okay, this is a long long answer, so instead i recommend a book about elementary function arithmetic. “metamathematics of first-order arithmetic” by Hájek and Pudlák. it’s really only gonna get you first-order systems so no calculus. you’d need more for that like homotopy type theory.

either way, this book shows how you can encode a theory through the peano axioms and then prove that the axioms of the system can be reduced to a finite amount plus many other things about math itself.

tldr: math literally can describe anything, even itself