I am writing a paper about a flaw that I found in a published paper. There, the statement is called “Theorem 2”. In my paper, I am reproducing the other paper’s definitions, and steps leading towards that statement, and now I’d like to reproduce the statement, immediately followed by the counter example that I found.


I am tempted to reproduce the statement labelled and styled as a theorem in my paper as well, so that the reader can easily find and recognize it, and so that I can continue to refer to it as “Theorem 2”. But is that really valid, given that only correctly proven statements are, by definition of theorem, theorems? Or can there be such things as “false theorems“?



How to refer to a theorem that you have shown to be wrong
You can have a look to the paper "A counterexample to a 1961 “theorem” in homological algebra" by Neeman and use his style. By the way, I think that the paper is very very good.


