As one might infer from my user name, I am currently pursuing an autodidactic path in pure mathematics while awaiting the real math classes next year at university. I recently bought Dummit and Foote's (yes, I know this is a more "advanced" text for a beginner but my mentor in mathematics told me that I was up for the challenge) text to learn abstract algebra and while I absolutely love reading it and trying to prove the theorems (before I read the proofs)/do the exercises, I am having a hard time judging my level of comprehension.
For example, I had some success proving the first isomorphism theorem before I read the proof but I became stuck on the second isomorphism theorem. Once I had reached an impasse, I would scan the proof just to try to pick up on the "trick"/direction of the proof, then close the book and try to go at it again without looking at the proof. I've been fairly successful going about it this way and I've made it a point to drill myself when ever I have a spare moment of boredom to get a sheet of paper out, write down a theorem and then prove it off the top of my head (I wouldn't say it is from memory though as I always think through the logic of the proof, just remembering key points along the way).
So anyways, with all of that said, is being able to reproduce the important results of a text from scratch a good metric of my understanding? I will say that every time I work through a proof, I feel like I notice something new about it or I gain some degree of clarity about why the proof is structured a certain way. However I know that when it comes to mathematics, it is especially easy to delude myself into thinking that I understand something when I really don't. I have tried to be ruthless with myself and force myself to prioritize deep learning as opposed to superficial breadth but I am struggling to know when exactly I have achieved a deep understanding and how to keep this deep understanding while moving through the text. Any insight/experiences into the matter would be of tremendous value.
Also it might be worth noting that I currently attend a non-traditional high school where I get a great deal of freedom to work on what I choose so time is not really a factor for me.