So in a way, I allowed myself to be a mechanical executer through the rules of algebra/calculus I've used, and then I re-engaged my intuition to understand what is happening.
It might even be my unwillingness to accept the mechanical approach purely that poses a big hindrance to fast tracking a lot of learning in this domain I have to do. Maybe I should just shut up and calculate as they say, but it's hard.
This just makes it all the more true that learning "languages" is the best way to become smarter. "Smarter" is a weird personal word here, but I'm at a loss for a better way to put it. What am going for is: languages can be an abstract lever that allows our limited cognitive potential to build culturally, which is distinct and will definitely interact with the knowledge ladder, but in a distinct way. "Languages" here are more general than just the textual/oral/syntactic, and am not talking about Russian/Arabic/French either.