The way I often say it is that most of people's mathematical education - even most of the math that people take in college, up to about junior year - is mechanical and recipe driven. It's usually about "in this situation, do this to solve the problem." You don't need much actual insight into what's going on, you just need to be able to recognize the patterns and know when to apply what. This makes sense, since the vast majority of people who take even differential equations are not people who need that kind of deep knowledge - they're often engineers or scientists who need to know how to solve a particular kind of problem when they encounter it.

In undergrad, I thought I was good at math. Then I got to grad school and took grad level courses in algorithms and operations research. That was when I realized that I had learned - necessarily - mostly recipes, not fundamental mathematics.