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I have recently discovered some mistakes in a published maths article. I have contacted the author pointing out politely my concerns, but I got no specific answer, just a "polite" one, that the aspects I am addressing are clarified in some of his other papers (without mentioning which are these papers). Although my remarks where specific and could have been answered with a simple counter-argument (if there was any), the author avoided a direct answer. What is also concerning is that these errors are "copied" by others who base their research on this published paper.

My question is how do you signal these errors to the community? What is the right process if the authors avoids to take credit?

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How about writing to the editor of the journal in which the paper with errors was published? Of course, you need to be absolutely sure that it is the author who is mistaken, and not you. –  J. M. Aug 8 '12 at 8:26
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Presumably you are writing a paper of your own on some related research. If so, it would be acceptable to mention in passing the error in the other article, and what the correct statement/argument should be ( or what a counterexample to the other author's claimed result is). If you do that, though, you should send the other author a copy of the preprint of your paper. –  Geoff Robinson Aug 8 '12 at 8:50
    
Is it a relatively recent paper, or something older? Is there a MathSciNet review of the paper? If so, does it mention anything? –  Arthur Fischer Aug 8 '12 at 10:17
    
@ArthurFischer: The paper in from 2011, it is indexed in MathSciNet and it labeled as Reviewed in 2012, yet the review is only a copy of the abstract (i.e., Summary: " ..."). –  digital-Ink Aug 8 '12 at 10:41
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up vote 6 down vote accepted

The most polite way of pointing out a mistake in a previously published paper is first to pass it to the editor of that journal along with your well written claims. In this case the editor can take action and make it public such that other people is also aware of this mistake and dont use those results anymore.

It might be the case that the editor doesnt take any action or it doesnt bother him much. In such a case the report should go to the chief editor of that journal indicating all the story. It is quite likely that one of them will solve the problem. However, according to my experience, it is also possible to address the mistakes in the same journal paper most probabily in the "correspondence" part.

Human beings can make mistakes and it is disappointing for a mathematician to have mistakes in his paper. Very great mathematicians can even make mistakes therefore I think any claims should carry the best of politeness.

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I agree that mistakes appear, even in published papers, against our best intentions or the efforts of the reviewers. Yet, I also think that mistakes should be assumed, together with all the recognitions that come from a published work. –  digital-Ink Aug 8 '12 at 10:48
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I think what the OP did was the most polite, decent and considerate thing to do: to write to the author pointing out mistakes/doubts about that paper. Assuming the points were written in a decently clean, mathematical way, the author is expected to address these points in a decent, polite way, and even be very grateful for that. My experience shows that even rather world famous mathematicians tend to be pretty nice and grateful about these things, something one learns pretty soon in undergraduate school after the first 5,6 or 34540934 mistakes one makes. –  DonAntonio Aug 8 '12 at 16:41
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