Here we try to collect some manifestations about the process of refereeing mathematical papers.
Can we hope that Artificial Intelligence helps in the process? My answer is: Maybe after sufficiently long time and this implies that it is better not to bet on it.
So, let's say one possible approach: Divide the refereeing process into two parts:
General decision on the level of the paper's novelty by one (more) referee(s) anonymously with the collaboration of the Editorial board.
Technical report on the validity of results with referees who may sign the report. As it may not be anonymous, the referee can talk with the authors and create discussions with other researchers or students to do the best and rapid referee work.
Some benefits:
A. It may be easier to avoid referee's errors and possibly reduce the time of publishing papers.
B. Young researchers can get credit for their work and accept more papers to referee.
issues:
The issues that I can imagine are of the psychological order and may have some negative effect in such a way that people do not accept to act as referee, as it seems to be forced to talk with the authors. The process can get stressful and create conflicts.
Maybe the community can test this procedure in some specific journals for some time.