There's an additional problem that you kind of glancing hit at, which in the US at least, there are at least two maths. Math for non-math major is grinding out

There's an additional problem that you kind of glancing hit at, which in the US at least, there are at least two maths. Math for non-math major is grinding out some class of problems until you internalize the mechanism for solving that class of problems. You continue, adding a new class of problems on top of the old ones. This eventually culminates in something like calculus, where you do algebraic transforms until it's in a form you know how to mechanistically derive or integrate. Math for math majors is usually about finding proofs. This also just requires a lot of work, but it has a very different feel that the math classes for engineering students (source: was math and CS major). I found that it wasn't very difficult to learn the same mechanisms someone programmed into Wolfram Alpha (though it was tedious), but being good at proofs requires 'mathematical maturity,' and this is something else altogether. There seems to be something innate here. I was decent at it, but it took a lot of work for me to get there. Others were better than I'll ever be and they were 15 years old while I was a college junior.