Math progression looks roughly like the following:
1. "Concrete" math, where you learn how to manipulate mathematical constructs, usually guided by worked examples. Little proof involved. (up to advanced HS / junior college level)
2. Proof driven math, use of worked examples becomes more rare (undergrad math)
3. Highly abstract math, where worked examples are more or less entirely abandoned (grad school math)
The vast majority of world will never be exposed to math beyond (1), and even people in the STEM field will only be limited to (2). You almost need to study math at a high level, or something very adjacent to math, in order to reach (3).
But it should be mentioned that one part of why worked examples diminish as you work your way up, is that you're kind of expected to make your own examples - meaning that you can take highly abstracted mathematical constructs/objects, and relate them to something tangible.
Some people have no problem learning math that way, while others struggle. I personally struggled to learn math without any examples, so getting my mind into graduate level math was rough.
Luckily there are so many resources to higher-level math, these days. You're not bound to a handful of "bibles" that are filled with "... is left as an exercise for the reader"
1. "Concrete" math, where you learn how to manipulate mathematical constructs, usually guided by worked examples. Little proof involved. (up to advanced HS / junior college level)
2. Proof driven math, use of worked examples becomes more rare (undergrad math)
3. Highly abstract math, where worked examples are more or less entirely abandoned (grad school math)
The vast majority of world will never be exposed to math beyond (1), and even people in the STEM field will only be limited to (2). You almost need to study math at a high level, or something very adjacent to math, in order to reach (3).
But it should be mentioned that one part of why worked examples diminish as you work your way up, is that you're kind of expected to make your own examples - meaning that you can take highly abstracted mathematical constructs/objects, and relate them to something tangible.
Some people have no problem learning math that way, while others struggle. I personally struggled to learn math without any examples, so getting my mind into graduate level math was rough.
Luckily there are so many resources to higher-level math, these days. You're not bound to a handful of "bibles" that are filled with "... is left as an exercise for the reader"