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Inspirational chemistry teacher: Eric James

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Opening the gates of mathematics
Freeman Dyson Scientist
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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.

Born in England in 1923, Freeman Dyson moved to Cornell University after graduating from Cambridge University with a BA in Mathematics. He subsequently became a professor and worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics and biology. He has published several books and, among other honours, has been awarded the Heineman Prize and the Royal Society's Hughes Medal.

Listeners: Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

Tags: WInchester College, Cours d'analyse de l'Ecole Polytechnique, 1909, Principia Mathematica, James Lighthill, Camille Jordan, GH Hardy, Alfred North Whitehead, Bertrand Russell, Kurt Gödel

Duration: 3 minutes, 4 seconds

Date story recorded: June 1998

Date story went live: 24 January 2008