The three levels Tao lists (roughly paraphrasable as novice - master - true master) can be applied to many other endeavors, e.g. art, martial arts, programming, as other point out in other comments. What I'd like to stress is the damage that's generally done in going from Level 1 to 2 in math teaching.

As a specific example take Analysis, generally taught using Rudin. I took this course in my graduate EE studies and detested it. I later thought about this and came to the conclusion that the main reason was the manner of exposition in Rudin where the classical approach is used: each chapter contains an endless sequence of lemmas, minor theorems, etc., one after the other with no discernible purpose and at the end of the chapter you get to prove a big result by using all that machinery. This approach, which dates back to at least Gauss (commonly attributed quote, which I couldn't find the source: "no self-respecting architect leaves the scaffolding in place after completing the building") not only is backward to the real course of events, it sucks the motivation by being so. At least it did so for me and for some other otherwise intelligent friends.