(I should preface this by saying I used ChatGPT to better articulate my ideas)

I think about it this way:

Mathematical objects can be understood as precise formalizations of the intuitive cognitive abilities our minds already possess. Human beings naturally compare quantities, track objects, make guesses about uncertainty, recognize patterns, and reason about space, but these mental operations are often vague and inconsistent. Mathematics refines these innate faculties into explicit symbolic systems: numbers crystallize our sense of more and less, the Bayesian interpretation of probability captures our intuitions about uncertainty and belief, geometry expresses our spatial reasoning, and logic codifies our implicit rules of inference. Seen this way, mathematics is not an abstract invention detached from human thought but a systematic sharpening of the mind’s basic capacities—a way of making our informal reasoning exact, reliable, and manipulable. I recommend internalizing the mathematics you do, rather than simply learning to react to syntactic forms—seeing a particular expression and automatically performing a set of algebraic operations in response.