As Galileo famously observed, "The laws of Nature are written in the language of mathematics". But a natural thought is that mathematics is just a language, a helpful means of representing how things are with physical objects in an ultimately physical world. Yet mathematics has its own subject matter: numbers, functions, sets, and the like. And these objects are usually thought of as abstract, non-physical things. Does the use of mathematical language in our descriptions of the physical world commit us to believing in a realm of objects beyond the physical? While some philosophers have argued that the descriptive use of mathematics could be accounted for even if we viewed mathematical objects such as numbers as merely useful theoretical instruments, the existence of mathematical explanations of physical phenomena requires us to adopt a 'Platonist' view of mathematical objects as really existing abstracta. I will present some examples of mathematical explanations of physical phenomena and consider how such explanations have been used to motivate a realist view of mathematical objects.