Every textbook on math I have ever read always start with intuition behind the idea, and then present definitions and proofs. Only some reference books, intended for look ups only, only enumerate formulas. I never understand why anyone claims that they only learn math by memorizing formulas.
Because they learn math in junior high where they really don't care about the subject, so it gets boiled down to "remember this to pass the exam", regardless of what the book says.
People claim they only learn math by memorizing formulas because for most, that's all the math they see before getting irreversibly turned off by the subject. Most people learn math by memorizing plug and chug formulas in high school. Aside from 9th grade euclidean geometry, I can't recall an instance where I had to derive anything in my hs math courses. College math courses, of course, are usually much more rigorous.
