An effect of learning while building the same theory you are learning is you start seeing deeper insight into why things are defined the way they are. Whenever I encounter someone who criticizes the mainstream frameworks of mathematics or physics, it always turns out that they have some very fundamental misunderstandings about the basic issues. Don't get me wrong, I know plenty of people who study alternative foundations for mathematics, they are called Set theorists (😂😂😂) and they don't have much grievance about the mainstream framework, because its limitations are known by everyone in the field.
😅I totally agree. all my fav teachers are the ones who build the theory with us.(my discrete math, numerical analysis, linear algebra and analysis2 teachers) Are you their fav student?
I'm not sure they have favorites :)
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