Both proof and explanation seem to be important. Two experiences with explanation made a particular impression on me.
First I found it hard to get much out of a Real Analysis course when I was a grad student. Only partly because of lack of explanations, admittedly. Probably even more of a problem was another kind of cultural mismatch between physical scientist me and the math prof that taught the course. My interest was mostly that I was actually doing path integral Monte Carlo calculations (for my Chemistry thesis) and wanted to make sure I understood the fundamentals. The prof, like many (most?) mathematicians seemed to be more interested in investigating ingeniously weird boundary cases. So the course didn't seem to teach me much about the gotchas that might come up in actual statistics or numerical analysis, and instead more about the ingenuity of mathematicians in constructing absurdly farfetched abuses of e.g. the axiom of choice. But besides that cultural mismatch, lack of an explanatory framework sure didn't help. Thus, I was very happy decades later when I ran across Terence Tao's book on measure theory (available as a free manuscript online), which had a lot of the same kind of material with quite a good framework of motivation and explanation wrapped around its proofs.
I also like Vapnik's _The Nature of Statistical Learning Theory_ which as I understand it is highly parallel to a much longer proof-heavy version of most of the same material. I much preferred this book to the approach in my undergraduate course in statistics. Again, the difference wasn't only lack of explanations (also, e.g., not enough enough grounding in proof or plausibly provable propositions, and too narrowly based in a frequentist worldview assumed without any explicit justification), but the lack of explanatory framework sure didn't help, so later I welcomed Vapnik's explanations of his approach. I have never been motivated to read the proof-heavy parallel book by Vapnik, but I do find it reassuring that it exists in case I ever work with problems that were weird enough to start raising red flags about breaking the comfortable assumptions in my informal understanding of the statistics.
First I found it hard to get much out of a Real Analysis course when I was a grad student. Only partly because of lack of explanations, admittedly. Probably even more of a problem was another kind of cultural mismatch between physical scientist me and the math prof that taught the course. My interest was mostly that I was actually doing path integral Monte Carlo calculations (for my Chemistry thesis) and wanted to make sure I understood the fundamentals. The prof, like many (most?) mathematicians seemed to be more interested in investigating ingeniously weird boundary cases. So the course didn't seem to teach me much about the gotchas that might come up in actual statistics or numerical analysis, and instead more about the ingenuity of mathematicians in constructing absurdly farfetched abuses of e.g. the axiom of choice. But besides that cultural mismatch, lack of an explanatory framework sure didn't help. Thus, I was very happy decades later when I ran across Terence Tao's book on measure theory (available as a free manuscript online), which had a lot of the same kind of material with quite a good framework of motivation and explanation wrapped around its proofs.
I also like Vapnik's _The Nature of Statistical Learning Theory_ which as I understand it is highly parallel to a much longer proof-heavy version of most of the same material. I much preferred this book to the approach in my undergraduate course in statistics. Again, the difference wasn't only lack of explanations (also, e.g., not enough enough grounding in proof or plausibly provable propositions, and too narrowly based in a frequentist worldview assumed without any explicit justification), but the lack of explanatory framework sure didn't help, so later I welcomed Vapnik's explanations of his approach. I have never been motivated to read the proof-heavy parallel book by Vapnik, but I do find it reassuring that it exists in case I ever work with problems that were weird enough to start raising red flags about breaking the comfortable assumptions in my informal understanding of the statistics.