Yes, mathematics 'is' a vital tool in physics, and in the understanding of physics. But, it is not by any means the only route to understanding physics, or making a contribution to physics... I believe it was evan-au who recently stated to me that Einstein himself had to rely on colleagues with greater mathematical skills than he to describe the concepts he'd come up with.

It sounds as if you are saying that if you do not understand the maths for general relativity then you cannot understand physics... I've been speaking to physicists of considerable note for quite some amount of time now, and not one has been able to give me a blow by blow account of how the GR field equations are put together, usually completely ignoring me subsequently. The most honest account of abilities I've come across is "I'm a bit rusty"... and little wonder when Leonard Susskind himself states in his GR lecture, concerning the field equations, that he's not going to give an example of the equations in use, and anyone wishing to use them should refer to a computer program!