By George he's got it!
Despite reading mathematics at university many moons ago, I never formally studied quantum mechanics or relativity. This was because I was much stronger in the general areas of probability theory and statistics than in physical methods so I chose my options accordingly. I still try and catch up with what's going on in the world of theoretical physics from time to time but though I think I have a decent heuristic grasp of quantum mechanics and special relativity (i.e. I think I 'get' what the mathematics mean though I couldn't actually work the math) until yesterday I really struggled with general relativity. So yesterday I was poking around some nifty stuff on the Caltech website and I suddenly realised where I had been going wrong. The fourth dimension of the standard space-time geometry isn't t as my brain had been insisting all these years (which is ironic as I know Maxwell's equations perfectly well) but ct. Suddenly space-time as a geometry makes sense and the effect of the distribution of mass-energy also falls into place. And it has only taken me just short of thirty years to figure this out!