I just encountered this quote from Salomon Maimon, and it expresses the way I have approached mathematics (which is I believe different from the way most people approach it). The reason I learned to study this way is that I believe so intensely what I believe, I must be careful what I believe. For example, it takes me long arduous effort to disentangle myself from other people's thinking flaws. So I had to learn to let my own intuition guide my understanding of new ideas, rather than letting the narrative of another thinker -- who may have accepted underlying axioms and premises which I do not accept -- carry my thinking.
In the first reading I reached a vague sense of each section, which through subsequent readings I then sought to make determinate, and by this to penetrate the meaning of the author. This is what is properly meant when one thinks oneself into a system. Since I had already used this method in mastering the systems of Spinoza, D. Hume, and Leibniz, it was natural that I would be led to think of them as a ‘Coalition-System.’ This I actually discovered, and by and by set it out in the form of notes and observations on the Critique of Pure Reason (GW I, 557 | LB 253).
This is from the Stanford Encyclopedia of Philosophy entry on Salomon Maimon.