"But it is not a study of it! Mathematics is a tool, not the thing being studied."
Who knows? Mathematics turns out to such an acute tool for understanding physics. One might be inclined to say that we live in a mathematical reality. The quoted statement is more a statement of philosophy than of fact.
One might be inclined to say this if one doesn't understand the difference between physical nature and our consciousness of physical nature.
Mathematics does not exist outside of human minds. It is a method for measuring and describing the world around us that happens to lend itself to the study of its own conceptual structure.
Nothing in nature follows mathematical laws. Protons don't consult logarithm tables before they move through space. Particles don't consult statistics textbooks before they "decide" if it's time to decay. They act according to their nature, and that's all.
Who knows? Mathematics turns out to such an acute tool for understanding physics. One might be inclined to say that we live in a mathematical reality. The quoted statement is more a statement of philosophy than of fact.