[OskarS]

I don't think that it's "memorization" that's the key: I think it's repetition. Learning anything, but especially mathematics, requires you to just sit down and solve problems over and over again. That is what builds the right connections in your mind, gives you a feel for the shape of the solution, and gives you good intuitions about problems.

Like: it's a pretty useless skill to have memorized what the anti-derivative of the cosecant function is. But if you solve enough integrals, and are familiar with the techniques, you can see the path to the solution of the problem, even without having memorized every single function and anti-derivative.