Relative importance of research publications for grad school admissions (theoretical physics/pure mathematics) 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?
The main thing that graduate school admissions committees are looking for are good researchers. Publishing papers demonstrates such ability; publishing papers in well-known journals is even better. However, it's difficult, as an undergraduate, to publish papers as first author (which is the most important position when one is applying as a student). Typically, they will be working in consultation with a more experienced student, who will be the lead author. In that case, while the credits are of themselves useful, they need to be coupled to strong letters of recommendation from the co-authors, testifying to the student's original efforts in executing the work.

At the same time, one should not totally sacrifice depth in a single area for breadth; grad schools want to see some evidence of concentration, but complete devotion to one area is also too much of an extreme. Try to balance the two somewhat, so that you've explored a few areas, and worked at least one or two areas in depth.