TITLE: Does a referee have to check carefully the proof ?
QUESTION [64 upvotes]: I have always checked very carefully the papers I was refereeing when I wanted to suggest "accept". Actually I spend almost as much time checking the maths of a paper I referee than checking the maths of a paper of mine (and this is very long !). But I have some doubts. Is it really my job as a referee ?  
This question is related to Refereeing a Paper but only a few comments were made on that point in the above cited thread (mainly Refereeing a Paper).

REPLY [11 votes]: I believe that the referee should check the proof is correct, or at least that the logical deduction of its claimed results from the assumed results it quotes is correct. It probably is unreasonable to expect referees to check the correctness of cited results in a paper- this could easily become a never-ending task. While there is probably a general consensus that responsibility for correctness rests primarily with the author(s), the community needs safeguards to ensure that genuine mistakes by authors are caught before they become assimilated into the body of accepted mathematical knowledge.
However, I also believe that authors who quote previous results in their own proof have a responsibility to ensure as far as possible that they fully understand the results they are quoting, and their correctness. If a quoted result turns out to be wrong, the person who quoted it can't evade their own responsibility by blaming the referee of the paper quoted.
Of course there is a conflict between idealised behaviour, and what is attainable in the "real" world, but in the long run, Mathematics, perhaps above all other human endeavours, strives for an idealized perfection, and abandoning that striving would be fatal for the subject.