If you don’t have a good intuition for and understanding of the concepts, how can you know when it’s appropriate to cut corners / use various approximation techniques on messy data? Or how can you combine a bunch of techniques for real world applications without doing something nonsensical?
Good point. I see what you mean and I agree that having an intuitive understanding of math concepts helps us choose the right tool for the job, but as soon as that decision is made, intuition doesn't play much role anymore. I really wanted to think that intuition (or even learning about the history of various math concepts) would be useful somehow, but every time I would end up getting lower scores than students who would just memorize the formulae and were able to calculate things quickly.
Well, I think I know what your mistake is, because I made the same mistake for a long time before I realized the error of my ways.
Intuition and deep understanding is important, and you won't go far without it. It's arguably the most important thing. But memorization / "knowing" things is important as well, and if you avoid doing that completely, you're just like a two or three legged stool. You need both, for true mastery.
I can't persuade you of this on my own, but if you ever trust something you saw on the internet without proof, hopefully this is the one thing! Haha.
I don’t really understand this critique.