From what I understand the math required for physics majors isn't extremely rigorous (except for the most theoretical of branches). I have also gathered from this forum that the reason for this is physicists use math as sort of "tool" and don't study it as a science (this may not be the appropriate term but I'm not sure of a better one) as a mathematician would. That being said, is a deep understanding of math required to get a deep understanding of physics? Or is it truly just a "tool"? For instance, can someone have a deep understanding of General Relativity with only a "working knowledge" of tensor calculus? Thanks.