I have to agree with all of that: If you are working in the field, studying in the field, then you absolutely must master the math to get ahead, to understand the details and find the exceptions, and to make contributions.
But that's not the question I took the OP to be asking. If the OP had asked "What maths must I learn to advance the state of the art in GR?" I would have agreed with others who posted a standard undergraduate-followed-by-graduate program of study (because you ain't advancin' anythin' with undergrad calc and algebra, unless you are a physics/math major and your undergrad includes advanced PDs, complex analysis, advanced stats, and advanced analytic geometry).
I took the question as "What do I need to understand to be able to get more out of the more advanced physics articles found here on /. and other interesting places?" - hence my agreement that you don't need math, Jack.
In fact, I would go so far as to assert that for most of us, trying to understand some of the more esoteric stuff outside our fields, math only gets in the way: A quantitative and precise understanding of most of today's hard science requires considerable specialized mathematics, and unless already has quite some specialized mathematics in one's own field, one will be unable to jump easily to and get anything out of the specialized mathematics of another field.
So this leaves the curious seeking high-quality, qualitative, non-mathematical articles and explanations.
(With the caveat that at some relatively simple math is a really good idea, since it can so encapsulate the physics. E=mc**2 is beautiful in its simplicity, beautiful in the equivalence it expresses.** As is the Lorentz transformation when applied to the relationship between t and c.)
(** Re the post commenting how muddy things get when you set c==1 in E=mc**2: I disagree completely. The physical point is that E=m; mathematically, E is proportional, of course, but the physics is that they are the same thing - that was radically new. That's the first beautiful point of the statement. The second, far more subtly beautifully point, is that the constant required to make the proportion an equality is the speed of light squared. OMG ponies! Why on earth should that be? Investigating that leads to some really interesting physics.