Prelude: In 1998, Robert Solovay wrote an email to John Nash to communicate an error that he detected in the proof of the Nash embedding theorem, as presented in Nash's well-known paper "The Imbedding Problem for Riemannian Manifolds" (Annals of Math, 1956), and to offer a nontrivial fix for the problem, as detailed in this erratum note prepared by John Nash. This topic is also discussed in this MO question.
Of course, any mathematician who has been around long enough knows of many published proofs with significant gaps, some provably irreparable, and some perhaps authored by himself or herself. What makes the above situation striking–and discomforting to many of us–is the combination of the following three factors:
(1) The theorem whose proof is found faulty is a major result that was published in 1950 or after, in a readily accessible source to experts in the field . (I chose the 1950 lower bound as a way of focusing on the somewhat recent past).
(2) The gap detected is filled with a nontrivial fix that is publicly available and consented to by experts in the field (so we are not talking about gaps easily filled, or about gaps alleged by pseudomathematicians, or about false publicly accepted theorems, as discussed in this MO question).
(3) There is an interlude of 30 years or more between the publication of the proof and the detection of the gap (I chose 30 years since it is approximately the age difference between consecutive generations, even though the interlude is 42 years in the case of the Nash embedding theorem).
Question to fellow mathematicians: what is the most dramatic instance you know of where all of the three above factors are present?
Best Answer
In 1970, I. N. Baker published a proof of a basic result in holomorphic dynamics:
A completely invariant domain is an open connected set $D$ such that $f(z)\in D$ if and only if $z\in D$.
Baker "proved" a more general statement that: there cannot be two disjoint domains whose preimages are connected.
The "proof" was a simple topological argument which occupied less than one page. Since then this result has been used and generalized by extending his simple argument. In summer 2016 I was explaining Baker's argument to Julien Duval, he was somewhat slow in understanding and kept asking questions. Few weeks later he found a gap in the proof. It also took him some time to convince me that there is a gap indeed. Specialists were informed.
Half a year later an amazing counterexample has been constructed in https://arxiv.org/abs/1801.06359 by Lasse Rempe-Gillen and David Sixsmith. This paper contains the full account of the story. This is a counterexample to Baker's more general statement only, not to the highlighted theorem itself, which is now an important open question.