Galileo considered mathematics the language of nature. However, Wigner thought the effectiveness of mathematics in physics "miraculous" and noted that much of the mathematics needed for quantum mechanics had been previously developed by mathematicians for purposes having nothing to do with physics. I argue that Galileo's view is correct; but that the examples cited by Wigner in support of his view can be explained using two deep truths, one about mathematics and the other about physics. These truths are: (1) Since the advent of non-Euclidean geometry, new mathematics has been developed by abstracting and generalizing old mathematics. (2) New physical theories have old physical theories as limiting cases.
David Garfinkle