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Suppose that I found a technical flaw in one of the papers coauthored by my previous advisor. This mistake will substantially change their major result, but their contribution will be still worthwhile after the correction. I am 90% sure about my findings. It is not a difference of ideologies or subjective beliefs, but a mistake in purely technical analysis.

My previous advisor is among the top-three worldwide in his narrow field, and that paper was published on the top journal. He was neither the corresponding nor the first author. The first and corresponding author was also his previous student. So here is my possible options (any other suggestions are also welcomed):

  1. Write a short paper and submit to the same journal. The journal welcomes this specific type of submissions. Best case is, if my previous advisor is happy to see his previous students are still contributing to this field, then I will get a top publication. Worst case is, since many of the referees are also his previous students, they could possibly defend our teacher and deny my submission, and I lost all the precious time redoing the analysis and writing the paper.

  2. Talk to my previous advisor. Since he keeps constant contact with the journal’s editor, he can definitely update that mistake, much faster than me; that way I will lose a worthy publication. He can also decide to ignore my findings or even try to prevent my findings to be published because they significantly challenge his result.

How can I choose between these, or is there a third way?


Update: I am preparing to send a friendly inquiry, politely say things like:

Dear XX, It was a pleasure to read your exciting work titled XXX. Could you do me a favor by explaining your analysis in ABC? I was hoping to do analysis XYZ such that your results can be refined and here are my preliminary findings. Do you feel this approach promising? Would you like to help? Thanks for sharing thoughts, again.

How do you feel about the tone? Shall I be more explicit?

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    Why not email the advisor, write him about what you found, and offer writing a paper on it together? Seems like a win-win. If he doesn't want to, or tries to defend his mistake, you proceed as in 1. – user68958 Mar 2 at 9:13
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    I’m struggling with the implication that you don’t trust your advisor (previous or not) enough to have a frank conversation about their results, without fear of your ideas being stolen. – JeffE Mar 2 at 9:31
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    Shouldn't the fact that the paper is by your previous supervisor mean that you contact him/her? – Alchimista Mar 2 at 14:29
  • @corey979 I am a little worry about the possibility of ideas being stolen... – High GPA Mar 2 at 22:53
  • @JeffE This is exactly what I was struggling with... – High GPA Mar 2 at 22:53
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If you trust your previous advisor, I would:

  1. Talk to him (or his co-authors) to figure out whether you are really correct about that mistake. Also state that (if correct) you would like to get a publication out of this due to the effort you put into this. If he accepts the mistake, you may then benefit from having him on your side (be it as a co-author, reviewer, etc.). If it turns out that you were wrong about this, you save a lot of time. If he doesn’t agree, but also cannot convince you otherwise, you can still to have an open scientific debate about this.

At least in my fields, contacting the authors is the common first step when noticing potential mistakes in papers, independent of the relationship to the authors. This is less to give them a chance to correct it, but to give them a chance and use their capabilities to dispel potential wrong arguments.

If you do not trust your advisor and pre-prints are a thing in your field, consider having a pre-print ready for submission when talking to your supervisor, so you can outrun them (or use any of the other methods to prove priority). At least in any reasonable journal, you shouldn’t be able to correct a fundamental mistake just like that. Corrections need to undergo at least some review as well.

Finally, if you think that your field may be so corrupt that corrections of mistakes can be completely suppressed, you should seriously ponder whether you want any reputation in that field anyway. If your answer is no, you have nothing to lose, and may as well try to publish about the mistake. Either you succeed or you can make a fuss about the way you were rejected.

  • I am following your advice by preparing a informal inquiry (updated in the main question). I will update their responds if there is any. – High GPA Mar 2 at 21:40
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Two suggestions:

  • You found that someone was wrong in a good journal. The fact that the error was published in a good journal does not mean that it is worth working on. You should decide if this error is really worthy of your research efforts. It might be better for you to work on something more important.
  • If you decide to pursue the error, you can choose to present your correction as a new idea. If you tell people that you have found a new idea that advances the state of the art, that makes you look good. If you tell people you have found someone else's error, that makes the other person look bad but may fail to make you look good. The actual substance of the research can be the same, but the way you present it makes a world of difference in how it is viewed.
  • Thank you for your suggestions! You just did me a huge favor by sharing your precious experience. Not sure if my following understanding is correct: a paper with "new idea" must have innovated designs and methods, while a "correction paper" usually use the same approaches and the same methods as the original. You recommend me to do the first one? Do I need to explicitly say that the previous results were wrong in my "new idea" paper? Thank you again for your help. – High GPA Mar 2 at 8:23
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    Don't you just love academia, can't even say somebody is wrong because "it might make you/somebody else look bad"... maybe we need a 4chan of journals where you don't have to worry about your reputation because nobody has one. – Matti Virkkunen Mar 2 at 20:13
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    @MattiVirkkunen I agree with you. If I just love academia, I suppose to work on the flaw in the most efficient manner, regardless of reputation or publications. – High GPA Mar 2 at 22:47
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    @MattiVirkkunen I believe the concept you are referring to is etiquette. Not unique to academia. – Lightness Races with Monica Mar 2 at 22:54
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Unfortunately, depending on the topic, published mistakes can damage reputation (e.g. in math, as far as I know). This may, depending on topic, affect your advisor. Publishing a correction oneself can mitigate that. Other fields are less sensitive to honest mistakes.

So, the question becomes:

Do you have a good relation with your advisor? Then it were just an act of friendliness to give them the opportunity to fix their mistake. If you make it public, it means that you do not feel friendly enough to give them this opportunity and you feel that you need to go formal.

Which is acceptable and not wrong, but it clearly sends a message that you do not feel obliged to give your advisor the opportunity to rectify, in favour of getting a few pages in this journal, or else - as suggested elsewhere in the thread - that you do not trust them to do so.

The question is really if you think that this correction is so worthwhile to be published as standalone that you go possibly contrary to your old advisor and his friends.

To be sure: if one thinks something is seriously wrong with a given important research and the original researchers are not prepared to fix it, then one should report it (one has to balance this feel of duty with the fear of potentially ruining one's career).

But this is different from above: you do not know yet how they will react as long as you haven't given them the opportunity to correct the mistake. In this case, however, it is certainly not about getting a correction paper into a journal; the stakes are higher. Any backlash, if they are unhappy with your suggestion and you end up publishing a correction, would counteract any advantage from getting your paper into that journal. You should do this because it is the right thing, not because it advances your career.

  • Trying to communicate with the first author. My email is updated in the main question. I will give more updates later. Any comments welcome. Thank you agina! – High GPA Mar 2 at 22:19
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Talk to your previous advisor and just say I read the paper you were co-authored in, why didn't you do X analysis?

  • Doing it right now – High GPA Mar 2 at 22:19
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I have been working through a paper by my PhD supervisor published in a very reputable journal. I wasted a lot of time before I realised that one of his equations was wrong.

What was the reasonable, professional thing to do? In my opinion, without any question, it was to contact him and say, frankly, I think that X is wrong, maybe it is a typo. His answer "I have looked at my original papers: "it was wrong then and is wrong now: it was not a typo."

A few weeks later I found another mistake, as I thought, in the same paper (actually on the same page of that paper). Same procedure. Answer - brief but conclusive explanation from my supervisor as to why it was not wrong at all. He was right.

Moral of the story: everyone can make mistakes, including your supervisor and YOU. As Oliver Cromwell put it: "I beseech you, ..., think it possible you may be mistaken." Having done so, approach the person concerned to express your comments with appropriate recognition of your own fallibility.

  • Thank you for taking time sharing your stories. I will try to be frank... – High GPA Mar 2 at 22:49
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Probably more likely than not that he either doesn't like it or defends the old calculation. That's human nature.

Thus, I counsel course one: a corrective paper, not a discussion as in course two. Just put the thing out there and let more people judge versus trying to convince your advisor.

  • Thank you for your ideas! The difficulty is, since this field is so narrow, my submission is likely to be ended up on the hand of his friends and/or students. – High GPA Mar 2 at 8:01
  • Well, you can decide to fight it or wash your hands. I would think there are ways to get a publication out. There are so many journals out there. But it depends if you think it's worth your bother. – guest Mar 2 at 8:06
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    @HighGPA People overestimate their ability to figure out who reviewers will be. If there are only a few people interested in this topic, why are you bothering to work on it? – Anonymous Physicist Mar 2 at 8:16
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There are many aspects of this.

People make mistakes. Even top mathematicians make mistakes.

People have egos. Top mathematicians are no different. See the movie Good Will Hunting for a dramatization.

There are a lot of different sorts of mistakes that one can make in mathematics:

Suppose someone publishes a theorem with a "proof" that "A is true". And suppose that you have a "proof" that "A is false". Assuming that the axioms aren't inconsistent, one of the "proofs" is wrong and needs to be resolved. It could invalidate a lot of other work if A is false.

Suppose, on the other hand, that someone publishes a "proof" that "A is true", but you find an error in the proof. Without more work, the truth of A becomes unknown. Perhaps you can supply an alternate "proof", establishing "A is true". This is a proper advancement and deserves publication even if no one has questioned the truth of A.

You describe a somewhat intermediate case, of course. A is 'mostly' true, presumably with a proof.

In mathematics, often enough the proofs are more important than the theorems, if they give a certain previously unexplored insight that permits the proof of other things.

However, you say you are 90% sure of your work. That doesn't seem very high to me, but that is just a guess, as your estimate is likely also a guess.

How to proceed.

Write up what you have found as a proper publication, citing the earlier work and complete in every way. You can submit it to a journal (any journal, actually) or you can submit it to your advisor for comment. Send an email stating that you think there is a problem/issue/error and the enclosed paper develops the idea.

Either way you will get feedback, either from reviewers or from your advisor. But it is feedback that you really need. You might learn that you, too, have made an error. You might get a request for collaboration if you send it to your advisor. You might get a request for co-authorship, though that would seem to me to be less valid.

But, the bottom line here is that it is the mathematics here that is the important thing, not the egos. Yes, your advisor will "feel bad" if s/he has made an error, but, like I said, people make errors. There are a lot of published errors in fact.

One reason that errors get published, other than simple carelessness, is that in an esoteric corner of a field there are only a few people qualified to review a given paper. Likely all of them were similarly trained and have the same, or very similar, insights about that field. If the author missed something, it isn't especially unlikely that a similarly trained person will also miss it. If you "expect" something to be true, in the middle of a complex proof, you won't be as likely to notice that it isn't. There are many papers by prominent mathematicians with this sort of error. They are worth correcting, especially when the correction leads to new ways of proving things or new kinds of insight.

Politically, the proper course is to send it to your advisor, rather than first to a journal. But this depends a bit on your past and expected future relationship with the advisor, as well as your judgement about how ego driven they are.

But, among other things, you need to reduce the 10% uncertainty you have to zero or near zero.

  • You are right. I should not do this correction for my career; I suppose to do it for "science". So regardless of the tier of publication I have to put in time to reduce the 10% uncertainty. Thanks for your advices. – High GPA Mar 2 at 21:13

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