Thank you very much, John, for agreeing to meet today for an interview. Before we start, I have to say that a few years ago you came up with the brilliant idea that we should interview people when they are retiring in order to keep a record of the thought of their memories in mathematics and their life. So my first question for you is how does it feel to be in the hot seat now that you've initiated that process? As a victim, yes. It's it's poetic justice.
It's very good. So I just wanted to have an idea of you early life starting in high school or before. When was the time that mathematics came into your life? I remember one or two instance. I remember I had a very good teacher at school who wrote an equation, sort of three plus, and then he put his hand over it and equals six. And he says, What's under my hand? And then he took his hand away.
And what we said three and he said, Will, could it x? He said, This is one of my first memories of mathematics. I thought that was a great idea. And the discovery of X. Yes. So that was early on. But at some point, presumably in secondary school or maybe before you decided mathematics was something of interest to you. What? I was naturally good at mathematics. And my brother, my I had an elder brother and my father was an engineer. And so my brother did engineering at Cambridge.
And so I decided that I would do something different in mathematics was a different thing. Yes. But right at the start, before you you studied in Cambridge or right at the time, you all do had a little spell in in real life industry in the British Aircraft Corporation. Can you tell us a little bit about that? Yes, I was working on what were called mishmash charts, which are now, of course, entirely computerised.
But at that time, it was you had to calculate at what engine rows you decided if you had an engine failure on takeoff, at what engine revs, you had to put on the brakes and. And if it happened after that, you would you would take off. So this is what I worked on. That was a mathematics problem that you were doing as an intern. Were you was it was it was more that it was not so it was a little bit of mathematics, but it was more computing.
So it was at the time when computers suddenly started getting much faster. So it's a time where industry needed teasing you with the men by computers, with people doing the computation. That's actually I sometimes I did what were called ghosts, which were at night you you you looked after the computer. And when it had a power failure, which would happen sometime, you had to go in and alter it and then it continued on. I see you were manually debugging. Yes. Okay, so let's go.
So you went to St John's in Cambridge, so I was aware two years, which was mathematics like in the sixties. Well, for me it was I found it and I suppose it's like many other people, you know, when you're at school your the best or one of the best and then you, you get to university and you find out there are so many really brilliant people. So St John's was a big mathematical college and it had in my fantastic mathematicians actually, and so I felt quite inferior to too many of them, I think.
And anyway, I was not very good at doing exams, so I didn't do brilliantly and but it was an incredibly exciting course. Oh are there any particular professor or pupil at the time that that's. Marlon Brando. Yes, I remember well, I remember lectures.
I went to one off lectures. I went to Dirac's last lecture as Lucasian professor, for example, and and I remember I was studying quantum mechanics at the time I had to supervisor and I said I was reading Dirac's book and I couldn't understand it because he says that do the world notice all according to the Schrodinger equation until you observe it? So why isn't this this chair observing everything all the time?
And I remember him saying, Well, you should leave thinking of questions like that to Dirac, which which I didn't think was a very good answer for that. But then when I heard Dirac speak, Dirac was talking about all the difficulties of his theory and maybe it would require advances in mathematical logic to take to cure them. So I was reassured that even he thought there were difficulties in my mind.
One of my first memories of reading Quantum Mechanics was finding Dirac's paper neutron and realising that the date of submission was the 25th of December. So he had worked for Christmas time, something like that. Okay, so you you finish mathematics then what's what's what are the options you have a degree with? Well, I had a degree, but I didn't have a very good degree. And some reason I wanted to I was convinced I wanted to do research so well.
I was lucky in that I applied to Oxford to do algebra and I was well, I was accepted to do a one year course. But since I. Didn't think I was very good at the exams. I decided to go somewhere else. And so I took a sort of easy option, which was to go to Sussex University, where there was a former school teacher of mine who was in the Applied Sciences Department. So I ended up working with him. Hmm. And at the time, you.
You entered in mechanical engineering, but you rapidly found that, again, mathematics was the real pool of us somewhere in between. Well, I was very I mean, many people have helped me, but I was very lucky because because the said school teacher, in fact, didn't really know anything about research, but he'd already had research students who. Well, not one very good research student, actually, who's more or less funded for himself. And he saw in me, I suppose, some kind of talent.
And he and he and he went to the dean of the engineering department and said that, you know, you've got to transfer this guy to, you know, so the same trouble that happened to him didn't happen to me. It was really, really great. And we were both very lucky because at that time that was David Edmonds was in the maths department and he was running a research program on partial differential equations and a lot of incredibly famous people were there.
So I remember I went with this guy, Mike Alford, to one of the lectures of Stan Pacquiao. He was just Deepak. He was giving a course, and it was the second lecture.
And at the after the lecture, we were just sort of chatting amongst ourselves, saying how wonderful it was, which indeed it was, because you could listen to Stone back and you understand everything and saying, What a shame it was that we missed the first lecture and he overheard us and came into, Would you like me to give the same the first lecture again to you? So we said, No, of course, but. Okay. And at the time I saw you, you were maturing.
So how did you come about you research topic or your interests was that. Well, my my former schoolteacher was interested in mechanics and I was in a mechanical engineering department. And so I started reading through those books, the introductions to these books, which are just wonderful, of course. So somehow I got this great enthusiasm for for mechanics, but I had no idea what to do, actually. And so then Robyn Knops came to give her a talk in this.
PGA, a program that David Edmunds was running. And we were talking to him, and I was saying that I hadn't got any project. And he talked to Stu Antman and Stu Antman came to some conference later. And and I remember it was it was extraordinary. So Michael Ford was was driving his mini car from the campus in Sussex to Brighton Station. And in the front of the car was Everett Douglas.
And in the back of the car was me and Stu Henman and Stuart and said, Well, our problem was telling me that you don't have a project. Well, here's something you could do. You can go and look at this paper by Dickie, and this is what he does, and this is what you could do to it. And this was just a complete revelation to me. I had never understood that anybody could understand research at this level, which is still true of still to today.
Yeah. So I remember we were talking a little meeting about wrinkling basis. I see what these guys do. It's a good question and I know how to do it better, but I don't know if it was the time to do it. So we had the you knew exactly what to do it with this problem in order to improve it. He wasn't quite sure it was the right questions. So it's quite wonderful to have so much ideas and to share with others. So you you see, this was on the dynamics of beams, something you couldn't really done much.
But I find it something very interesting in, in your approach, which has always been the duality that you can see in your work. It is this is starting with problems from engineering or elasticity or mechanics in general and trying to extract from its mathematical principle on the underlying principle. And I don't want to embarrass you, but here is a quote from a young John Ball, 24 years old, from his thesis.
And I think it's very interesting because I and I want you to comment on it because I see like the the seed of of what we did evolve later on. And it's on page two trying to explain what is your approach. And I think it's quite important even in the context of the time of the research in applied mathematics in the UK.
You said at this point synthesise that in contrast to the physical approximation used to obtain, this equation of deduction from this equation would be mathematically rigorous since all physical theories are in some way approximate. This is not an inconsistent approach where we to use an approximate mathematical techniques, it would be impossible to distinguish between shortcomings of the model and tools of the analysis.
Nevertheless, we hope that it will be possible to extend some of the methods to better model and more complex situations. So with how do you see that young John Vaughan, do you think? I'm not sure. That was entirely from my head. I think I've probably got it from Truesdale or somebody, but I still believe it anyway. That in a way shaped the way you approach science and mathematics.
Yeah, I think I think I think, you know, rigorously rigorous mathematics and theorems are tremendously important and applied mathematics. And and we see we see examples, you know, of numerical schemes that converge beautifully, but not to the answer to not the solution, the equations you think you're trying to solve and so on. So it's really, really important, particularly when when the equations have singularities or something like this.
So then you can run into a lot of trouble without some rigorous theory. It's not that I'm against non rigorous mathematics either, but but I think that it has a but what was was it a different view of the most accepted view of applied mathematics and mechanics at the time in the UK, yes, I had a quite a hard time from, shall we say, British Applied Mathematics.
At that time it was really dominated by Cambridge and there were just one or two people like Brook Benjamin Bryce McLeod, who were in some sense involved in applied mathematics and doing rigorous things, was really a minority and in some sense persecuted might be a strong but oppressed minority.
And I remember once I gave a talk in, in it's a meeting of British theoretical mechanics cloakroom, I think it was in Edinburgh actually, and it was after my work on elasticity and I was, I was saying what I thought that, you know, the, the, the, the growth conditions didn't cover the case of the new education material. And somebody I've never heard was, but I won't say asked this question.
He said so. So the reason you think that there's there isn't a existence for the new hooking material is because you can't prove it. So this is now my first encounter with a truly aggressive question where the reason is that the gross conditions were wrong. Yes. Yes, it is still problematic. It is still an open question. It's still an open question. Yes, very good. But I mean, probably can come back to that.
There's been quite an evolution in the landscape of applied mathematics in the UK since that period. Yes, yes, a lot. And you've you've come to play an influential role in setting a different type of agenda. But the it's. Do you still think you still see your feet of friction between communities or different approaches? Not so much now, I think. I mean, there was a period when there really was such a friction, but not now. I think it's it's over. So you finish your thesis and you go to Brown.
So Brown at the time must have been quite exciting. It was a big centre of applied mathematics, critical mechanics, right? That's right. And and this lovely old building really enjoyed being there. Is that would that an influence for those things to come?
Because in terms of your research, I mean, you have this interesting model to apply analysis site, but you went to the centre of dynamical system and later on in your life you were interested in a number of problem related to dynamical systems approach to infinite dimensional systems. Yes, my thesis work had strong connections with people like Jack Hale on the head of Loss and Marshall Slemrod, actually, who I think who'd been at Brown but had left.
And but when I got there, I it was I was on a postdoc and somehow I felt that I should. Try to do something perhaps more. Significant. And also, I think I was a little bit. Not ashamed, but worried about. The questions I'd worked on in my thesis where they really sort of good equations. And so I knew from a lecture that student one had given, I think in Newcastle, maybe that I'd been to that there was this problem of existence in elasticity.
So and when I went there, the fellows very quickly told me what the, the real issues were. And so then I started working on it. He went off to, to Greece and something. And I just spent these times long hours in the library. There's a wonderful library now, maybe libraries and also, you know, the places where you really spend a lot of time. But then it was a fantastic library. I could go back to all the old papers. And so I worked really hard on this. It was a very hot summer.
And, you know, so the seed of your work on the resistance theorem for elasticity was there and you come back to it. What? I did it. I thought that was all. I did it. And and I remember it was very, very hot. And I was one afternoon I was just sort of lying there trying to survive. And and and then I saw this. I sort of made this connection between determinants and volumes. And I realised that the volumes should be sort of.
Preserved under weak convergence because it was just the area inside the boundary. And so this was, I guess, the crucial that was crucial moment. You had the spark here also. So you, uh, after after that brief spell you would was six months or so in the in brown you come back and start that it what. Right away. Yes. Yes sir. And I was, I was that change what that was that was it was it was great.
We were in, in the building in Chambers Street and and Adam, I was in an office which was below the sloping floor of a lecture theatre. So, you know, people would be tapping their feet and boredom at the lecture on, you know, above your head and and were quite sort of clank, slowly steaming the pipes and so on. So it was an unusual place to be. So fairly soon we moved out to the new campus in record time. But Robin Knox had sort of created this department.
And. And it was. Very lively and I learned. More about continued mechanics from him. It was a it was a great time, actually. And eventually I had these I was so lucky. I had these incredible students and post-docs. Stuff on my life like image for art to shrink away. I mean, you could not hope for better people and argue with us. What's the secret ingredient, you think? I mean, you see sometimes in different feel.
Some people come together in a in a given place for a few years and create this centre. The change paradigm changed the way people think about a discipline. Right. And really see how do you see looking back what what were the ingredients that made that place special of the time? Well, it was a nice it was a small department. So it was a kind of family atmosphere. But I think it was it wasn't in some sense locks. Stephan Mueller, for example, he came on a while doing his undergraduate degree.
He came to do a year with me, and then he came back to do a Ph.D. So he obviously, in some sense enjoyed it. And Vladimir Sharrock, he came, he was interested in work at dawn and first ability, and he'd done some wonderful stuff on invisibility and he came for that. So I think it was just in some sense luck. You know, you, you, it has to be like serendipity and you cannot try to recreate it in that way or who writes it.
But it always depends. I mean, I've seen that in a few, few places, and usually it depends on a few individual, right? One is not enough, but you have two or three that are like minded and truly change. So that's where there Robin was. There was there. And you know, the main players that made the scene and we we had a lot of we applied for some grants and we had a lot of good visitors coming. I looked at our policy and many people Marshall Slemrod, Gerry Marsden and.
So it was an exciting time, but it was a small place that I think that's interesting because now big, it's beautiful. You know, we have all these centres for doctoral training and so on and I suppose I've come to understand that that's a good way of doing things. But well, these people's careers were not damaged by being in this small place with maybe not very good library facilities.
You know, it was having time to think. Yes, yes. So not you know, it's not the model we use now, but maybe somebody should think about. So it is I mean, you spend 23 years in area. To what? So you went through the rank. At some point it's you became professor, is it the professorship was professorship of apply. And that is is that a title you chose for yourself? I think so. Where you the first you think? I think you could choose your own.
Yeah, I think I want to know what was behind you is that is defining you feel or I'm not sure with I think that phrase was used at the time so it was just a natural. I probably didn't think about it very much because there was a chance. You know, you mentioned all the people you brought into the centre or what brought in the UK. There were it was not the typical UK applied mathematics or even mathematics in general.
You were bringing something different, right? It's the that place was a seat for the rest of the UK as time went by. I remember getting one person who gave a lot of support was Jemmy Wales from Warwick. I think that he saw that that was something interesting happening. So that was, you know, just odd comments like that are kind of good for one's morale actually. But but episode was SIRC.
I don't maybe I'll see. I think they gave us the money so it was it was not it was it was sort of institutionally blind in some sense. So it was it was good. And at the time there was the Applied Mathematics Community in the UK, but there is also the mathematics in the UK which increasingly recognised that as an important part of mathematics. Is that the case? Yes, I think so. I, I think it I mean, there was there were other factors.
There was some point there was an influx of Russians to doing sort of differential equations in the UK. They were working on maybe things I'm not myself so interested in spectral theory and so on. But it did, it did increase the, the, the mass of people who had this different view of about how applied mathematics could be done. But but but we didn't have so many students. I mean, people like John Toland and myself didn't have so many students that populated universities.
Most. Most of the people, I think, came from outside. I think that's still still the case. So when when you look back at his years at Earth, what's I mean? There's a great number of distinct work or branches of your work that you've that initiated at that point. Wright's work on dynamical systems, methods for elasticity, work on the ensemble of function interpretability and things like that.
So when you look back at it, was it did you see it as the most productive part of your academic life, full of maybe the most productive for the study, the ones to come? That's always difficult, isn't it? Because I think people always think that what they're doing is the thing at the time is the best thing. But of course, other people, they think think differently. Just when I look at the number of single author papers that you produce, they're indifferent.
You know, big papers sitting in very clear terms in theory, in a given field that become the first work, the reference work. You know, you work on cavitation only at the reference work and you can trace all of the work that came after. The same is true for a number of on the order of the topics that you started that you started at the time. So was it a productive? It certainly was a productive time. But how do you see it or do you remember it? That's what I remember.
I mean, one thing I remember is somebody we haven't mentioned is Jack Carr. Yes. So I was just you know, it was Memorial Memorial meeting and Edinburgh and we're very good friends and we would often go to sort of football games together and talk about mathematics. And and we worked together with Oliver Penrose, who was another important influence. So he came from the open university. And so that developed a new a new topic. And that's the work on the cognitive fragmentation equations.
That's right. But it was not just that because Oliver was the person who sort of sort of convinced me that it was okay to to work with non convex energy functions, even though apparently they might be denied by statistical physics. But since he was statistical physicist, this was a big reassurance. And is that what opened the doors to you work on phase transition that came later with Dick James. Well Dick was visit Dick was a visitor to Heriot-watt on one of these grants.
I mean he certainly was a sort of reassurance that that came because well, I'd met Dick before, but it was very interesting, actually. He he said. He asked me someday. Well, but what would I? A minimising sequence for energy looked like that didn't converge to a minimise. And so it was interesting. So I drew some kind of half space and some consonant gradient below there and then some kind of sequence like that, like this.
And he said, That reminds me of something. And the next day he came back and he said, That's an Austin Mountainside interface. So this is how it happened. I'm not under the moment where you can you can trace the spark. That wasn't the one discussion that made the other one or the other. You came about the problem of cavitation your long standing interest in singularities right now? I'm not sure. I'm not sure how.
I think it probably came from these growth conditions and seeing I mean, so what what could happen if. The growth conditions were not sufficiently strong and I began to realise that maybe an ex of a little max was something. And then I thought maybe of holes and I see because the growth condition is infinity, I realise of the opening the cavity right the stretched the divergence. So you have, you don't have to go to infinity to realise that it's there.
So actually my, my, my paper on cavitation was communicated by Brooke Benjamin and I, Brooke was a great expert in cavitation. His thesis was on cavitation interference and, and he told me a lot about these things. And so at that time, I think you could maybe have more influence on the publication process than you can now. So this paper got a got a pretty negative referee's report, I think it was from Rodney Hill, actually. So maybe it was not so not negative as I read it.
Anyway, I remember Brook taking very forceful action to get it to get this paper accepted. So I have to thank him for that. So here we are, two what's 23 years? And so what was your next step after that come about? Was that special connection with Brooke Benjamin? Well. I was very happy with her and I was really well treated as I have been in Oxford, that I should say. But. So I thought of I've been offered one of two things in the US, but I sort of decided I didn't want to go to the US.
So if I was going to move from Heriot-watt, which seemed eventually to be a good idea, just on general sort of grounds, it was probably to Oxford or Cambridge and and then this chair came up in Oxford. And so quite suddenly, quite suddenly I suddenly, of course. And. Yes. And so. So. Well, I didn't apply for it, actually, at that time. It was it was almost that if you applied for a chair at Oxford, you would. You would not get it. So. So I didn't.
I didn't apply. Eventually, I got some kind of feeler from somebody saying, well, might I want to apply? And eventually I sort of did it did apply at some level. And then I was offered it. And then it was a long kind of. Negotiation period. This was because I was first of all, I was very well treated at our ward and I was asked to and had to take a cut in salary to come to Oxford. And I was really mad about this. And so I was negotiating on this.
So I had this idea of it and not understanding anything about the college system that maybe if one because this chair was attached to Queen's, maybe if one chose a different college, I could maybe get at least twice my salary. So that was market. Then I was told that this would require an act of parliament. So this idea was was scotched. And but eventually I eventually I accepted and swallowed my pride.
So the chair of Natural Philosophy, the oldest science chair, and go with going back to the 17th century. Is there any other chair of natural philosophy that still exists that you know of? Well, that was the nuclear case Lucasian chair and Cambridge, of course, which was once held by Newton. But. And so there is I always feel that there is something special about the name natural philosophy so that it does it fits you you view of science and mathematics and the unification of both.
Yeah, perhaps. I think its main effect was that I get all this public publication stuff on books, in philosophy. I think by mistake, I think. But it's a it's a suit that fit fitted you in a way. Right, since it's coming in being professor of Metro. Yes. No, no, I was I was very happy to come here. And it's been a wonderful experience. So you come in Oxfords and you start developing around. You have a group mostly known in our partial differential equation.
Right. You've been an advocate trying to push let's get to the UK, which to start with it was very slow actually. There was a sort of one. I mean part of my negotiation sort of was that there was one position which was more or less in my gift I suppose, which, which went to go to Africa. So and he didn't stay such a long time. And then it was several years before things started to expand. No, we had a lot of support from from successive chairs of the department, liquid house, some house.
And so and we've got this what's called Science and Innovation Grant, which, which forms the Oxford Centre for PD and after that the CGT and PD. So. So. So then it became a, you know, a group with critical mass. But for several years, it was quite sort of delicate, actually. So when you look back at it, do you see it as something that evolved naturally or a lot of work in pushing it or fights that you had to go through?
Or is it. Well, I think I mean, Oxford has a unified department of pure and applied mass, which is one reason why I felt it had a sort of big advantage to Cambridge. But but still within it's a very big department. And of course, there are people in it who have different views about what. Applied maths means. And so those two are certainly tensions.
That's correct I think. But. I suppose slowly they may have dissipated, but a bigger factor was probably support from the top within the department, I think. But at the same time, by by the time you came to Oxford, of course, you work had been recognised both nationally and internationally, so you came with a certain way. So yes, I think my friends in the fields, you know. But you know, a lot. Nobody has so much influence in our.
I think I remember that before I came to Oxford, I asked Michael Atiyah, who, of course, had spent many years here, whether he had any advice. And he said, Well, don't raise your blood pressure by thinking you can change Oxford overnight. He was he was certainly correct with advice. So academically, intellectually, you come to Oxford, it's a different environment or the change your research or we've seen just as a continuation of. Yeah, I think it was it was a continuation.
Of course, it was possible here to recruit, if you like. High quality faculty, which would not have been so easy, whatever it was, probably, even though there were very good people there. So in some sense, everybody wants to come to Oxford or at least well, think with think of coming to Oxford. So that was a big, big plus about being here. I had good students here, but I wouldn't say they would necessarily. But the students I had before.
But I have I've had wonderful students and post-docs after. I think it was a it was an it was a natural progression, of course. And I was involved in some European networks. These were important influence on Trend Network. Was the US also with the with the US, the US to what should mention Europe and how important it was and still is to us. I see. So you had a number of very, very well-known research student in your life.
So what's what's your general philosophy? How do you deal with students about giving them problem or letting them come with problems? You have a general approach or advice. I think it depends on the quality of the student. And actually, I'm much less sort of worried about the. Ability of the student and some other people. I. What's important to me is that well-motivated. And so but I think how I treat students depends on some kind of assessment I have of their current background or qualities.
So maybe I might be more directive for a student who I think needs more direction. And of course, sometimes you have a problem which you really think, Well, I really would like to see somebody work on this or work with somebody on this. And and at other times, maybe you don't have such natural problems, but you think that there's some kind of area and you get to read in that sort of area, and then you try to develop a problem.
With with somebody, which I think is this has worked quite well in some cases anyway. So, yes, in the in the article about truce that you wrote with Dick James, you quote truths that, let's say, or two or 200 students. You see the truth that says us as long as as long as they're ready to work hard. You should be giving them time. But if they're not, they should be scorned. If they don't remember that I've tried not to scold students, but as you say it, it doesn't matter.
But the ability, it's the attitude. I think so. I think so. And it's amazing how people can develop their produce. And then we should be looking at the test course so closely. And I suppose, you know, my own my own career that I didn't do particularly well and in exams at Cambridge has always influenced me. I mean, so I, I know many, many of the world's best mathematicians and so in some sense and. And I know you know how quickly some people think.
I know, I think much more slowly than this. But then then there are for researchers, something different. You know, it's it's a question of what you work on. And the timescales are completely different. And there are different kind of qualities that can be successful, which are not tested in three hour examinations. So thinking faster process, that's a wonderful it's a wonderful ability to have and are so used to you or at least 50 years of living in the world of mathematics.
You've as you said, you've you've met a lot of mathematician, maybe most of the top mathematicians in the world. Is there anybody who really stands out that you have memories of that's, you know, the natural. Well, I just came back from Oregon, where I met Jerry Erickson, who's now 94. So he's one of my. Scientific heroes, I think. And you know well the really great figures in mechanics. So he he was very important to me and and we had some correspondence.
So at that time, people actually wrote letters, handwritten letters, and we had some very interesting discussions. And he certainly put me right on a number of things. Yes. And which is interesting. Right. Because Erikson was not one to collaborate, but he was. But he was ready to potatoes. But he was exciting. He was very interactive. Very interactive. And of course, when whenever you asked him a question, he would ask you a question. And it was. And he still does.
Yes. Yes, very good. So over the years, of course, your work is recognised and it's natural that you are asked to step up more for the community. And you've done a number of you had a number of important positions in the mathematical world, including being presidents of the IMU in general. How do you see that as a role of a more, I would say, senior mathematicians versus the time that you need to do proper research?
What's the balance there? Well, it's it's something that suits some people and doesn't suit others, I think. I suppose I. I'm not sure how I. Sort of got I mean I was four four I'm you I was on the UK delegation to to the international Congress and I suppose, I suppose that's how I began to. I said once I get interested in it, become informed by it and know some people. And I suppose it kind of grew from there. Yes. Obviously, some people are more natural.
If you like I say administrators, but. More natural for such positions than others and and at top. But that's just just the way it is. I've been very lucky to have these positions. I've enjoyed them immensely. And so you get to the I am you and you sit as a president. You said you you've made some change. I mean, the Fields Medal is something of a bit of a. Mystery, shrouded in great secrecy for various reasons.
So maybe you can give us some insight since you've seen the process from from from the inside. Well, I was twice on the Fields Medal Committee once as a member, and then when I was president, it always used to be the tradition that the president chaired the Fields Medal Committee. But when Jackie Williams was president, his son Pierre-Louis, was a potential candidate. So he felt he couldn't chair the committee. And and I think it was a did. And then for a couple of cycles this continued.
But we reverted to the president chairing chairing the committee, which I think is important because there are guidelines for the Fields Medal that have not always been followed. So for example, two important guidelines are that you can award from 2 to 4 medals with a strong preference for four. And another is that it should respect a diversity of fields. But in some cases, this is didn't didn't happen.
And I think this was one of the reasons why we, if you like, took back control of the process. So you feel you your contribution was to make sure that guidelines were followed? Well, yes. And well, that was that was maybe something I was so. There was also the question of the age limit, which was kind of interesting that you have to be under 40. So there was a question about exactly what under 40 means.
So if you go to the Army website, you can read what I wrote, which defines precisely what 40 to 40 means. Very good. Including the latitude. And that's okay. Very good. But at the time there was a singular event also that in terms of the Fields medal is that's one of the nominees for the Fields medal was Grigory Perelman's. It was he was awarded the medal. And the question knowing him was whether or not he would accept it.
Can you can you tell us about that? Yes. So. Well, Paramount proved the Poincaré conjecture, but at the time when the Fields Medal Committee had to make its decision, it was not completely clear that. Everything had been proved. This was one problem. But earlier than that it was more or less clear that whether or not he had proved the correct conjecture ahead, he was a very likely candidate for a Fields medal and was this kind of past history. So the executive committee of I am you considered.
What would happen were he to be. Awarded the Fields medal and declined to. Accept it. And we very soon came to the conclusion that, well, as far as we were concerned, he would have the Fields medal if he declined to accept it. And that was his business. Because if you think about the other alternatives, they were not tenable actually. I mean, you couldn't just say award three medals and not name who the fourth person was.
This would just be ridiculous. And and also we felt that it was important to. Recognise the piece of mathematics that if one didn't recognise this very important piece of mathematics and somehow would not be doing the job. So anyway, so in the in the end, so that was a kind of preliminary decision that was made, which turned out to be, of course, what actually happened. And. And then we, we, we decided to award my fields medal and.
Well, it was it's a tremendous story that you can read about in in Wikipedia, which is which is pretty accurate, actually. But at some point I. Called him up and said, Well, would you accept the Fields medal? And he said, No, I wouldn't. And I said, Well, can I come to Saint Petersburg to so I can understand the reason? He says, Yes, you can come. Okay, so and so you had to do it without anybody really knowing. Otherwise he would revealed. Yes, that's right.
And and and and the four years, not the four year cycle of the International Congress is, of course, the same as the four year cycle of the World Cup. So so, in fact, the day that I went to Saint Petersburg, England, were playing, I think Paraguay and the World Cup. So I went straight from the airport to some Russian baths to watch, to watch, to watch this game. But then I spent a couple of days talking to Powerman and he well, he maintained his his position and.
So it was a very interesting time. We walked a lot around St Petersburg and. And then there was, well, various other strands to the to the story. But but one was the article written in The New Yorker by Silvana Sau, who mentioned your trip was. Well, yes and no. It said it was controversial because because some prominent mathematician from Harvard didn't go. Yes, well, i11 thing that I was lucky that I had that I did. Prudent, if you like, was that I talked to Marcus de Soto beforehand.
So I knew that this was going to be some kind of. Reasonably big story. I had no idea how big a story would become, but and so he told me exactly how you deal with journalists. You know, you can you can say if you say this is off the record, they cannot quite anything at all. So most of the time I was saying that was off the record or it could be non attributable or something.
But the Harvard mathematicians who were quoted in civil Nassar's article maybe had not had the benefit of such such advice, but what, what, what terrified me was that they were going to publish this article with the night with the fact that Paramount had a Fields medal before the International Congress because the Fields medals are announced at the International Congress.
And so I asked her to ask the editor of The New Yorker not to publish until the day of the Congress, especially the electronic version. And he refused. But he did it, but he didn't publish until they more or less the day of the Congress or maybe one day before or something. It must have been by the time a more or less open secret. Oh, well, you know, there are people who know the people who don't know, of course. But it was obviously not likely to be the case.
But but at the time at the time, we still didn't know that he had proved the point. Correct. Conjecture. When did that come? Which is. Well, I mean, that would have been. A few months later, if you look at the citation for the Fields medal, it does not give credit for for freedom. Yes, we were pretty sure. Yeah. But there were these different groups and that was the story about the plagiarism. And it was it's a really interesting story.
It's not every day you have affairs or scandal in the world of mathematics and maybe the biggest in recent time, but it's also one of the biggest results to prove it. But it touched it. See, I thought that Perelman would get a bad press for. Seeming to be ungracious. Yeah, right. It's very opposite. He. He became some kind of popular hero of somebody with integrity, you know, turning down a prize in the process because he also got the, you know, the Millennium Awards or the cliff.
And then that that really was turning down money. And he turned down $1,000,000. Yes. So just for my own, this was in around 2006. So it's almost 15, 12 years ago. What's the situation now with Paramount? Yes, with Paramount. Well, I don't know. I don't think anybody knows. But the assumption is that he's not doing mathematics. But who knows? But for the iyamu, he has a Fields medal. Yes, he has a Fields medal. He could come and get it. And I think for the foundation, the money is there.
No, no. That money was handed over to the institute or a banker. Uh huh. Yeah, that is at his request. So it's probably not at his request. I see. Okay. Very interesting. So in your in your work, I mean, if you look if you look back again, you as as we said, you have interests motivated by science and you have but as you wrote in your thesis, you want to do rigorous mathematics.
And there is always a balance between the two. But the first question that often student asks us, how do you choose a problem to work on? What's what is your view about that? Which is. Well, I think. One thing is you should take responsibility for the model that you're working on. You shouldn't just say that. Well, some physicists have told me that this is the right equation and then you just work on them on the mathematics of this and don't try and understand the physics.
I think you lose a lot by this. I think I think that to get good new problems, you have to interact with people good if you like applied problems, you have to interact with with people who ideally do experiments. I think I think if you talking directly to experimentalists is very valuable, then you you cut out. Somebody in the middle who may have some sort of theory which is not but not so great if we make a mess of the beautiful film.
But of course, in talking to experimentalists or sand Santas in a different area, you know, that's a that's it's a very interesting thing to do. But it's it takes a lot of time to learn some of this language. And then you have to have this kind of mixture of. Confidence that you can say something about this particular field. Maybe could could be useful to that particular field, but also some kind of humility to, you know, because you don't understand this other field.
So it's it's a kind of difficult but interesting process, I think. And I hope you experience reception from the material science community or do they see your work in general? In general, it's been. It's been. Very good. It's a slightly. I mean, so I've worked twice. On sort of these modern static phase transformations which was interacting with material science and also more recently on liquid crystals.
So I think the liquid crystal community is perhaps more traditionally receptive of mathematics. So there was really no pushback at all. But for material science, there was a bit of a pushback. You know that you know what you're you're ignoring. You know, you're taking this idealised model and doing this, you're ignoring this, that and the other, you know, because materials are, in fact, a complex that's just unbelievably complex.
So you mentioned liquid crystal. You came about you started working about ten years ago. And I guess all of you come about that as a topic of interest, because I was asked to be external examiner of a polymer diamond as a thesis and Bristol and so. So I'd heard many talks in liquid crystals over the years from from Frank Leslie, in particular in Scotland and and Gerry Eriksson. So. And of course, it was in some sense similar to elasticity.
So it's a multi-dimensional directional problem, at least in statics. And so I. It was not such a difficult thing to sell in the cities, but it made me think about. This problem in a way I've not thought about before. And it's just, you know, one little detail and you start thinking about one little detail and then it turns into. Which underlines the importance of doing service. Things like examining things that made people die seem like a drag on your research.
Let's, let's let's you. You remained open to other things. The stimulus. So is how would you say what time you main research areas right now. Well it's I suppose on more or less half still working on modern static phase transformations and half on liquid crystals and the little new interest.
I've just. So sometime last December Jen Kay who was was a postdoc of mine in a turret what he was one of the organisers of Newton Institute program on image processing and service organising workshop and you could you give it it was like in the old days when you were assigned a topic to talk on which was elasticity and image processing of which which I think I know a little bit about elasticity, but nothing about image processing.
So, so now I've got quite interested in this because there really is a connection between elasticity and image processing, or at least there are some elasticity based methods. Yeah, sure. So maybe this is a new area now just starting.
And that's I mean, image processing is becoming increasingly important and it's naturally related to a lot of the big data fashion that we see is what's what I you've you would say, you know, people from outside would say you're a traditional mathematician because it's mostly theory improving and maybe working with people doing computation, but doing forward computation based on model of the universe. So how do you see that's the new era of mathematics or science?
Well, I think there's something genuinely exciting that is happening. On the one hand, of course, it's maybe. Like many sort of new things, hyped a little. What's striking to me is, is the the. It's as if traditional science and some of these machine learning methods are working in parallel universes. So, I mean, for example, if you. If you gave some machine learning program to the data for planets moving in the solar system. Right, which of course, historically, this is what happened.
You know, people had the data for and and well, would such a program, you know, get you Newton's laws of gravitation and Newton's laws of motion or so? So there are and well, it will probably do a very good job in predicting planetary paths, unless, of course, it reached some kind of instability, which would not which was not there in the original data.
So I think I think I think that there's a big challenge now to in some sense, bridge the gap between traditional science and these these these new methods. I mean, no amount of machine learning will will predict something that happens in a small region of parameter space, which the data doesn't cover. But nevertheless, it can help us make maybe we haven't learned to ask the right question, some of the right questions, but there's certainly an exciting and exciting time, I think.
Of course, it's, I suppose, a little worrying as a mathematician to. To see these developments and that. So computers will. Well, I increasingly able to check proofs and when they check proofs, oh, no doubt be able to find proofs. And I went to a talk at a meeting last week when somebody from, I think it was IBM was talking about programs for creativity and so on. So I think the role of mathematicians is going to change, maybe not so much in our lifetime, but in the lifetime of all students.
It will change really, really dramatically. Probably, yes. So one thinks that often mathematicians do as part of the natural evolution process, is that they're turning to either historian of science or philosophy of science in general. That's, you know, and I wouldn't say they pontificate, but they reflect on the entire field. It's something that I've not seen in new work is that you don't feel you are that project or you don't. It's not new kind of things in general.
You have natural philosophy in your title, but you resist philosophy of a role that would be I do resisted. I mean, I I'm actually I've always liked looking at old papers. It's amazing when you read papers that analysts at the beginning of the 20th century and how clearly they're written in prose descriptions of lumbago while something like this. It's it's really great to read to read these papers so I'm interested in the history of science.
And I think it's very important for people to sometimes go back to read to read some of these papers. But I've not felt. The urge to write things on the history of Silence of Trouble is like so many unwritten papers, not to say an unwritten book or uncompleted book that some I think probably if I feel that at some point that the creativity is dried up, I think it would turn probably into writing.
And this book I've been writing with Dick James for four years, that's probably more likely to be written for it. So apart from your role in being a good citizen of mathematics and science and promoting in various society, you've also been very active and I was always very impressed in helping developing countries scientifically or in the mathematics level. You describe your activities there and what what you do think it's important?
Yes. I mean, I suppose that something also I might do more of if and if I the creativity goes or it hasn't gone already. Well well, when when I became president of. I am. You know, one of the things that struck me was that the budget for helping developing countries was was just pathetic compared to the. The demands, the need. It's of course, things have changed now in that maybe 25 years ago it was largely a question of access to information.
Now, if you've got a. You've got a decent Internet connection, which of course not everybody has. Then you can access anything, you know, Sai Hub, you can get any, any paper sign up. So it's but of course, accessing the information is not is not enough. You need to know what to do with the information.
Right. I mean, I so I think the story I told you about when student one suggested this problem shows how, you know, unless, you know, personal contact from somebody who knows how to do it and it was done it themselves is absolutely essential. So especially with the amount of information. Yes. Yes. Where to look. Exactly. And so. So which are one of the projects I'm involved with is this mentoring African research for mathematics.
And so that's one of the ideas to link up people from UK and elsewhere with research groups and in Africa to, to try to, to help them. But, you know, it's a question of maximising the pool of human talent. So it's good for everybody. And and, of course, having good contacts with all sorts of countries is, I think, a factor for, you know, world peace, if you like. But you also done things at a lower level before research and all that with Tibet.
Yes. Well, you tell us a little bit about this activity. Well, my wife is is is from Tibet and. And so I visited three times. Each time I think also taking in the University of Leicester and my. My research student. By saying sorry. He's the only Tibetan who has got a Ph.D. in mathematics in modern times, and he did his Ph.D. here, and he's now back in Russia at the university. So you you've mentioned a few times you mentioned again to your wife of an award. You mentioned your family.
It's always a surprise for people sometimes that you can be a mathematician and have a well-balanced and healthy and happy life at the same time. So can you tell us what is what's the role of you family within within your own work or within your own lives? Well, I mean, you've you've met Cyrus, you know that. She's a very interesting. And I've been so happy to. Be married to her. But we're very different. We're very different people with different, different views on life often.
And and our children. Yes. It's it's it's it's of course, the great experience of life having children. But it's not always, not always easy. But that's how you like. But we but we we just like for the important thing is we all talk to each other. We're all good friends. So if we would like mathematics to be easy, you know what? You want it to be interesting. Just like your family life. I guess this cannot be interesting.
Yes. When? The last time you mentioned that to a very different person, I think I said I said, oh, you have? Yes, I agree with you on that one. So what would be you know, we always being pulled in different direction. That's and have to do a number of things every day. But what would be your perfect day if you could choose? It's you know. That's a difficult that really is a difficult question as well.
I mean, sort of mathematically, of course, it's when you finally solved the problem you've been worrying about for two years. That's good. But of course, that's good. And it's it's it's a it's a great moment, but then you've got to write it down. It is not it doesn't last as long as you might think. Right. Well, you know, and and there's always new questions, right. You know what little we said about that when you have that moment. Stop right there and go enjoy it. Because it might not last.
Well, it might, too, because that's what I thought. That's another point, of course, that often that often that happens. Yes. So you should enjoy the way it lasts. Well, thank you very much, John, for for taking this time. Is there any other memories you would like to recall? I think we've probably gone through it all through enough. Thank you. Thank you again.