Berkeley Lecture 2012

The first Berkeley Lecture took place in Physics Hall on the South Campus of NUI Maynooth at 4pm, Thursday, 26 April 2012. It was given by Fields Medallist Professor Timothy Gowers of Cambridge University.

Title Will computers ever be able to do mathematical research?

Abstract There is a widespread view that computers, while extremely helpful to mathematicians in a number of ways, could never do interesting research. The rough reason often given is that computers can only ever do what you tell them to do, so if they solve mathematics problems it will be because a programmer has had all the interesting ideas in advance. If this view is correct, then it suggests that there is a boundary between the routine tasks that computers are good at and the sort of research that is typical of what humans undertake. I shall look at a number of candidates for where this boundary might lie, arguing in each case that it does not in fact lie there. The conclusion I draw from this is that there is no boundary and that computers will in due course be better than humans at solving mathematics problems. However, this view is controversial and I do not expect to persuade everybody of its correctness.

The Berkeley Lecture will be an annual event at NUI Maynooth in which a talk in the general area of mathematics and philosophy will be given by a high-profile visiting speaker. It is sponsored by the Department of Mathematics and Statistics and the Department of Philosophy at NUI Maynooth.

This event is named after the famous Irish philosopher George Berkeley (1685–1753), who made major contributions to several areas of philosophy and had a keen interest in the philosophy of mathematics. Bishop Berkeley’s 1734 treatise The Analyst made a detailed criticism of the Calculus of Newton and Leibnitz. This caused a major headache for mathematics and over the next century, many great mathematicians tried and failed to overcome the problems highlighted by Berkeley. But, by highlighting problems that were eventually overcome, Berkeley’s criticisms ultimately benefited mathematics by putting calculus on a firmer footing and making it safer for use by non-experts by eliminating the possibility of error through plausible but incorrect arguments. It also made the subject easier to teach, although it is still challenging material for students!