The title of this talk is the same as that of an influential article published in 1960 by the physicist and mathematician Eugene Wigner. Wigner's thesis is that mathematics is obviously an effective tool in the sciences (especially physics), but it is unreasonably so: much more successful at describing natural laws than could reasonably be expected. He concludes, ``The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.'' I will survey the evidence that led him to this conclusion, examine some later attempts to explain this miracle, and hint at my own viewpoint. I hope to hear yours as well.