[chongli]

This seems like a contradiction but I don’t think it is. What it’s really saying is that experience is a precondition for intuition.

When a high school student looks at a high school math problem they’re drawing on all of their experience in K-12 math to get intuition for how to solve the problem. When they leave high school to study math in undergrad they struggle because their experience is no longer sufficient. They’re faced with a lot more abstract problems and the demands for rigour are much higher. The problems also tend to operate at higher levels on Bloom’s taxonomy [1] than high school math, something with which the average high school student would have little or no experience. It is this unfamiliar territory where intuition is hard to come by.

After gaining more experience (later undergrad and into grad school and beyond) the intuition starts to come back. But it’s fundamentally a different kind of intuition. In high school math it was often a visual/geometric intuition that teachers were trying to build. In higher math it’s an intuition for abstractions and for the tools you need to attack problems. This is really no different from a programmer looking at a problem and saying “I need a hash map and then this problem is trivial.”

[1] https://en.wikipedia.org/wiki/Bloom's_taxonomy