[Green_man]

I'm very curious about the type of math you have learned this way. Every math class was heavy on repeated exercises and memorization, but real understanding didn't come until outside of class (or after the semester) where reflecting on larger ideas lead to mental connections and analogies. I'll freely admit that I have to look up the integral/derivative of simple trigonometric functions every time, despite every attempt from the instructor to hammer those in during Calc II. Doing hundreds of integrals on homework and study guides kind of worked to learn those rules, but only imperfectly and temporarily. Doing hundreds of exercises over and over again has been even less useful for my later math classes. If some proof doesn't make sense, the next step is not to go through 100 examples, it is to break down the pieces into logical structures that are recognizable. All real understanding of math fundamentally works this way. (disclaimer, my math past calc/linear algebra has been in CS classes, so I'm definitely open to hearing how those from other backgrounds or those with more formal math education disagree with me)

If you think you understand some mathematical rule, but can only show 100 problems from memory, you don't actually understand it that well. If you can convincingly show why no counterexample exists, then you understand it in the strongest possible way.