[sweetjazz]

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I think it's a bit of an anthropic principle cannard. If mathematics weren't useful in describing the world, it never would have been developed.

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This doesn't directly contradict what you wrote, but there are areas of math that were studied purely out of interest (without applications to the real world) that were later used to describe the universe. One example is group theory (the study of symmetries) which has been very useful in molecular chemistry. Another example is the discovery of non-Euclidean geometry (which took place in the mid 19th century), a result that was purely of theoretical interest until Einstein discovered in the early 20th century that space-time is a naturally occurring non-Euclidean geometry.

So the mystery of why mathematics can be used to explain and describe natural phenomena may still remain.