Weston: What do you see as the cause of the malaise in our mathematical education?
Kalton: One fact which people need to understand is that mathematics is hard. All reform of the curriculum is geared to the goal that it should be made easy. Maybe it is just hard, and the only way to reform under those circumstances is to ask for less and less. A lot of reform is based on the principle that "We can do it better." No reformer is going to conclude that the old, classical way of doing things is best.
Another problem with mathemtics is that, at its core, it is an anti-democratic subject. In a sense, we say to students, "You must learn this, and we shall explain later why." We also say, "You must solve these problems and their use will become clear after a while." Students spend two years studying the basic proofs in analysis and still do not see where this is leading them until they reach the borders of research. They have to believe implicitly in our guidance. But now this trust has broken down, and everyone wants to vote on whether or not something is taught. "What is the use of this work?" is asked. We who teach have to double back and try to find some artificial use for something. It is as if a two-year-old child, learning to talk, asked, "Why should I have to learn? What is the advantage to me? After all, aren't you going to feed me anyway?"
__ From an interview with Nigel Kalton after he received the 2004-2005 Banach Medal of the Polish Academy of Sciences. Kalton was a mathematics faculty member at the University of Missouri - Columbia.