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Jun 8, 2013 at 0:30 comment added paul garrett Indeed, journal editors these days most often emphasize the issue of whether a paper is "up to their standards", not whether or not it's correct, sometimes even explicitly noting that it's not the referee's job to determine correctness. "Significance" is obviously subjective to a considerable degree, and when referees see authors' names, prior reputation and connections have the potential to sway them about "significance".
Jun 7, 2013 at 23:42 comment added John D. Cook The correctness of a math paper is objective, but the importance of a paper is not. If you're not sure how much of a contribution a paper is, but it's written by someone respected in the field, you give them the benefit of a doubt. An outsider doesn't get that benefit. That's another reason a young researcher needs to ride the coattails of a more established researcher, writing papers and grants together until he or she develops some name recognition.
Jun 7, 2013 at 22:56 comment added Asaf Karagila While I don't know whether or not mathematics suffers from the same illness as the rest of the academic world, I'd like to think that it suffers less, in the sense that regardless to the name on the paper it is usually not beyond a reasonable effort of an expert to judge the correctness of a logical inference, and thus decide if a paper is correct or not. True, there are still mistakes, but the politics is less important here. But then again, what do I know about publishing? I'm just starting my career...
Jun 7, 2013 at 22:56 comment added Deane Yang Which is why it's rather important for the student to establish a good relationship with the people working in area B and, if possible, get one as an advisor. At the very least, this way the student can get ongoing feedback about his progress and thesis. Without this, things get very dicey for various reasons, including the one stated in this answer.
Jun 7, 2013 at 22:35 history answered John D. Cook CC BY-SA 3.0