We had this library at the school which is - I visit there from time to time - the library is still excellent. It's in an old building with the right kind of musty smell of old books and there was there a great treasure house of books which, as far as we knew, nobody was aware of except us, I mean just the four boys. And Lighthill actually discovered this Cours d'analyse, which is a classic textbook of analysis written by a French mathematician, Jordan, about 1900 I suppose, in three volumes and they are still there in the school library - I verified that recently - and nobody knows how they got there. It seems very strange for anybody to put such a heavy textbook, all written in French, for English schoolboys - but anyway, it was there and Lighthill discovered it, and so we worked our way through the three volumes, one after the other. And that was opening the gates of mathematics in a way that very few people had that chance. And only many, many years later we found out that Hardy [Godfrey Harold Hardy], the great mathematician whom we afterwards got to know in Cambridge, had also read Jordan's Cours d'analyse as a young man and been inspired by it, and it also happened that he was a boy in the same school. So almost certainly it was he who put the books there, because, typical of Hardy, he did that anonymously. There was no record in the library that he had given it. There was also the Principia Mathematica of Whitehead and Russell which was not so illuminating but also great fun to go through. And that's also three fat volumes, and it's trying to reduce the whole of mathematics to logic. It's extremely pedantic, just full of enormously complicated constructions to reduce complicated things to the simplest components. And it was a monumental failure. It was demolished in the end, of course, by Gödel's theorem [Kurt Gödel]. The idea was that one could construct a consistency proof for mathematics by reducing it to logic, and Gödel proved that that is impossible. The whole thing was based on an illusion, but nevertheless it was fun to go through. So it gave us a feeling for what the foundations of mathematics were all about. And with an inkling that this is probably not the way to do it? Yes. We certainly understood that, I think, after going through the three volumes. There was clearly a difference between Whitehead and Russell on the one hand, and Jordan on the other. Jordan was really doing real mathematics, and Whitehead and Russell were not.
