Purpose of studying something.

What is the purpose of studying something? Knowledge? Well, yes. To the
extent that one is able to absorb enough ability to
read/write/understand things in written, studying, as in schooling, is
quite necessary and vital too. However, isn't it that the ultimate aim
of all this is to be able to "apply". One learns algebra, for example.
But the reach of algebra does not settle down to passing an exam and
moving forward to the next class with another myridad set of such
subjects to be digested, studied for the exams and to be forgotten
later. Sure algebra must be taught, no say against it. However, the
perspective has to be more resulting. One needs to absorb the abstract
nature of how things work in that domain and apply it to another one to
result something.
Let's say one reads a research paper, puts in considerable amount of
effort, hard effort. But in due course of repeated studying of the
research paper, one's mind gets tuned to that paper, with the thinking
getting limited to the first and the last pages of the paper. Hence, one
should not overdo. In terms of Pattern Recognition systems, this could
be called overfitting in which the (PR) system learns just a bit too
much from the training data (the research paper in this case) and gets
too nicely suited to it that it fails to correctly classify novel inputs,
which actually was the aim in the first place.