The simple answer, is practice. I know this is absurd sounding, but it really is the goal here.
While I agree that you should continue down the path of Math, there's other ways to practice abstracted thinking. Pick up some kind of artistic hobby. Painting, music, poetry, story telling, etc. These are all just things that force you to think creatively. Whatever you find interesting. It probably isn't a coincidence that a vast number of high level practitioners in science were also artists in some form or another (Einstein, Newton, Feynman, etc). Abstract thinking is often associated with connecting ideas from different subjects (abstract: disassociated from any specific instance ).
Additionally, focus a lot on creating analogies for things you are studying. This has 2 major benefits (to you). #1, it helps you remember. #2, you have to abstract a concept to create an analogy. Remember that the point of an analogy isn't to be precise, but rather to create an elegant means to abstract a concept (this also is why they are good for communication). An analogy primes you to remember a concept, it doesn't describe it exactly. After all, that high precision is difficult to express and comes with a lot of assumptions.
Lastly, another pure math method: study abstract algebra.