Retractions in mathematical journals

Question

The number of retractions in some scientific fields like medicine, life and material related science seems rising in the past years. However, retractions in mathematics seem rare because of its rigorous nature. I wonder if there are retractions in mathematical journals.

Answer 1

The Daniel Biss case is one example where the retraction is due to legitimate mistakes (not misconduct). These retractions are rare because much of the time, incorrect proofs can still be salvaged with some work (recall Wiles and Taylor) and even papers with wrong results often contain enough correct material to be considered useful. Also, there are much fewer people that have the time to properly evaluate a paper in mathematics than in (say) psychology, where anyone with a decent understanding of statistical fallacies can find half a dozen bad studies per day.

There are also, quite likely, some cases where plagiarism has led to retractions.

Then there is the Ted Hill GMVH controversy (Quillette, Gowers's blog 1, Gowers's blog 2, Retraction Watch). NYJM has removed that paper from its archives, which can be construed as a kind of informal retraction, albeit easier to construe as a mess-up in the face of unexpected hostility from parts of the community. (The explanation given for the retraction is that the paper did not fit the journal's scope and level; note, however, that this is an extremely unusual grounds for retraction in academic publishing.)

RetractionWatch has a tag for retractions in mathematics.

Answer 2

Many years ago I saw a page in an Eastern European mathematics journal retracting a past paper. It seems the paper had originally appeared in a Chinese journal, and some enterprising guy in Eastern Europe translated it into English and submitted it under his own name. The journal only found out about that fraud years later.

Answer 3

I definitely think there are field differences. Psychology and medicine are much more prone to issues with sample size, confounding variables, etc. Plus there is a huge amount of money pumped into biology/medical research (look at NIH budget versus NSF) and this likely leads to issues of worse scientists, declining returns on investment, etc. (Add in business drivers of drug research, political biases on social policies, etc. and it becomes even worse.)

There are some sketchy mat sci papers (nanoscience, devices) where there is hype science present and even deception. But in general, I bet mat sci has more solid stuff than psych and medicine. Math even more so.

A lot of times when people talk about the replication crisis, they really mean fields like psych, nutrition, cancer, education, crime, etc. I don't see general replication issues in chemistry. Yeah, there are a very small percentage of mistakes (wrong crystal structure). But in general if you repeat a chemical synthesis for a new molecule, you get the new molecule. Try that in a priming study! https://en.wikipedia.org/wiki/Priming_(psychology)#Criticism