The Applicability of Mathematics to the Physical World

The applicability problem asks why mathematics, often developed for its own internal, purely formal reasons with no eye toward physical application, turns out to describe the physical world with such extraordinary precision — a question given its canonical modern formulation by the physicist Eugene Wigner in his widely cited 1960 paper "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" (Communications on Pure and Applied Mathematics), which calls this fit a "miracle" that "we neither understand nor deserve" any ready explanation for.