The "top layer" of maths being this is one thing. Now imagine another layer of this. Then another. Then another. Then another.

At one point intuition helps to build out usage of the math itself. See stuff like "oh I can do rotations through matrix multiplication"-style ideas.

It is helpful for us to be able to reach for those tools quickly. The more tools that require advanced prep to use, the less we'll be able to use the results in easier contexts. Everything will be hard

Of course nothing really prevents people from looking for the simpler tools and proofs. Lots of math stuff starts off complicated and gets simpler.

Just important that this is still a goal in mind