The higher, the more useless. Chinese students are good at math, yet they do badly in creating.
I had a Chinese student 10 years ago who fit this statement. The problem was not in math but in the lack of the ability to create a problem worth solving. Research in math and science requires one to define a problem, work on a solution, and along the way ask critical questions about the problem that may lead to new problems. My student was working on a thesis that involved a lot of applied math, but after we agreed on an initial question, I found that he would solve the simplest aspect of the problem, but not see the new directions that initial problem led. I had to continually prod him towards each step in his thesis. In contrast I found that my American students were more likely to see the new problems in each solution and they needed far less prodding to follow leads that an initial solution generate.
So I wouldn't say that the higher math was useless, but if the study of higher math was not coupled with a curiosity to seek and solve new problems it could be wasted.
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