I want to start by explaining some of the terms I shall use in this lecture. First, there is pure mathematics. Anyone who has done Ordinary Level Mathematics has some idea of what pure mathematics is about. Degree, or postgraduate pure mathematics for that matter, is—to quote A. N. Whitehead—“the science concerned with the logical deduction of consequences from general premisses”. The humbler algebra and geometry of school mathematics is concerned with exactly this, or should be. And in both cases, it is all done, at least in principle, for the fun of the thing with no application to the real world in mind.