But when it comes to how did it affect my career, I think the answer is really ‘not at all’ because I was here doing… involved with teaching, which is what I wanted to do, and there were no offers coming through that really attracted me particularly because Cambridge was the place to be. We get the best students, as… as I think the rankings show, and teaching and researching here in Cambridge, I can’t… can’t really think of… of a nicer life. I think Cambridge colleges play a very valuable role in teaching young scientists because you… you have that close contact, which other universities seem… seem not to have, Oxford perhaps, but we have this supervision system where you meet students, not quite on a one-to-one basis but on a… on a three-to-one basis typically, where you give them weekly tutorials and just talk physics. And if they’re good students they’ll ask you difficult questions and I think I can say that really I learnt most of my physics by teaching it and answering questions and supervisions because that’s where you get the… the really penetrating questions that… that good students ask you. And preparing for supervisions is… is a wonderful way of… of really understanding the subject. I’ve… I’ve been involved with college teaching all my life and when I was first a graduate student I was… I was starting to do it. And I think I really understood the lectures, my own physics teaching for the first time, when I had to teach it to other people. It… that one-to-one contact is an extremely valuable thing and you sometimes have very brilliant students – you try and teach but they often… often teach you. The student I… I remember from Churchill College who was a bit like that was Brian Green, who was one of the founders of string theory, a brilliant… a brilliant theoretician. And as a student he was always… could also… always answer the numerical questions quicker than I could usually and especially the ones on relativity and suchlike, but… because I wasn’t involved in that professionally. But when I asked him to explain what he was doing, he could… he could always write down the mathematics and get the right answer, but I said, ‘Can you explain the physics of that?’ And he was terribly bad at trying… at explaining the physics, and so I… I think there is a division in physics between… between people who sort of have mental images of what goes on and… and people who… juggle equations in their head. And Brian Green, of course, because he’s one of the inventors of string theories, is the equations man and he thinks in terms of equations, not in physical models. And that could be an advantage and it could be a disadvantage because modern physics is a very mysterious subject and following the mathematics through to its conclusions is a very necessary feature of it. And… and if it doesn’t make sense, maybe that’s just because you’re not… you can’t get your mind round it, but the mathematics is the key and he’s one of those sort of people. But… but you meet students of that calibre in Cambridge. I think he’s… he’s the one I… I remember most. But the fact that he couldn’t really explain what he was doing was a revelation to me because it seems to me that you really… if you’re really going to get to the bottom of things, you want to be able to do both. And looking back at Einstein’s writings, he was one of those people who could do both and I think he… he had a bit of a problem with… with mathematics just like I did, because when it came to writing down the mathematics that went to his general theory of relativity, I was interested to read in his biographies that he had to work hard at that and it didn’t come naturally to him.

And that reminded me of my experiences just after leaving university for the first time when… when I got involved with wartime research because the… mathematics I’d been taught in my first year at university in 1942, ’43, they tried to teach me Fourier analysis and so on, and I… I could see the equations and see… see the identities and so on, but it didn’t add up to anything that seemed to me to be a sensible thing to be doing. Why express one function in terms of other functions? It didn’t… it didn’t make a lot of sense. But during the war I had my 3 gap years and… and that’s when I really began to understand the basics of things like that because I suddenly realised in applying Fourier analysis that this is a way of breaking down what could be a really difficult problem into a whole lot of easy ones. And that’s essentially what Fourier analysis does. And when I’d seen that, the penny suddenly dropped and I thought, yes, this is a wonderful tool and I could see how to apply it and I was interested in that sort of thing evermore. But that was something that the mathematicians hadn’t managed to teach me when I was taught about Fourier analysis. It was just a mathematical identity: you can express this function like this in terms of this way, and… but they didn’t say why that was useful and so on. And that came back to me, actually, later on as a… as a teacher when I… I was giving a popular lecture and I talked a little bit about some mathematical functions I’d been using. And a mathematician came up to me after I’d given this popular lecture and he said, you know, you’ve taught me more in half an hour in your lecture – which I’d just dashed off – you’ve taught me more in that half hour than I learnt in a whole term from my mathematics lecturers. So I began to feel encouraged by that, but there really is a… if you’re really going to understand something, if you can put it in physical terms, it’s so much… so much better and even… that works, even for mathematicians. So that gave me some encouragement that the sort of teaching I was involved with, which I’ve always taken great care over and spent time on, is a really worthwhile thing to do.