Numeracy will move closer to centres of competence and we have been desperately slow and unimaginative about teaching mathematics, about introducing what Virginia Woolf called “the common reader” to its creative powers and beauty: that being the other great universal language. Please, let’s have no nonsense about Anglo-American being the planetary language. When I was at the Institute in Princeton as a young man, one was allowed, by the grace of Oppenheimer, to sit in sometimes on the seminars, even if you could not understand. I watched at the board some of the princes of the world, Japanese, Russian, and American, working together at top speed without sharing a word of each other’s language: Leibnitz’s great dream, mathematics with its dialects, its wit, its sadness, its grandeur, belonging to the whole world. Everyone could speak to the man next to him as they worked together. The most eerie and wonderful moment was when they laughed. Either, as I gather because it had gone wrong or because there is a wit, which we can’t fathom, as there is in many Haydn studies. Many Haydn cadenzas are funny and are meant to be funny. Music and mathematics: the two codes of universality.

All I am doing is quoting Plato, of course. We haven’t tried to understand how to teach. Give me any child from any background and I will put on the blackboard one, two, three, four, five, six, seven, eight, and underneath, the even numbers, two, four, six, eight, ten. I will ask the child, “How can there be as many even numbers as there are numbers?” I will try to have the nerve to let the silence settle, because it is out of the silence that there may come very slowly, tentatively, God knows, the spark of the question, of the wonder, of the exasperation which will lead, believe it or not, to the notion which Descartes says is the proof of God in us: the notion of the infinite, because only that can help you understand why these two series are homological, one to one to one. And there will be in that room children for whom the fire will start. And it need never go out if they are properly taught and loved, if they are not condescended to. And they don’t need to know that transfinite cardinal numbers are a damned difficult concept, far beyond me. They don’t need to know that. That’s how this demonstration starts. We can start there and stop at a much earlier moment, with the sheer joy of it, the sheer animal joy of understanding something infinitely deep.