> but on the other hand the best researchers/engineers I know have a huge number of facts and examples memorized and ready at their fingertips
The US is staunchly anti-memorization. It wasn't until I did a year abroad in a French university where the power of memorization was so obvious. One of the math students I spent time with told me it's the French tradition to "carry everything around in your head". They were studying symplectic geometry in their sophomore year of their bachelor's!
I don't understand where this coming from. In my experience learning and teaching math in the US, I've found it's almost _entirely_ about memorization. Calculus students are usually able to regurgitate algorithms for differentiation/integration, but can't answer the most basic questions about what they're doing really means.
This is just an aside. I'm not against memorization. I think memorization is the first step necessary for deeper internalized understanding since it lets you take the basic stuff and put it on autopilot so you can think about the rest that isn't as basic. That said my main complaint about US teaching of math is that that second step seems rarely to be taken and instead focus entirely on the memorization.
I guess our experiences are both anecdotal, but I'm having trouble wrapping my head around your idea that the US is anti-memorization.
This might be the case for k-12 and maybe lower level courses, but this was _definitely_ not the case for when I was taking group theory, real analysis, etc.
With that said, someone else in the comments mentioned that while it might seem there's an emphasis "regurgitation" it's mainly because going beyond that and really digging into the why of things is vastly out of scope for the class.
The US is staunchly anti-memorization. It wasn't until I did a year abroad in a French university where the power of memorization was so obvious. One of the math students I spent time with told me it's the French tradition to "carry everything around in your head". They were studying symplectic geometry in their sophomore year of their bachelor's!