[placebo]

I'm also very interested in this question. My current understanding is that mathematics only works well because the mind is only capable of conceiving a mathematical reality, i.e math is basically the end result of an evolved mind, a tool that divides experience to concepts (including objects, properties, relationships) which at first approximation don't change with time (a lion will remain a lion, a lion will remain dangerous). Later, higher level observations that are constant are also observed (e.g location that linearly changes with time is a constant speed, every triangle on a plain has 180 degrees etc.) - my point is that the mind is geared to find relationships that are constant (in every level of abstraction), and once we find such a constant we call it "truth" (or if we're more honest, we at least admit it's a good model). So I think the bigger question is not why mathematics works (it works because reality, including thought itself, can be seen through the filter of concepts that appear to be self consistent), but rather why reality lends itself to being categorized in the first place into "things" that have internal integrity and consistency.