True, looking at real proofs is what changed the game for me.
Before I actually went through 3-4 books on basics of proofs, math felt... almost meaningless , a game of remembering the right thing at the right time.
Saying that as somebody who oscillated between being "good in math" and "top in class" for all 18 years of studying.
To me proofs never where the interesting part of maths - the ideas and intuition which made the proof possible were.
Proofs were a way of formalizing something and, well, making sure the intuition was actually correct, but they were just a tool and not the game itself.
The best math teachers/professors I had were the ones who focused on the ideas .
Yup, and once again, it depends on how we learn. I'm a strongly "learn by doing" kind of person. For instance, I'd get almost nothing out of reading a math book that was full of ideas but no problems or proofs. Doing problems and proofs is how I wrestle with the structure of the subject matter, and internalize the ideas.
Before I actually went through 3-4 books on basics of proofs, math felt... almost meaningless , a game of remembering the right thing at the right time.
Saying that as somebody who oscillated between being "good in math" and "top in class" for all 18 years of studying.