unreasonable effectiveness of mathematics in the natural sciences, especially in physics

Note that with respect to the power of mathematics, it's as easy to view the cup as half-empty as half-full. Here's Jaynes on the issue:

Phenomena whose very existence is unknown to the vast majority of the human race (such as the difference in ultraviolet spectra of Iron and Nickel) can be explained in exhaustive mathematical detail but all of modern science is practically helpless when faced with the complications of such a commonplace fact as the growth of a blade of grass.