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There are several publications which I was advised to read by my supervisor, and work on during my master thesis. At some point I tried re-deriving the presented statements formally, and found that there are major mistakes that make the publications wrong in a very large part. I have had several people re-derive the same results and arrive at the same conclusions as me since. The issue seems to have started with two publications which used informal (and wrong) logic to argue about the correctness of their main statements. This has been cited over a period of almost a decade and various formalizations and analyses have been done on top of that (including PhD theses) - most of which will turn out to be irrelevant if the results on which those are based are shown to be wrong. A lot of the follow up publications have been published in some of the most prestigious journals in the field.

I tried talking with my supervisor (which is a co-author in some of those) about the issue. Initially he wanted me to find cases in which the statements in the publications hold, however it turns out there are no such cases. Since I notified him of this fact, he has been dodging the issue, even when I suggested that we should at least contact the authors.

How should I proceed with this issue? The publications in question keep being cited and have resulted in even more wrong publications in the last years, as well as wrong conclusions in mainly correct publications.

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    You don't say which field. In mathematics the answer might be more clear than in, say, philosophy. – Buffy Oct 3 '19 at 11:56
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    @Buffy The mistakes are mathematical. The field is not mathematics however. From what I gathered they tried to fit the theory to the experimental results through informal statements. However, if a formal derivation is done then one arrives at different results. Additionally, the presented results can be expanded, and it may be verified that they result in mathematical nonsense. – lightxbulb Oct 3 '19 at 12:03
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It is hard to tell whether you are on firm or shaky ground. If the ground is firm, probably the best way to approach it is to write a paper yourselves with correct results and see if the same journal will publish it.

But, the ground may be shaky for the following reasons.

In mathematics, a failed proof doesn't leave the result false, just unproven. It gives no evidence for the validity of the claim. A counterexample, on the other hand, leaves the result certainly false. So, it may be that, while an argument fails to deliver, the overall result is still correct, just not provably so.

But a result that is (if true) contradictory to the original, then the original must be false. This is actually stronger than a counterexample, since a counterexample only shows that a general statement is false, but might leave some specialization of it true, provided that the specialization excludes the counterexample.

However, in this case you say that your analysis leads to different results. If those results are contradictory to the original claims, and if your reasoning is correct, then you may have the basis of a paper.

However (again), if your results aren't, in fact, contradictory, then your advisor is giving good advice that you explore the intersection of what it is that the original paper claims and what you claim from your analysis. This might also give you the basis for a good paper, leaving some of the original claims win place, but improving on them.

I suspect that the situation is complex enough that a simple letter to the editor of the journal, pointing out the error, isn't going to be sufficiently compelling for anyone to take action. If the journal in which you find the original is reputable, then many people have missed the errors, implying a certain subtlety. This leads me to suggest that a full paper laying out the situation is more appropriate.

And even if this invalidates some early work of your advisor, he is at an advantage in being part of the process that corrects it.

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    Maybe it wasn't clear from my comment, but the results are contradictory. Namely the expansion of the expression in their results leads to mathematical nonsense. There is no doubt that what they have is wrong (I have formally derived that it is wrong, and I have had others confirm my results independently).- most importantly, it is semi-trivial to prove that the result is wrong as long as one is acquainted with more advanced mathematical concepts. But as I said my supervisor keeps dodging the topic whenever I bring it up. – lightxbulb Oct 3 '19 at 13:07
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    Write the paper (outline is probably enough) and show it to the PI. See if he wants to contribute. – Buffy Oct 3 '19 at 13:09
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    I have the derivation in my thesis, he explicitly didn't want me to present the results related to it in the defense, if that tells you something. – lightxbulb Oct 3 '19 at 13:12

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