[rq1]

> “Why didn’t you tell me that?”

I got this impression on my own self while studying math in college.

I noticed it when I made the connection about the studied subject, wondering why didn’t the professor say it that way to begin with. Because everything made sense now…

After few likely moments I asked myself the question: was the last explanation really better or did I just happen to understand the thing at that particular moment?

Later on, you get the “better” explanation while practicing the art…

We’re usually not aware of the process of understanding itself.

[anyfoo]

It's important to note that sometimes in university or elsewhere, you are just getting rigorous definitions, and while those are unquestionable useful or important, they might be entirely insufficient to build the necessary intuition.

I've thought about this a few times, and written comments about it like this one: https://news.ycombinator.com/item?id=28122728

That being said, I do actually also literally rote memorize actual definitions and equations (using a flashcard program), because conversely, intuition is not enough. Rigorous definitions and "intuitive" ways to grasp math go hand in hand: One informs the other. It's immensely useful to be able to just recall complex definitions and equations while intuiting.

I think you hint at that, but often for me the definitions start out as "abstract nonsense" while learning them, and I just memorize them, but the further my intuition goes, the more the definitions themselves become crystal clear.