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I really like the collection of problems, but I'm not sure it is easy to teach this kind of problem solving. I, for one, would love to try someday. (I'm a mathematician teaching at a large research university in the US, and most of the courses I get to teach are not anything like this.)

I'm also not sure this can completely replace the more "traditional" way we teach math, which is not to say I don't think it has problems (there are lots). If I may make an imperfect team-sport analogy, traditional classroom teaching of mathematics is all drilling and very little scrimmage / play. These problems are sort of on the other extreme. If we are to (1) equip students with intellectual tools that they can use, and (2) convey, to at least a fraction of the students, the sense of beauty and joy that attracted many of us to mathematics in the first place, we would need a balance between the two. I get the impression that this is something like what Gowers is actually advocating, but I haven't had a chance to read all his blog posts on this topic to find out (will have to do that later)...

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