Do schools still teach Euclid? Yes, indeed they do, and my son did an excellent course on Euclidean geometry at high school in America. But sadly many British undergraduates in mathematics have never taken such a course, and are very unsteady on what exactly constitutes a proof. When they take an undergraduate degree, they have to get to grips with proofs in which the material is far more abstract than in Euclidean geometry. With the "new maths" they were supposed to be better at abstraction, but it doesn't seem to work that way. The "new maths" was a failure, but before you say the answer is obvious, that we should get back to teaching the basics, be warned that this is easier said than done.

The problem with teaching any subject is that the teachers themselves have to understand it. When you throw something out of the usual curriculum, the teachers of the future don't learn it, so it's not easy for them to teach it. In a subject like English it's not such a problem. A teacher who is unfamiliar with Shakespeare can always read a play and then do it in class, learning it better each time it is taught.

History, too, lends itself to this. But science and mathematics can be tough to learn well on your own, unless you're specially talented. In fact, mathematics is the worst of all in this respect. Ideally, a teacher should understand what he or she is teaching and a lot more besides. Most mathematics teachers, grappling on the very edge of their knowledge, are not in a good position to take on things they were never taught themselves. This was the problem with the "new maths", because most teachers didn't understand it well or see the point.

Perhaps in the 1970s it didn't seem to matter. If our children babbled about sets rather than numbers, why should we care? Who could overtake us? The Soviet Union? They had problems of their own, and even though their bright students got a fine education, they didn't look as if they were about to overtake the commercial and industrial might of the West. But today, China and India have no qualms about teaching the basics, and making sure that teachers understand them.