We have been approached by the authors of an article published about 19 years ago stating that they have found an error in a mathematical proof in their research. As a result, although the main theorem proposed in the paper should still be true, they would need to completely revise the text and intend in the longer run to find a new proof. They recognise that the paper as published cannot stand and so are willing to have the article withdrawn.
Questions for COPE Council:
1. Should this article be withdrawn or is there any other better option, so long after being published?
2. How should the publisher respond to the author?
Advice on this case is from a small number of COPE Council Members. Most cases on the COPE website are presented to the COPE Forum where advice is offered by a wider group of COPE Members and COPE Council Members. Advice on individual cases is not formal COPE guidance.
The appropriate response to this request depends on how seriously the mistake will affect the main theorem of the paper. If the original research is truly flawed and the proof was the main intellectual contribution of the article, then the article should be retracted (but not withdrawn: the original article should remain available and linked to the retraction notice). The editors could consider asking the authors to come up with a draft retraction notice, which should be checked and confirmed by the Editor in Chief.
Alternatively, if the authors have already made good progress on the revision with new mathematical proofs, an elegant solution could be to publish the new article together (which should detail the error and what has been done to correct it) with the retraction of the old article, and have the retraction notice reference the new article. However, the editors should take steps to ensure that any new proof really does support the existing theorem, for example by inviting an independent review.
If the current article still has intellectual merit despite the mistake then an Erratum or editor’s note might be more appropriate, explaining what the error was and why a new analysis has been performed. Again, this could be published in conjunction with a new paper.
The age of the paper should not affect the response from the editors.