The first type happens when you are enthusiastically engaged in a topic, which LLMs will likely enhance.
The second type happens as a by-product of solving a, perhaps deeply uncomfortably, difficult problem. This is what people are talking about when they say LLMs will hamper human cognition. Instead of sitting there for an hour and struggling, people will instead reflexively give in and ask an LLM to solve it for them.
I think in most cases, understanding is the point. we don't expect students to derive general relativity before doing astrophysics. re-invention is only a tool for understanding
you didn't re-invent it, you learned it from a teacher and then practiced until you understood it to the required degree
If you can't derive a result in mathematics or physics from first principles you fundamentally do not understand it.
The flip side is even more interesting. There’s a great number of electrical engineers with significant physics backgrounds who don’t really understand how electricity actually works, but they can still solve useful problems. By understanding I mean they can describe what underlying physical phenomena reactance represents etc.