How should a physics student study mathematics?

I feel very strongly about this question. I believe that for an experimentalist, it's fine to not go very deeply into advanced mathematics whatsoever. Mostly experimentalists need to understand one particular experiment at a time extremely well, and there are so many skills an experimentalist needs to focus all of their time/energy on developing as students.

I believe experimentalists should derive their physical intuition from lots of time spent in the lab, whereas theoreticians should develop their physical intuition from a sense of "mathematical beauty" in the spirit of Dirac.