And there are bridges. Two fields that should be part of early school training are architecture and music. Goethe said, when going to the temple of Sagesta in Sicily up on the mountain, “Now I know the gods have visited man.” It is perhaps the most perfect temple built. Henry Adams said when he wrote his book on Chartres, “Now I know that man’s aspirations can reach to God.” I hope many of you, like myself, have been to Bilbao to see the Guggenheim Museum. It will stand with Sagesta. It will stand with Chartres. It soars into infinity. I can’t put it any other way. The light travels along the walls, reshaping at every hour as the sun circles. There are areas of silence in it that have an indescribable power and beauty. At every moment it is counterintuitive. The architect has put the heavy on top and the light below it. When you read Mr. Gehry’s notes, and I hope you will, he says, “Careful, I didn’t do it.” He names the computer program in California that, far beyond the present possibilities of the human cortex, can figure out what critical curves are possible for walls of titanium. It can tell him how the light will move in different months of the year and different hours of the day. It will tell him – apparently a fantastically difficult thing – what happens to sight lines and noise when you have a lot of people in the museum, when you have a few people in the museum, or when they come from one hall to the other. This is entirely beyond our present computational mental abilities, but it is open to the computer. Of course, one wants to say to him, “But, Sir, you asked the right questions and that is an immortal achievement.” But it is already something very different from the architects of Chartres and Segesta To come somewhat near it, to teach children and ourselves what Plato knew by heart: the way in which architecture and mathematics play together with space and volume and light and sound is one possible program. The other, of course, is music.

From Vladivostok to Tierra del Fuego, on the Walkman, they are listening to the same hit as they walk down the street. Levi-Strauss defined this as “Le mystère suprême des science de l’homme,” the supreme mystery of the sciences of man, “l’invention d’une mélodie,” the invention of a melody. Music is a totally universal language. Children are magnificently good at it and responsive to it. Also, and I quote Boulez, “So much of my music now can only be fully understood by those who can read an algebraic algorithm.” Again, joy, the wonder, the fun of it, the marvellous fun of it, so much of which has gone out of traditional forms of humanistic teaching. These are not, in any way, utopian or science fiction counsels. They can be shown to work. They demand the solution that you pay your teachers in school, your teachers of languages and mathematics, as much as a university professor and see that the society honours them correspondingly. We now, in England, have a death-trap situation. Cambridge is, along with MIT, Stanford, and Harvard, still primus inter pares in mathematical teaching. They are good on research, but the excellent go immediately for vast salaries into public accounting and banking: salaries which even at the start, outstrip what a professor can hope for at the end of his life. And the very bad go to teach mathematics.