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To take a crack at one of those:

"Why is mathematics so effective in describing nature?"

At a guess, because we can keep playing with it until it fits. The most basic math was *invented* so that we could describe nature on a basic level (arithmetic and geometry).

At intermediate levels, developments in mathematics such as calculus were motivated in large part by physical questions (planetary motion, describing the shapes of certain curves, predicting the behavior of light, and so on).

So it's no surprise that basic and intermediate levels of math describe nature; that's what they were invented to do. We can count bears or gazelles or huckleberries using arithmetic because that's exactly what arithmetic was first made to do; we can describe planetary motion and ballistics with calculus because that's exactly what calculus was made to do.

As for more advanced math and how it relates to more advanced descriptions of nature (as in relativity and tensors, or string theory and the highly advanced mathematics associated with it), I think the explanation is thus:

Modern mathematics has questioned almost all the underlying axioms of 'conventional' mathematics, such as the ancient Greeks or the mathematicians of the Age of Reason would be familiar with. We can use it to describe virtually *anything*, because we can construct a mathematical description of any set of starting assumptions or conditions. Want to describe a universe shaped like a 5-dimensional doughnut? Math can do that. Want to predict how an arbitrarily shaped blob of stuff will spread out through that space? Math can do that, too.

Our mathematical toolkit is so broad that it's hard to specify anything we couldn't theoretically describe with it. So it may well be that we now have a description for every thing that the universe *could* be, simply because we've exhausted the possibilities by coming up with such an anarchically broad array of different mathematical techniques.