Comment by skydhash
There's things that you need to know (2*2 = 4) and there are things that you need to understand (multiplication rules). Both can happen with practice, but they're not that related.
Memorization is more like a shortcut. You don't need to go through the problem solving process to know the result. But with understanding, you master the heuristic factors needed to know when to take the shortcut and when to go through the problem solving route.
The Dreyfus Skill Model [0] is a good explanation. Novice typically have to memorize, then as they master the subject, their decision making becomes more heuristic based.
LLMs don't do well with heuristics, and by the times you've nailed down all the problems data, you could have been done. What they excels at is memorization, but all the formulaic stuff have been extracted into frameworks and libraries for the most popular languages.
[0]: https://en.wikipedia.org/wiki/Dreyfus_model_of_skill_acquisi...
I think the problem is that in spots where the concepts build on one another, you need to memorize the lower level concepts or else it'll be too hard to make progress on the higher level concepts.
If you're trying to expand polynomials and you constantly have to re-derive multiplication from first principles, you're never going to make any progress on expanding polynomials.