They aren't buzzwords, they are simple ideas and don't have to be referred to with those terms if they are triggering you. The OP just wants interactive, flexible systems to learn math from, which I wholeheartedly agree with.
Okay, my bad, then. Can you tell me what exactly is meant by a "hackable" math learning environment? And how will a REPL (however it is realized) make learning mathematics better?
Imagine if all the proofs in your linear algebra textbook were done in Isabelle, Idris or something similar to that. Then you'd be able to interactively explore the proof, it would be unambiguous, and you would know exactly like it worked. If you don't understand how a C program generates its result, you could start a debugger and single-step through it. With a paper proof, how can you convince yourself that there is nothing missing in the proof? Maybe you think you understood, but you didn't.
The great tragedy of maths education is that people come out the other side and think "fill in the box" is maths. No, that is doing you sums, not living in the world of mathematics.
The filling in of the boxes is most fairly compared to finding the typo in the complicated regex, or the file with incorrect permissions on the web server
"Fill in the box" is not referring to sums. It's referring to extremely rigid homework where you fill out each step in a process to finding out a result very precisely. It coincides with the horrific bubble tests where you select 1 of 5 answers and there is no partial credit.
This style of learning is what dominates US schools now from basic arithmetic all of the way up through advanced calculus.
