Suppose you collected for study that set of human experiences (i.e.: interactions with the world) for which mathematics proves particularly useful. And suppose you decided to call that “physics.” How far off would that be from what we actually do? I mean, when the math gets too messy or bogs down in ability to predict more, we set aside that set of experiences and call it chemistry or biology or psychology. In other words, there is no surprise finding math in physics if it essentially a defining characteristic of the field.