I'm thinking about doing some research in math next semester... pure math, focused on Algebraic Geometry. I'm currently doing research in theoretical cosmology, and it's been going really well, but the math research sounds really interesting to me. What would grad schools think of this? On one hand, I'll show that I have diverse research interests, but on the other hand, it might be more productive to spend the next semester continuing to do research in cosmology. What do you guys think? Is doing math research beneficial for prospective physics PhDs?