Not Lean in the wild

Stream: general

[Siddhartha Gadgil]

Just came across this in the wild (one of the author's is my thesis advisor David Gabai): https://arxiv.org/abs/2311.11196. No Lean here but a case for Lean.

Perron and Quinn gave independent proofs in 1986 that every topological pseudo-isotopy of a simply-connected, compact topological 4-manifold is isotopic to the identity. Another result of Quinn is that every smooth pseudo-isotopy of a simply-connected, compact, smooth 4-manifold is smoothly stably isotopic to the identity. From this he deduced that.... A replacement criterion is used at a key juncture in Quinn's proofs, but the justification given for it is incorrect. We provide different arguments that bypass the replacement criterion, thus completing Quinn's proofs of both the topological and the stable smooth pseudo-isotopy theorems. We discuss the replacement criterion and state it as an open problem.

[Kevin Buzzard]

In the Annals project we also ran into an erratum saying "this 1984 paper written by me and a now-dead co-author has a mistake in the last section and all the theorems announced in the last section are probably true but the proofs are now incomplete". I looked up the original paper and it had over 100 citations. I wondered whose job it was to go through the citations and check to see what damage was done.

[Ruben Van de Velde]

I fear "nobody"

[Ralf Stephan]

In biomed, there are retractions by journals. They are monitored by Retraction Watch. Since there is also a general abstract service (PubMed) which signals these, retractions are very visible. The RW database also is queryable by API.

And math?

[Kevin Buzzard]

We have errata.

A very senior person in my field usually has the errata to their n'th paper at the end of their (n+1)st :-) so they're not even easy to find!

[Eric Wieser]

has the errata to their n'th paper at the end of their (n+1)st

Presumably journals only allow this if paper $n$ and $n+1$ are practically continuations of one another?

[Kevin Buzzard]

Oh they're all in different journals

[Eric Wieser]

Tacking an errata onto a different paper entirely seems like a very strange way of disseminating it

[David Michael Roberts]

In the best case, there's a paper dedicated to correcting the mistake. In my specialty there's one 14 years after the fact (and it's a very small result in the original paper that as far as I know wasn't really used)

[David Michael Roberts]

And yes, it's in a different journal to the original paper.