Discourse on the interface of Matheatics and Physics: a panel discussion sponsored by DIT and the RIA
Chair). Brendan Goldsmith: The interface between mathematics and physics predates the emergence of the separate disciplines of mathematics and physics, but for a long time the relationship was perceived to be a somewhat one sided relationship with mathematics providing techniques and justifications which enabled physicists to develop further their justifications and insights into our understanding of nature suggesting interesting areas in which to find mathematical problems. The most quoted
... The most quoted examples of this are the interplay between the differential calculus and Newton's laws of motion, or Einstein's use of abstract concepts of geometry in his exposition of general relativity. There are of course many, many others. In more recent times, some would even say that situation has been dramatically reversed. For example, quantum field theory has had a significant influence in many areas of geometry from elliptic genera to knot theory and indeed Witten's work has provided direct connections between certain quantum field theories and topological theories in mathematics. And these developments continue apace. In some senses we are experiencing, really and truthfully the unreasonable effectiveness of mathematics in physics and equally the unreasonable effectiveness of physics in mathematics. Despite all this interesting and important collaboration, there are undoubtedly tensions that have surfaced. These are largely centred on questions of rigour, the nature of proof, philosophical questions concerning the very nature of mathematics, the social dimension of mathematics, the role of speculation etc, but these tensions of course are not new. One can think back for example to the early nineties when Paul Halmos wrote his very provocative article titled 'Applied Mathematics is Bad Mathematics' or indeed the much earlier article by Jack Schwartz at the beginning of the sixties; he wrote an article titled 'The Pernicious Influence of Mathematics on Science'. Add 1 to this the growing influence of computing and the fundamental issues arising from, for example, proving correctness of programs and software etc. and it would appear that there are a great number of issues to be discussed. Question: What do the panellists understand when they hear the words Mathematician and Physicist? Arthur Jaffe: I'm often asked if I'm a mathematician or a physicist. I like to think of myself as a mathematician when I work with mathematicians and as a physicist when I'm with physicists. I'm not really sure what the difference is except that some years ago there wasn't such a distinction between the two. A set of cultures has grown up though where you get a degree in one subject or the other and yet the ideas as Brendan outlined cross the boundaries in absolutely wonderful ways so that there has been this revolution bringing the two subjects together, which I think is not only historical but will last for many more years into the future. So I would like to think of myself, in answering your question, as both. Michael Berry: People occasionally ask me am I a mathematician or a physicist, I say yes. I've just learned a very nice expression this afternoon: I was reading the beginning of this nice book by David Wilkins on the correspondence between Tate and Hamilton, and in the very first letter from Tate, he states "I prefer to consider myself a mixed rather than a pure mathematician", and I think thats quite a nice expression. I'm paid as physicist, I don't prove theorems and I rather tend to define a mathematician as someone who proves theorems (maybe that's too old fashioned!) but if so, I'm not one. I was very generously described by Brendan as a mathematical physicist and I think that side of application is of people who prove theorems whereas theoretical physicists -I suppose this is what I would call myself -are people who use mathematical concepts and think about the world in mathematical terms but don't prove theorems. But it doesn't really matter actually.