A dilemma that is confronting right now is knowledge versus research. I am a second year physics undergrad, with a strong interest in mathematical physics, QFT, and an even more strong interest in pure mathematics. Right now, I am not sure what to pursue, hence ideally I would like to try out a lot of both the fields. However, most of the people I meet are advising against me saying I should just pick and area and stick to it, and try to publish papers, even if I want a remote chance of getting into the top grad programs in the US. So , I am confused if I should stick to a field, and get research papers published or explore a large number of areas. This boils down to the question how much importance does a uni give to a research publication over the knowledge the person has?
Ideally, research publications give a strong indication of not just how much knowledge a person has acquired, but how much has he been able to contribute to the existing body of knowledge. That, coupled with the fact that there aren't very reliable metrics to gauge a person's knowledge (grades are a very poor metric in that regard IMO), makes it obvious that you would be best served by focusing on churning out as many high-quality papers as you can!