[cornel_io]

It's a bit shocking to me: I still remember all the concepts quite clearly from when I studied Galois theory ~20 years ago, to the point where I can run through a lot of the proofs conceptually in my head, but the vocabulary is GONE. Like, completely a blank, I don't remember almost any of the abstract algebra terms that all of this is expressed in.

It reminds me of the truth of the advice that my category theory professor gave us, that the definitions are both the least important and the most important things, simultaneously. They're the least important in that they're just words that wrap up very simple concepts, and merely knowing the definitions doesn't actually mean you can work with the concepts. But they're the most important thing in that most of higher level math really boils down to picking out the exact right set of definitions to use, at which point proofs tend to pop out as trivial and obvious statements using those definitions. And at a more practical level, you won't be able to read any math if the definitions are not ingrained, so you might as well get a head start and just rote memorize them if you want to succeed.

But it's interesting that the language is far less sticky in memory than the underlying intuition. My guess is that because the intuition is so much harder to develop, it wires itself in much more deeply than the words themselves, which can be pretty easily learned in a few hours of flashcard work.