Engineers Discover In Nature Exotic Structures Envisioned By Mathematicians is the title of a Science Daily summary. Although the article is a few years old its message is timeless. From the article:
Three years before he received the Nobel Prize in Physics, Eugene Wigner published an article entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" (1960). He marveled at how often physicists develop concepts to describe the "real" world only to discover that mathematicians–heedless of that real world–have already thought up and explored the concepts. His own experience of the uncanny applicability of mathematical insights to the physical reality of quantum mechanics led Wigner to observe "that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it."
The belief that our universe was intelligently designed and is best understood through a design paradigm can be derived from many things among which is the "enormous usefulness of mathematics in the natural sciences." The rabbit/duck perspective is applicable. Wigner's observation is continually confirmed through scientific studies but Wigner's remark reveals his belief that there is no expectation of such a degree of mathematical utility. The fact that it exists is fodder for those who would interpret empirical findings within a broader philosophical outlook.
Debates centering around ID frequently polarize to opposing perceptions. Some pit arguments, based on empirically derived data, against beliefs based on blind faith. Yet actual beliefs are rarely pidgeonholed in this manner. Even empirical disciplines place faith in methodologies and philosophers are not isolated from the physical world. Wigner's point is consistent with the view of some historians that science was born in a culture that nourished the belief that the physical world is ordered and rational like the Judeo-Christian God who created it. The linkage is seen as causal and not incidental. Orderliness and rationality also are qualities of plausible belief systems. The "unreasonable effectiveness of mathematics" is one of several rational pillars of intelligent design.