The Definition-Theorem-Proof style is just a way of compressing communication. In reality, heuristic / proof-outline comes first; then, you do some work to fill the technical gaps and match to the existing canon, in order to improve readability and conform to academic standards.
Imho, this is also the proper way of reading maths papers / books: Zoom in on the meat. Once you understood the core argument, it is often unnecessary too read definitions or theorems at all (Definition: Whatever is needed for the core argument to work. Theorem: Whatever the core argument shows). Due to the perennial mismatch between historic definitions and theorems and the specific core arguments this also leaves you with stronger results than are stated in the paper / book, which is quite important: You are standing on the shoulders of giants, but the giants could not foresee where you want to go.
The Definition-Theorem-Proof style is just a way of compressing communication. In reality, heuristic / proof-outline comes first; then, you do some work to fill the technical gaps and match to the existing canon, in order to improve readability and conform to academic standards.
Imho, this is also the proper way of reading maths papers / books: Zoom in on the meat. Once you understood the core argument, it is often unnecessary too read definitions or theorems at all (Definition: Whatever is needed for the core argument to work. Theorem: Whatever the core argument shows). Due to the perennial mismatch between historic definitions and theorems and the specific core arguments this also leaves you with stronger results than are stated in the paper / book, which is quite important: You are standing on the shoulders of giants, but the giants could not foresee where you want to go.