It's an interesting article. I agree with much but certainly not all of it. He is unreasonably negative about acceleration and competitions. (I agree that school maths should be more broad, and that different people can be successful on different time scales.)
An interesting part was this (page 5 section 7).
Mathematics is amazingly compressible: you may struggle a long time, step by step, to work through some process or idea from several approaches. But once you really understand it and have the mental perspective to see it as a whole, there is often a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics.
This is absolutely right. (It is also, by the way, why some can learn maths much faster. They are ready for higher levels of abstraction and generality, and in fact they find it easier.) Thurston continues
After mastering mathematical concepts, even after great effort, it becomes very hard to put oneself back in the frame of mind of someone to whom they are mysterious.
I don't think it is necessarily hard to put yourself in someone else place in this way. But it's important to keep this in mind. For those of us with mathemetically precocious children, we can sometimes be stumped when they have an unexpected blind spot where they don't seem to understand or realize something that we think should be "obvious".
