The key to reading a math textbook is learning to be generative. In other words, it is not enough to be able to verify a proof, but to be able to construct the

The key to reading a math textbook is learning to be generative. In other words, it is not enough to be able to verify a proof, but to be able to construct the proof yourself. One of the most common failure modes is reading a textbook and nodding along as the author presents proof after proof. Most theorems, proofs, and definitions will sound similar to each other or give a tautological "why is this even a theorem" vibe [1], and reading by verifying is how to fall into this trap. (Cue a metaphor about NP-complete algorithms being able to verify a proof but (probably) not able to construct a proof in polynomial time.) This is why, like other comments have noted, doing exercises is so important. However, this is not the only way to train "generativity". I read textbooks very slowly by reading theorems and constructing the proof myself. (Hard mode: don't read the theorems and try to guess the next theorems and lemmas.) I like this approach because you can get feedback afterwards by reading the solution, while most textbooks don't have solutions for their exercises. It sounds like OP's strategy is another approach for being generative that I've yet to try myself. I like his approach because it seems to be more effective at filtering out a lot of the noise from linear reading and, instead, focusing only on the results and definitions that end up being used later. But no matter the technique, it seems that the common theme is to spend more time staring at your scratch paper than at the book. [1] https://xkcd.com/2042/ https://xkcd.com/2042/