In a famous 1960 paper, Wigner discussed "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." I suggest that the effectiveness of mathematics in producing successful new theories and surprising discoveries is even more unreasonable than Wigner claimed. In this paper, I present several historical case studies to support the claim that mathematics is often responsible for instigating scientific revolutions. However, that does not mean that mathematics is always the key to the universe, and other cases where mathematization was not successful are discussed in order to problematize a naïve Platonism.