This question: When did it become a norm for mathematicians not to read proofs of all the results they use?
I would expect answers to include evidence like "Mathematician X wrote that he had not read proofs". However, it was considered opinion-based and was closed. I don't know why.
Here is my take on your linked question.
It is impossible to answer it by anything other than an opinion, this is why it was closed.
I have read many math papers and books, I have never came across a statement of the form "I never understood this proof in [X], but I will use this theorem anyway." There are two types of notable exceptions to this (which are widely understood as exceptions):
a. Instances when mathematicians use results where full proofs are not yet available. (I know of two examples: One is in the theory of finite groups and one is in the low-dimensional topology.)
b. Instances when mathematicians use results where the only available proofs are computer-aided. In this case, it is not even clear what does it mean to "read and understand the proof," regarding the computer-aided part. As far as I know, the first such proof is of the 4-color problem, in the mid 1970s.
In these instances, more careful writers might acknowledge this situation, but that's it.
Assuming that my personal experience is a reasonably representative sample, the only way to find out what the current norm is, is to undertake some massive opinion poll of currently active mathematicians. As far as I know, nobody tried to do this and it is very unlikely that anybody will do this in the foreseeable future.
Repeating myself: I have never read a paper written before 1960s from which I could infer that the author(s) did not read proof(s) of theorem(s) that they use. In some cases, I can conclude that this did not happen since everything in a paper was proven from scratch, apart from usage of basic algebra/arithmetic, analysis/calculus and elementary geometry. (For instance, Poincare's papers are like that. For the record: Poincare's papers are the only original math papers written in the 19th century that I have read to some extent.) How representative is this (not using any older results by other mathematicians)? Answering by anything other than an opinion, would again require a massive effort, reading a variety of old (say, 19th century) papers, frequently written by obscure mathematicians using obscure terminology, etc. Nobody in their right mind is going to make such an effort.
