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I have seen question on here regarding a citation error in a paper here: Finding a mistake in a published paper, but the nature of this problem is very different.

Basically, I came across an error in a paper (call this error 2).

I have previously contacted the author before regarding a different problem (call this error 1, say) in this paper, and I got no response. (That was what I still believe to be an unproven proposition, and is actually also related to this problem.)

The reason I decided to ask here this time is the following:

  1. I am highly confident about error 2.

  2. Its correctness has a direct impact on my current research.

  3. The mistake cannot be easily fixed. (At least it appears to me, for the time being). I have spent months on a related problem before revisiting this paper and realised that I have tried this same technique in problem, which did not work in my problem, which led me to check why it worked in his paper - and it turned out, it did not.

  4. The result was probably the first/the only result of its kind in the literature and the paper is fairly important with 150+ citations.

What should I do here? I have previously contacted the author and I have no reason to believe he would respond this time. I want it to be correct/easily patched because of reason 2. This paper was published in 1997 so it has been a while....

EDIT: Precisely for reason 2, I would much prefer some way of getting the author to respond.

EDIT: I had a discussion with my supervisor. He immediately agreed with me it was a mistake. The thing is when we tried to use a similar technique for a different problem, we fell down the same trap about 10 times. At the moment, we have no fix and the mistake is serious enough that it takes away a lot of credit from the paper.

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If it is a substantial correction of an important paper (that you can also prove / clearly show), you may just want to write an answer paper yourself. This paper would start off by summarizing the core message of the original paper (plus reference, of course), then you would explain what is wrong, and conclude with what the important implications of the error are. –  xLeitix Apr 4 at 11:42
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It also seems to me like you assume that papers work like books, where you contact the author or editor about any errors, and they will fix them in the next edition. Research papers are usually written once and never updated. –  xLeitix Apr 4 at 11:43
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Write up your own paper. Seriously. –  Mad Jack Apr 4 at 14:10
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Can you patch the problem yourself ? –  Suresh Apr 4 at 16:34
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I would say: 1. clearly show the error(s) 2. fix the error(s) -if you can- 3. Upload it to Arxiv titled: "On the X of Y". where X is the error name and Y is the problem. Then email him/her a link of the paper. –  seteropere Apr 4 at 19:33

8 Answers 8

up vote 30 down vote accepted

The main answer to your question is easy: talk to your advisor.

I find it a little curious that you have not done this already. As a graduate student, you read a very famous paper (in mathematics, more than 150 citations is a very large number) that was written a while ago, and at the first sign of trouble you contacted the author of the paper. That is already a little strange: although both are possible, the probability that you, a relatively young graduate student, have misunderstood something in the paper (or are applying standards that are different from those of the field you will be working in, or some other similar issue related to the fact that you probably do not yet have expert level knowledge and experience in this field) is higher than that the author has made a serious mistake. Writing to someone that you don't know at all and who is much more senior than yourself and pointing out a mistake is not without risk: the risk is that you will be wrong and they will dismiss you in the future as a less than serious person.

Your advisor is there exactly for such things: she is the person who is helping you transition from a neophyte to a journeyman to an expert, and she needs to see your mistakes and flawed reasoning in order to do this properly. Some outside expert really does not: they can wait to see the finished product that you become. Moreover, you are presumably reading the paper because your advisor wants you to, perhaps even because she directly told you to read it. Therefore a mistake in the paper is your advisor's problem as well as yours. Why are you holding that information back from her? You shouldn't.

Having said that, I feel like the OP is getting a fair amount of advice that would be more appropriate in other fields than mathematics. Especially:

In mathematics it is very difficult to write a paper whose sole or even primary purpose is to point out a mistake (even if it includes a correction) in someone else's work.

This is a cultural reality of the field; it is certainly not entirely positive. In many other academic fields, one can "score points" by pointing out others' mistakes, and in some fields this is one of the best ways to score points. Mathematics is not like this: if you can get such a paper published it will "take points away" from the author and give you a certain amount of notoriety, but if this is for instance your first published paper then many people will look at you strangely, almost as if they expect you to make further trouble. (Again, I'm not endorsing this cultural practice; I'm just describing it.)

Similarly, I would say that contacting the editor of the journal in question is maybe step 10 of a procedure that is mostly designed to terminate after one of the first 9 steps. You should do this only after you have exhausted every other possible avenue.

In mathematics -- very much unlike in some other fields -- it is prohibitively unlikely that an editor will publish any "commentary/correction/erratum" by you unless she believes that you are mathematically correct in the point you're making, and convincing someone with standing in the field like a journal editor that you are mathematically correct is largely what you're trying to do anyway.

Finally, while I barely know what a white paper is and to the extent that I do I'm not sure it's the appropriate terminology here -- in content I do agree with @eykanal's suggestion: it will certainly help your advisor if along with communicating the surprising news that Famous Paper X is wrong, you can supply a written version of your arguments. This can be hard to do: explaining why a difficult argument is subtly wrong is one of the sternest expository challenges in mathematics that I can think of. It takes a lot to go from "I don't understand the argument and find it rather unclear" to "I am convinced that it is wrong." By the way, in writing to an author it is a good strategy to err on the side of the former quotation.

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Very well put. I'd reiterate the point(s) that a neophyte's not being able to follow an argument is not good evidence that the argument is wrong, or even that there's a gap, and that a neophyte should consider the very large possibility that by whatever "expert standards" the paper is fine. Or has known reparable errors. Or pointlessly mis-states things which are easily corrected by experts. So one should talk to an in-house, sympathetic expert. –  paul garrett Apr 4 at 19:46
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what you said is really good to know. I have updated the question to include my discussion with my supervisor. The mistake is a blunt 1st year analysis error but there is no easy fix to make it correct. I am a little concerned about what you said after 'mathematics is not like this'. And oh when I contacted the author the first time round, I already had a discussion with my supervisor and he could not see why something the author claimed was true. While I had my doubts, this time I was pretty confident. (else I would not have written here) –  Lost1 Apr 4 at 20:56
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Personally, I'd run it by at least three experienced practitioners before assuming that there is an error. Occam's razor suggests that if you're the only one to notice it, the mistake is probably (but not necessarily) yours; repeating the test with others will help check that (a) it's real, (b) it's significant, and (c) it isn't just a printing problem but actually carries through remainder of the paper. AFTER making darned sure of that, by all means bring it forward. –  keshlam Apr 5 at 1:08
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@NickStauner The thing is that we are speaking, almost surely, about a math paper, and math is different.. There are no shades of grey, and no place for interpretation. A proof is either true, or wrong. And if a proof in a paper is wrong, it is extremely unlikely that 100+ people which are doing research in that area read it and don't find the mistake... Not to mention that math research is like building a house of cards, most of the times if something goes wrong, everything above falls down fast... 150 citations means 100+ pieces of research build over it, chances are not that great ... –  Nick S Apr 5 at 6:25
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that so much research was build over shady foundations and nothing went wrong. Yes, it is not impossible. But don't forget that math research is different than all the other areas, which also means that the rules are different... Last but not least, because math is different in this way, if something is wrong, you can easily prove it wrong. Again, there is no shade of grey, and no interpretation.Which means that the moment one goes confrontational, one of the two parties is made a fool. So a little caution doesn't hurt, and one should make first sure he doesn't end the fool before starting. –  Nick S Apr 5 at 6:35

Ask someone else - your age listed in your profile suggests that you're a grad student. Have you talked to your supervisor about this? Even better, do you know someone in your own department that has collaborated with the paper's author?

Put yourself in the author's shoes. He's probably bombarded with emails all the time from grad students he's never heard of, so unless you've collaborated before then he may not even read your email. An email from your supervisor or one of the author's collaborators is much more likely to get serious attention.

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I will talk to my supervisor today. I actually thought about asking this after this the meeting. Your suggestion is helpful. I am not sure if anyone in my department collaborated with him before but there might be someone who knows him. –  Lost1 Apr 4 at 11:56
    
After talking to your supervisor, you might want to do some research on the authors. It's common in some fields for the last author to have supervised the first author, who may have moved on. It's perfectly possible that the first/corresponding author's email address as listed, or even as looked up online still exists but isn't used any more. Some fields have statements about which authors did what in the paper. It may then be worth contacting the supervising author if there is one. You may get further with them anyway - if it's 1 of many papers for them, the top paper for the lead author. –  Chris H Apr 4 at 15:44

I would do the following:

  1. Write up a rigorous white paper demonstrating the issue. This should be your first step, as putting the idea to paper will help you think of aspects you may not have thought of yet. If you can successfully convince yourself in a written paper that this issue is valid, then...
  2. Present the white paper to your advisor. This has numerous benefits:

    • Your advisor will critique your writing, which is always a good thing; you will become a better scientific writer.
    • Your advisor can provide specific feedback on specific aspects of your argument by simply referencing what you wrote and providing counterexamples. This will make the process of convincing him that there is a problem much easier.

    If you can sucessfully convince your advisor that the problem exists, then it's time for..

  3. Work with your advisor to reach out to the author. Working with your advisor will significantly increase your chances of success. You may also be able to progress to
  4. Write up your findings in a letter or article of your own, depending on the nature of the issue.

Do note that you state that this paper has been reviewed and cited many times. While it is possible that you have found something everyone else has missed, your ideas will need to be iron-clad before anyone will even listen to you. I would spend the most time right now making sure you haven't made a mistake before reaching out to the author.

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Related: What is a white paper? (i.e., don't assume everyone knows this). –  episanty Apr 4 at 17:48

I agree with Moriarty entirely. The first step is to get independent confirmation that there is an error.

The second is to judge its severity and how it impacts on the conclusions of the paper.

The third is to contact the authors directly and perhaps ask them to list or fix the errata on their homepage and on any pre-prints.

Mainly my answer is to introduce the fourth option. Many journals allow for publishing reviews, comments or corrections on papers that have already been published. Here's an example of this in a reputable computer science journal (TKDE). Particularly if the paper is highly cited and the error underlines grave concerns about its contributions, this option is recommendable.

If the journal does not allow corrections, you may consider writing your own independent "correction" paper instead (as others have suggested), but this way, you may be expected to present new results, not just pointing out errors.


But again, like Moriarty, I would highly recommend that you get the advice of a more experienced researcher, in particular before engaging in the fourth or fifth option.

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If you can give all the relevant details in a reasonably concise way, then it may be appropriate to ask a question on mathoverflow.net. I would strongly recommend that:

  • You prepare your question very carefully, and review and revise it several times before posting to ensure that it is as clear and complete as possible and correct in all details.
  • You phrase your question as "I do not see how this can be correct, please explain what I am missing" (even if you feel very sure that you are not missing anything).

If your problem is in an area that is well covered by mathoverflow, then this should be effective. Either someone will explain what you are missing, or the relevant experts will become aware that you have uncovered a genuine problem.

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I think this could be a very efficient way to resolve the issue. Let me say though I that I think the OP and/or his advisor should at least try to write to the author first. The OP mentions that he wrote to the author once before about an "unproved proposition" in the same paper. To me that sounds very different from a serious error. I think the author deserves to hear about the mistake first. If s/he is unresponsive, than MO sounds good. –  Pete L. Clark Apr 7 at 17:44

Let me share my personal experience in a vaguely similar situation: Back in 2007 and within a couple of months of publication I spotted a huge mistake in a paper published in a journal that used to be A class but is more like B class these days. I wrote a proof of the error, showed how to correct it, and sent it to the journal. It took over one year of back and forth between the editor and I to get him to admit he had published a profoundly incorrect paper and to publish my "Comment": but I'll say that I probably got lucky that he admitted his error, got lucky that he cared to correct it, got lucky that he read my correspondence, etc.. If my experience is any indication, it will be very difficult to get across to the editor(s). At some point, about 6 months into the exchange, when it was clear that the editor was assuming I was in the wrong (he never read the math bits), I wrote to another editor and asked him if he thought I could damage my reputation by insisting so much, and he told me not to worry and go ahead on the quest for truth (but there was nothing he could do to help). The bottom line is you will hurt several people's pride and could make some enemies. I personally couldn't care less, but I'm atypical. And if you looked at my career, you'd probably think twice about upsetting the editors of an influential journal. Whatever you do, all the best!

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My advice is pretty much the same as everyone else's: talk to your advisor, go over the suspected problem point with him; if there is no resolution, reach out to others in the department (your advisor should do this).

Having said this, I'd like to relate a few incidents from my own experience. As a graduate student, I independently discovered a result in number theory that did not appear in the literature. I was unaware of the significance of the result, but it came up in discussion with my advisor. He informed me that Professor X had found this result, but had never published it, and that I should not publish it, thereby "scooping" the (world-famous) expert.

While working with my second advisor, in a different area, I read a paper by a major player in that area who had developed a widely used technique. I mantioned to my advisor that there was a point in the proof of that technique that I didn't understand and he told me that no one understood the proof, but all assumed it worked.

Many years later, I now work in a different area. But while I was getting started in it I ran across a theorem in a book by a well-known expert in the field. What it said contradicted other things I had read. Not fully trusting myself, I reached out to the author who acknowledged that what he had written was not correct. He was very grateful for the correction and saved it against the advent of a second edition of his book.

Finally, I wrote a paper which contained an error, an error I should not have made because I was familiar with a counterexample to the statement I made. No referee caught the mistake, and only one person ever wrote to me about it, and I am very grateful to that person. Everyone reacts to these things differently, but I did not take offense at the correction. Granted this situation is a bit different than yours, because the correction came from a well-known source, and not from a graduate student. I would like to think I would have been equally accepting if the correction came from a student. I was embarrassed to be corrected by an expert, whereas I might have been peeved to be corrected by a student. However, were it you who wrote to me, you would never have known my reaction. I would have thanked you for pointing out the error, and perhaps have apologized for making it. But that's just me, and I'm far from well-known in the field. So, I have no idea of what my more famous colleagues have to deal with on a daily basis. The paper in question has never been corrected to my knowledge.

As I said, everyone reacts differently in these cases. Work with your advisor. The most important thing for you is to determine if there is indeed an error in the paper, and, if not, to understand why the paper is correct so that you can move forward with a correct grasp of what the paper established.

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Chris, you are describing a real dark side of our profession. The fact that you can, if you are sufficiently famous or connected, somehow "get credit" for merely announcing the proof of a certain result (or sometimes even a program for proving a certain result) has always been maddening to me. When the manuscript appears a year or more after the original announcement, I really worry about the ethics involved, and I think this is bad for the profession. –  Pete L. Clark Apr 7 at 17:49
    
Pete, as far as I know, the result never saw the light of day. I'm not even sure it passed into the folklore, but I've been out of that loop for some time. What galled me most is that it is not uncommon to see things like "this result was established independently by X and Y." A citation like that could have had consequences for my career and confidence. What was also disconcerting was that my advisor knew the expert, and even invited him to our school for a colloquium. I got to meet him. He was a genuinely nice person. A little mediation on my advisor's part could have helped. Oh well. –  Chris Leary Apr 7 at 21:00
    
Since I happen to be a number theorist, I am curious about the result. I would understand if you didn't want to disclose it publicly, but if you don't mind... –  Pete L. Clark Apr 7 at 22:46
    
Pete, This is going back almost 40 years. I don't remember what it was with any specificity. I was working on trying to find minimal models of Hilbert modular surfaces at the time. I believe I still have the notes on it. Next time I get to my office, April 23-24, I'll try to remember to look it up (I'm on sabbatical this semester). I know how to get in touch with you. –  Chris Leary Apr 8 at 0:12

The answer may be field-dependent, but in theoretical physics it is: write your paper. If the error is non-trivial, showing why something not works (or an counterexample) may be valuable. The same thing if the error is relatively simple, but most people are not aware of it.

Sometimes a critical flaw in one paper gives raise to a new field - see How the No-Cloning Theorem Got its Name by Asher Peres (or for a longer story, How the Hippies Saved Physics by David Kaiser).

An erroneous paper (with an error being non-trivial at this time) resulted in the non-cloning theorem, and later - quantum cryptography, quantum information etc. The error (assumption that a machine could copy any quantum state) could be addressed by a few lines of an elementary proof there no such machine could exist.

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@PeteL.Clark No. So here is a recommendation to write a paper pointing the error. –  Piotr Migdal Apr 4 at 23:22
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@PeteL.Clark: There are plenty of statistical publications that point out others' errors. Have you never seen such an article in mathematics? Here's one in mathematical statistics, in case you haven't. Close enough, no? (It's a good read BTW, not just a handy example.) Another precaution: encouraging someone early in his/her career to hand off major project responsibilities to others without strong justification can be just as detrimental to career advancement as taking chances by critiquing others. What if he's got a genuinely good critique? –  Nick Stauner Apr 5 at 6:00
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@Nick Stauner: To answer your question: no, I do not regard the paper you cite as a mathematical paper. I just checked and it is not archived in MathReviews/MathSciNet, the online repository of all math papers. Statistics is a different field, very close to and sometimes overlapping with mathematics, but with different cultural practices, so the answer to your question "Close enough, no?" seems to be "No". –  Pete L. Clark Apr 5 at 16:49
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To answer your question more directly: no, I have never seen a published article in a high-quality mathematical journal whose sole goal is to point out an error in someone else's work. Very occasionally I have seen preprints uploaded to the arxiv doing so: the implication here is certainly that the author of the preprint tried and exhausted more conventional avenues first. So you should be aware that you are recommending something that I (a 2003 math PhD) have really never seen done in my field. –  Pete L. Clark Apr 5 at 16:59
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@Nick: I agree by the way that the paper you linked is unusually interesting. It is written by some eminent people (including mathematicians, yes) for a rather noble purpose: more like public service / debunking than any attempt to garner "academic credit" in the conventional sense. I would be interested to hear from a statistician whether this is in any way a typical statistics paper. I would guess that it is not. –  Pete L. Clark Apr 5 at 22:18

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