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I have found a basic mistake in one of the published paper in a top tier Applied Mathematics journal. I have told my research supervisor about it and he also agrees with me. I found the issue when I was working on one open problem mentioned in the paper. Please suggest what to do.

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That depends on the consequences of the mistake. Does it invalidate the main conclusions of the article or is it only a side issue? If the former, you can write up what the consequences are and present the new results as an article an submit it. If it is only a side issue, you can mention it in a footnote when writing up your results for the open problem.

In the former case, keep the tone professional: don't use any adjectives to describe the mistake and certainly not when refering to the authors, i.e. it is a mistake not a basic mistake. Focus on the point you want to make, and let the strength of the argument speak for itself.

  • Yes, it is the former. I have asked the authors, but they have not replied. – RIchard Williams Feb 25 '17 at 15:03
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    Sounds like you have an article to write. Just keep the tone professional: don't use any adjectives to describe the mistake and certainly not when refering to the authors, i.e. it is a mistake not a basic mistake. Focus on the point you want to make, and let the strength of the argument speak for itself. – Maarten Buis Feb 25 '17 at 16:12
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Here are a couple of previous posts on math SE and academia SE that are relevant to your question: Post 1 and Post 2. The discussions following these posts are quite illuminating.

Although not an answer to your question, there is also this article that I found to be a very interesting read on addressing mistakes discovered in previously published papers.

  • It's helpful if you quote or summarize the contents of the linked article. – aparente001 Feb 26 '17 at 3:05

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