Abstract math (type B) is a very rigorous discipline that underpins the other kind used by engineers (type A). Type A is indeed learned by repetition along with understanding. It is very important to simply do the math to become better at it and understand what you can expect from your calculations.
Type B on the other hand far more about understanding. You will never understand the theory of a mathematical space and how to apply it, by simple repetition. That is a far more theoretical and creative endeavour. You need to learn it and apply it to understand it. I suppose you could call the process of applying it some kind of repetition, but in my opinion the insights comes from applying it to concepts you already know.
A formal learning path is a very good idea, because people with more knowledge know what order you can progress in, in such a way that you actually apply your knowledge in a natural way and build on previous learnings. And it is definitely a huge help that teachers can help you guide your learning when you are stuck.
Proofs in abstract algebra, for example, require the ability to quickly and correctly manipulate symbols on paper (using already discovered rules/lemmas/theorems).
The repetitive practice is in this manipulation of symbols. It takes a long time and deliberative practice to learn this skill. You just practice by doing symbol repetition in different contexts, instead of doing the same thing over and over again like multiplication tables, because your symbol manipulation abilities have to be general [1].
If you try to teach, you will quickly discover that there is a wide difference in this ability for math majors by their final years. And the students who have poor symbol manipulation abilities inevitably struggle at the higher level concept application, because they keep making mistakes in the symbol manipulations and having to redo it.
[1] Contrast the training of 100m sprinters (multiplication table), who only run 100m on a fixed track that they will eventually race on, and the training of cross country runners (symbol manipulation), who practice on a variety of routes, because their races are on different routes.
Type B on the other hand far more about understanding. You will never understand the theory of a mathematical space and how to apply it, by simple repetition. That is a far more theoretical and creative endeavour. You need to learn it and apply it to understand it. I suppose you could call the process of applying it some kind of repetition, but in my opinion the insights comes from applying it to concepts you already know.
A formal learning path is a very good idea, because people with more knowledge know what order you can progress in, in such a way that you actually apply your knowledge in a natural way and build on previous learnings. And it is definitely a huge help that teachers can help you guide your learning when you are stuck.