Academic publishing is a mess and it makes culture wars dumber

It seems to me that most of the blame lies with the editors for handling it badly. As you say, they should have owned their decision and printed a retraction. The academics (including at least one respected mathematician), who criticized the paper were exercising their own academic freedom, and the authors theirs. The reviewers would bear some of the blame but, as @sme points out, research institutions don’t place much value on peer review with a predictable and pervasive result in quality control.

Even good and respected mathematicians are capable of faulty research. One retraction wouldn’t really be a prevailing reflection on him or his abilities.

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