The whole world is always on an exponential growth. You know, when I was starting off the... the number of universities was... was small, there were very few jobs, you know, the number of students would be smaller; so the number of people active in the mathematical thing would have been much less, both here and internationally. So... so obviously now there's much more activity, many more people, many more universities. Probably in terms of the number of really top level people, you know, doing frontier work and really pushing the thing forward, that may not be so much different. I mean I suspect it's not, but each of the people in that position probably have larger groups working with them, and so the total body of work is greater. And again there's... there’s the… the scenes shift, you know, the… or the current activities at any given moment, where the action is, change and it's... it’s moved, you know, areas from what it was probably when I was… although Cambridge, and to some extent… strength was traditionally in number theory. On the one hand with Hardy and Littlewood and others, and Mordell and so on; and in classical algebraic geometry with the Baker school and then with Hodge, and so in some sense those two strands are still... still there.

I think there's a kind of continuity in, you know, what you might call national cultural strengths which are very long-lived, you know, because you train people in your... your own image or your own field, they go on to do… perpetuate the system and there's a tremendous built-in reservoir of expertise. And so there's a natural tendency for countries to remain strong in their fields for probably hundreds of years. It's very difficult to change, unless you're in a place like the United States where everybody's always on the move and you can create departments out of nothing. But in... in Europe I think you'll find that traditions in this country and in France and in Germany… in Germany, of course, had the terrible upheaval of the Second World War, but despite that the traditional strengths of Germany are to some extent still present and they're... they’re deeply embedded in... in the culture. So that is really quite surprising.

So I think we're still strong in the things we were strong, even though the subjects have moved on, and they no longer solve the same problems, but there're still major areas and lots of activity going on. So I think the… I would say that the strength of British mathematics… of course when I was starting it was just shortly after the war and, you know, people were picking up the pieces, so it was still the reputation of the pre-war generation that was there, so one had to get restarted again. But it's... it’s probably as good as it was in... in international comparative terms as it used to be; hard to say whether it's any better. Standards have risen, I mean there's more... more countries to compete with, but I think it's kept its... it’s kept its place, I would say, in... in the areas where it, you know, always was strong and doing... doing good work.