculation that
    invalidates a proposition and several results following from
    the proposition. However, as I alluded to above in the
    Navier-Stokes analogy, the corrected
    results have the same character as the erroneous results.
    I would walk on a bridge that was built using the general
    characteristics of the results, and not walk on a bridge that needed
    the specific results.)

    oversight or omission - This is stating a fact as true without
    sufficient folklore to back up that fact. In some cases the
    author doesn't include the backup to ease the paper and because
    the author thinks the audience can provide it. More seriously,
    the omission occurs because the author thought the fact was
    true and that there was an easy proof, when actually the fact
    may or may not be a fact and the author actually had a faulty
    argument for thinking it true.

    major blunder - This is claiming a result which is true,
    and turns out not to be true in a socially accepted proof
    system. Proofs of Euclid's fifth postulate from the other
    four fall into this type.

    The above taxonomy is suggested to help determine the type
    of response to be made by the discoverer. Also, degree of
    severity is probably not capable of objective measure, but that
    doesn't stop one from trying. However, there are two
    other considerations:

    - Degree to which other theorems (even from other papers)
    depend on the error in the result.

    - Degree to which the error is known in the community.

    In my specific case, I do not to what degree these other
    factors occur. If someone thinks they know what area of
    mathematics my case lies (and are sufficiently experienced
    in the area), and they are willing to keep
    information confidential, I am willing to provide more
    detail in private. Otherwise, in your responses, I ask that no
    confidentiality be broken, and that no names be used
    unless to cite instances that are already well-enough
    known that revealing them here will do no harm. Also,
    please include some idea of the three factors listed
    above (error type, impact on other results, community awareness),
    as well as other contributing factors.

    This feels like a community-wiki question. Please, one
    response/case per answer. And do no harm.
    ----- END -----

    If things go well, I will post this version in about 12 hours from this posting.
    Again, constructive criticism is welcome.

    Gerhard "Ask Me About System Design" Paseman, 2010.07.10
    • CommentAuthorWillieWong
    • CommentTimeJul 10th 2010
     
    I also feel this question is appropriate. At least as career guidance for young researchers (a friend of mine is in a bit of a situation similar to this...)

    For wording, perhaps the parenthetical comment about the nature of your particular case should come after the entire taxonomy is listed, not interjected between miscalculation and oversight.

    Also, you should probably also clarify miscalculation: in my friend's case, the specific error he found is a miscalculation (a sign error), but the cumulative effect is halfway to a major blunder: a slightly weakened theorem is true, but cannot possibly be proved using the methods introduced by the author.
    • CommentAuthorgrp
    • CommentTimeJul 10th 2010
     
    Thanks to all for the input. Final version has been posted.

    Gerhard "Ask Me About System Design" Paseman, 2010.07.10
    • CommentAuthorgrp
    • CommentTimeJul 13th 2010
     
    I just figuratively opened my big mouth and suggested in a comment to an answer that people use MathOverflow to determine errata in other's work. What is MathOverflow policy on this kind of question? Can/should people use MathOverflow to suggest (promote) errors in published work?

    Gerhard "My mouth is a size 10" Paseman, 2010.07.13
  19.  
    @grp : I think that would be a terrible idea. While it is fine to ask specific questions about papers, suggesting errors in published work on MO would not seem to fit what it is about. Plus, it doesn't seem like a very professional or polite venue for this. I can just imagine anonymous slurs on papers cropping up...
  20.  
    I agree with Andy!

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