1 00:00:12,610 --> 00:00:17,020 Thank you very much, John, for agreeing to meet today for an interview. 2 00:00:17,620 --> 00:00:24,669 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 3 00:00:24,670 --> 00:00:32,500 they are retiring in order to keep a record of the thought of their memories in mathematics and their life. 4 00:00:32,920 --> 00:00:39,370 So my first question for you is how does it feel to be in the hot seat now that you've initiated that process? 5 00:00:39,730 --> 00:00:42,940 As a victim, yes. It's it's poetic justice. 6 00:00:43,370 --> 00:00:56,050 It's very good. So I just wanted to have an idea of you early life starting in high school or before. 7 00:00:56,710 --> 00:01:02,410 When was the time that mathematics came into your life? I remember one or two instance. 8 00:01:02,410 --> 00:01:13,540 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. 9 00:01:13,720 --> 00:01:17,830 And he says, What's under my hand? And then he took his hand away. 10 00:01:17,830 --> 00:01:23,860 And what we said three and he said, Will, could it x? He said, This is one of my first memories of mathematics. 11 00:01:23,870 --> 00:01:29,379 I thought that was a great idea. And the discovery of X. Yes. So that was early on. 12 00:01:29,380 --> 00:01:38,080 But at some point, presumably in secondary school or maybe before you decided mathematics was something of interest to you. 13 00:01:38,200 --> 00:01:45,670 What? I was naturally good at mathematics. And my brother, my I had an elder brother and my father was an engineer. 14 00:01:46,360 --> 00:01:51,280 And so my brother did engineering at Cambridge. 15 00:01:51,280 --> 00:01:57,240 And so I decided that I would do something different in mathematics was a different thing. 16 00:01:57,250 --> 00:02:03,460 Yes. But right at the start, before you you studied in Cambridge or right at the time, 17 00:02:03,820 --> 00:02:09,940 you all do had a little spell in in real life industry in the British Aircraft Corporation. 18 00:02:09,940 --> 00:02:18,310 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. 19 00:02:18,770 --> 00:02:25,480 But at that time, it was you had to calculate at what engine rows you decided if you had an engine failure on takeoff, 20 00:02:26,140 --> 00:02:29,500 at what engine revs, you had to put on the brakes and. 21 00:02:30,470 --> 00:02:35,150 And if it happened after that, you would you would take off. So this is what I worked on. 22 00:02:35,300 --> 00:02:38,300 That was a mathematics problem that you were doing as an intern. 23 00:02:38,300 --> 00:02:43,790 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. 24 00:02:44,540 --> 00:02:49,579 So it was at the time when computers suddenly started getting much faster. 25 00:02:49,580 --> 00:02:55,830 So it's a time where industry needed teasing you with the men by computers, with people doing the computation. 26 00:02:55,830 --> 00:03:03,260 That's actually I sometimes I did what were called ghosts, which were at night you you you looked after the computer. 27 00:03:03,740 --> 00:03:11,300 And when it had a power failure, which would happen sometime, you had to go in and alter it and then it continued on. 28 00:03:11,780 --> 00:03:17,329 I see you were manually debugging. Yes. Okay, so let's go. 29 00:03:17,330 --> 00:03:24,620 So you went to St John's in Cambridge, so I was aware two years, which was mathematics like in the sixties. 30 00:03:25,040 --> 00:03:31,009 Well, for me it was I found it and I suppose it's like many other people, you know, 31 00:03:31,010 --> 00:03:40,999 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. 32 00:03:41,000 --> 00:03:48,680 So St John's was a big mathematical college and it had in my fantastic mathematicians actually, 33 00:03:48,680 --> 00:03:53,870 and so I felt quite inferior to too many of them, I think. 34 00:03:54,770 --> 00:04:02,300 And anyway, I was not very good at doing exams, so I didn't do brilliantly and but it was an incredibly exciting course. 35 00:04:02,560 --> 00:04:10,040 Oh are there any particular professor or pupil at the time that that's. 36 00:04:11,570 --> 00:04:16,250 Marlon Brando. Yes, I remember well, I remember lectures. 37 00:04:16,250 --> 00:04:22,520 I went to one off lectures. I went to Dirac's last lecture as Lucasian professor, for example, 38 00:04:22,520 --> 00:04:33,049 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 39 00:04:33,050 --> 00:04:43,670 couldn't understand it because he says that do the world notice all according to the Schrodinger equation until you observe it? 40 00:04:44,330 --> 00:04:48,350 So why isn't this this chair observing everything all the time? 41 00:04:48,860 --> 00:04:54,320 And I remember him saying, Well, you should leave thinking of questions like that to Dirac, 42 00:04:54,920 --> 00:04:59,330 which which I didn't think was a very good answer for that. But then when I heard Dirac speak, 43 00:04:59,600 --> 00:05:08,800 Dirac was talking about all the difficulties of his theory and maybe it would require advances in mathematical logic to take to cure them. 44 00:05:08,810 --> 00:05:14,490 So I was reassured that even he thought there were difficulties in my mind. 45 00:05:14,780 --> 00:05:19,340 One of my first memories of reading Quantum Mechanics was finding Dirac's paper 46 00:05:19,640 --> 00:05:23,990 neutron and realising that the date of submission was the 25th of December. 47 00:05:23,990 --> 00:05:28,580 So he had worked for Christmas time, something like that. 48 00:05:29,510 --> 00:05:37,370 Okay, so you you finish mathematics then what's what's what are the options you have a degree with? 49 00:05:37,730 --> 00:05:46,820 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. 50 00:05:46,820 --> 00:05:53,959 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. 51 00:05:53,960 --> 00:05:58,590 But since I. Didn't think I was very good at the exams. 52 00:05:58,590 --> 00:06:05,069 I decided to go somewhere else. And so I took a sort of easy option, which was to go to Sussex University, 53 00:06:05,070 --> 00:06:11,410 where there was a former school teacher of mine who was in the Applied Sciences Department. 54 00:06:11,430 --> 00:06:14,430 So I ended up working with him. 55 00:06:15,120 --> 00:06:16,989 Hmm. And at the time, you. 56 00:06:16,990 --> 00:06:24,300 You entered in mechanical engineering, but you rapidly found that, again, mathematics was the real pool of us somewhere in between. 57 00:06:24,630 --> 00:06:31,830 Well, I was very I mean, many people have helped me, but I was very lucky because because the said school teacher, 58 00:06:31,830 --> 00:06:37,350 in fact, didn't really know anything about research, but he'd already had research students who. 59 00:06:40,740 --> 00:06:44,639 Well, not one very good research student, actually, who's more or less funded for himself. 60 00:06:44,640 --> 00:06:48,840 And he saw in me, I suppose, some kind of talent. 61 00:06:48,840 --> 00:06:55,680 And he and he and he went to the dean of the engineering department and said that, you know, 62 00:06:56,010 --> 00:07:01,930 you've got to transfer this guy to, you know, so the same trouble that happened to him didn't happen to me. 63 00:07:02,190 --> 00:07:12,419 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 64 00:07:12,420 --> 00:07:22,050 running a research program on partial differential equations and a lot of incredibly famous people were there. 65 00:07:23,070 --> 00:07:30,630 So I remember I went with this guy, Mike Alford, to one of the lectures of Stan Pacquiao. 66 00:07:30,780 --> 00:07:34,650 He was just Deepak. He was giving a course, and it was the second lecture. 67 00:07:34,770 --> 00:07:41,009 And at the after the lecture, we were just sort of chatting amongst ourselves, saying how wonderful it was, 68 00:07:41,010 --> 00:07:46,260 which indeed it was, because you could listen to Stone back and you understand everything and saying, 69 00:07:46,260 --> 00:07:51,270 What a shame it was that we missed the first lecture and he overheard us and came into, 70 00:07:51,270 --> 00:07:56,310 Would you like me to give the same the first lecture again to you? 71 00:07:56,640 --> 00:08:00,720 So we said, No, of course, but. Okay. 72 00:08:00,780 --> 00:08:04,030 And at the time I saw you, you were maturing. 73 00:08:04,040 --> 00:08:09,260 So how did you come about you research topic or your interests was that. 74 00:08:09,500 --> 00:08:15,260 Well, my my former schoolteacher was interested in mechanics and I was in a mechanical engineering department. 75 00:08:15,260 --> 00:08:22,790 And so I started reading through those books, the introductions to these books, which are just wonderful, of course. 76 00:08:23,300 --> 00:08:31,250 So somehow I got this great enthusiasm for for mechanics, but I had no idea what to do, actually. 77 00:08:31,940 --> 00:08:39,620 And so then Robyn Knops came to give her a talk in this. 78 00:08:40,620 --> 00:08:46,650 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. 79 00:08:47,940 --> 00:08:54,899 And he talked to Stu Antman and Stu Antman came to some conference later. 80 00:08:54,900 --> 00:09:07,020 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. 81 00:09:07,740 --> 00:09:09,840 And in the front of the car was Everett Douglas. 82 00:09:10,290 --> 00:09:18,180 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. 83 00:09:18,870 --> 00:09:27,510 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. 84 00:09:28,430 --> 00:09:31,610 And this was just a complete revelation to me. 85 00:09:32,030 --> 00:09:40,930 I had never understood that anybody could understand research at this level, which is still true of still to today. 86 00:09:43,130 --> 00:09:48,720 Yeah. So I remember we were talking a little meeting about wrinkling basis. 87 00:09:49,070 --> 00:09:54,770 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. 88 00:09:56,450 --> 00:10:00,439 So we had the you knew exactly what to do it with this problem in order to improve it. 89 00:10:00,440 --> 00:10:06,650 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. 90 00:10:09,020 --> 00:10:17,450 So you you see, this was on the dynamics of beams, something you couldn't really done much. 91 00:10:17,690 --> 00:10:25,610 But I find it something very interesting in, in your approach, which has always been the duality that you can see in your work. 92 00:10:26,060 --> 00:10:32,210 It is this is starting with problems from engineering or elasticity or mechanics in general 93 00:10:32,510 --> 00:10:37,820 and trying to extract from its mathematical principle on the underlying principle. 94 00:10:38,270 --> 00:10:44,750 And I don't want to embarrass you, but here is a quote from a young John Ball, 24 years old, from his thesis. 95 00:10:45,290 --> 00:10:53,779 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. 96 00:10:53,780 --> 00:10:57,620 And it's on page two trying to explain what is your approach. 97 00:10:57,950 --> 00:11:04,340 And I think it's quite important even in the context of the time of the research in applied mathematics in the UK. 98 00:11:04,760 --> 00:11:10,430 You said at this point synthesise that in contrast to the physical approximation used to obtain, 99 00:11:10,440 --> 00:11:18,950 this equation of deduction from this equation would be mathematically rigorous since all physical theories are in some way approximate. 100 00:11:18,980 --> 00:11:24,950 This is not an inconsistent approach where we to use an approximate mathematical techniques, 101 00:11:24,950 --> 00:11:30,620 it would be impossible to distinguish between shortcomings of the model and tools of the analysis. 102 00:11:31,040 --> 00:11:38,119 Nevertheless, we hope that it will be possible to extend some of the methods to better model and more complex situations. 103 00:11:38,120 --> 00:11:44,260 So with how do you see that young John Vaughan, do you think? 104 00:11:44,990 --> 00:11:53,090 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. 105 00:11:53,600 --> 00:11:58,250 That in a way shaped the way you approach science and mathematics. 106 00:11:58,260 --> 00:12:05,989 Yeah, I think I think I think, you know, rigorously rigorous mathematics and theorems are tremendously important and applied mathematics. 107 00:12:05,990 --> 00:12:13,040 And and we see we see examples, you know, of numerical schemes that converge beautifully, 108 00:12:13,040 --> 00:12:18,049 but not to the answer to not the solution, the equations you think you're trying to solve and so on. 109 00:12:18,050 --> 00:12:25,400 So it's really, really important, particularly when when the equations have singularities or something like this. 110 00:12:25,400 --> 00:12:29,870 So then you can run into a lot of trouble without some rigorous theory. 111 00:12:31,070 --> 00:12:39,979 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 112 00:12:39,980 --> 00:12:44,350 accepted view of applied mathematics and mechanics at the time in the UK, 113 00:12:44,360 --> 00:12:50,420 yes, I had a quite a hard time from, shall we say, British Applied Mathematics. 114 00:12:50,720 --> 00:13:00,650 At that time it was really dominated by Cambridge and there were just one or two people like Brook Benjamin Bryce McLeod, 115 00:13:00,650 --> 00:13:05,420 who were in some sense involved in applied mathematics and doing rigorous things, 116 00:13:05,440 --> 00:13:13,430 was really a minority and in some sense persecuted might be a strong but oppressed minority. 117 00:13:13,700 --> 00:13:22,669 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, 118 00:13:22,670 --> 00:13:29,059 and it was after my work on elasticity and I was, I was saying what I thought that, you know, 119 00:13:29,060 --> 00:13:34,190 the, the, the, the growth conditions didn't cover the case of the new education material. 120 00:13:34,760 --> 00:13:39,829 And somebody I've never heard was, but I won't say asked this question. 121 00:13:39,830 --> 00:13:48,260 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. 122 00:13:48,740 --> 00:13:57,260 So this is now my first encounter with a truly aggressive question where the reason is that the gross conditions were wrong. 123 00:13:57,260 --> 00:14:01,100 Yes. Yes, it is still problematic. It is still an open question. 124 00:14:01,100 --> 00:14:04,970 It's still an open question. Yes, very good. 125 00:14:07,070 --> 00:14:11,000 But I mean, probably can come back to that. 126 00:14:11,630 --> 00:14:16,970 There's been quite an evolution in the landscape of applied mathematics in the UK since that period. 127 00:14:17,030 --> 00:14:26,210 Yes, yes, a lot. And you've you've come to play an influential role in setting a different type of agenda. 128 00:14:28,800 --> 00:14:38,170 But the it's. Do you still think you still see your feet of friction between communities or different approaches? 129 00:14:39,820 --> 00:14:47,469 Not so much now, I think. I mean, there was a period when there really was such a friction, but not now. 130 00:14:47,470 --> 00:14:54,970 I think it's it's over. So you finish your thesis and you go to Brown. 131 00:14:55,780 --> 00:15:02,860 So Brown at the time must have been quite exciting. It was a big centre of applied mathematics, critical mechanics, right? 132 00:15:02,870 --> 00:15:08,110 That's right. And and this lovely old building really enjoyed being there. 133 00:15:08,560 --> 00:15:11,799 Is that would that an influence for those things to come? 134 00:15:11,800 --> 00:15:19,810 Because in terms of your research, I mean, you have this interesting model to apply analysis site, 135 00:15:20,230 --> 00:15:25,270 but you went to the centre of dynamical system and later on in your life you were interested 136 00:15:25,270 --> 00:15:31,150 in a number of problem related to dynamical systems approach to infinite dimensional systems. 137 00:15:31,300 --> 00:15:38,620 Yes, my thesis work had strong connections with people like Jack Hale on the head of Loss and Marshall Slemrod, 138 00:15:38,620 --> 00:15:43,569 actually, who I think who'd been at Brown but had left. 139 00:15:43,570 --> 00:15:52,960 And but when I got there, I it was I was on a postdoc and somehow I felt that I should. 140 00:15:53,890 --> 00:15:57,900 Try to do something perhaps more. Significant. 141 00:15:57,930 --> 00:16:04,760 And also, I think I was a little bit. Not ashamed, but worried about. 142 00:16:06,000 --> 00:16:09,480 The questions I'd worked on in my thesis where they really sort of good equations. 143 00:16:09,840 --> 00:16:14,540 And so I knew from a lecture that student one had given, I think in Newcastle, 144 00:16:14,550 --> 00:16:19,440 maybe that I'd been to that there was this problem of existence in elasticity. 145 00:16:20,340 --> 00:16:28,110 So and when I went there, the fellows very quickly told me what the, the real issues were. 146 00:16:29,020 --> 00:16:33,120 And so then I started working on it. He went off to, to Greece and something. 147 00:16:33,120 --> 00:16:36,960 And I just spent these times long hours in the library. 148 00:16:37,020 --> 00:16:43,770 There's a wonderful library now, maybe libraries and also, you know, the places where you really spend a lot of time. 149 00:16:44,580 --> 00:16:49,530 But then it was a fantastic library. I could go back to all the old papers. 150 00:16:50,100 --> 00:16:54,330 And so I worked really hard on this. It was a very hot summer. 151 00:16:54,480 --> 00:17:01,770 And, you know, so the seed of your work on the resistance theorem for elasticity was there and you come back to it. 152 00:17:02,020 --> 00:17:08,489 What? I did it. I thought that was all. I did it. And and I remember it was very, very hot. 153 00:17:08,490 --> 00:17:13,200 And I was one afternoon I was just sort of lying there trying to survive. 154 00:17:13,200 --> 00:17:16,530 And and and then I saw this. 155 00:17:19,080 --> 00:17:22,200 I sort of made this connection between determinants and volumes. 156 00:17:22,200 --> 00:17:25,290 And I realised that the volumes should be sort of. 157 00:17:26,370 --> 00:17:30,059 Preserved under weak convergence because it was just the area inside the boundary. 158 00:17:30,060 --> 00:17:34,250 And so this was, I guess, the crucial that was crucial moment. 159 00:17:34,260 --> 00:17:36,710 You had the spark here also. 160 00:17:37,710 --> 00:17:47,790 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. 161 00:17:47,790 --> 00:17:57,749 Right away. Yes. Yes sir. And I was, I was that change what that was that was it was it was great. 162 00:17:57,750 --> 00:18:09,180 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. 163 00:18:09,180 --> 00:18:14,280 So, you know, people would be tapping their feet and boredom at the lecture on, you know, 164 00:18:14,280 --> 00:18:19,530 above your head and and were quite sort of clank, slowly steaming the pipes and so on. 165 00:18:19,530 --> 00:18:25,230 So it was an unusual place to be. So fairly soon we moved out to the new campus in record time. 166 00:18:26,520 --> 00:18:30,210 But Robin Knox had sort of created this department. 167 00:18:30,840 --> 00:18:36,540 And. And it was. Very lively and I learned. 168 00:18:38,370 --> 00:18:42,930 More about continued mechanics from him. It was a it was a great time, actually. 169 00:18:44,190 --> 00:18:50,130 And eventually I had these I was so lucky. I had these incredible students and post-docs. 170 00:18:50,610 --> 00:18:54,380 Stuff on my life like image for art to shrink away. 171 00:18:54,390 --> 00:18:58,670 I mean, you could not hope for better people and argue with us. 172 00:18:58,680 --> 00:19:03,120 What's the secret ingredient, you think? I mean, you see sometimes in different feel. 173 00:19:03,510 --> 00:19:08,760 Some people come together in a in a given place for a few years and create this centre. 174 00:19:08,760 --> 00:19:13,350 The change paradigm changed the way people think about a discipline. 175 00:19:13,680 --> 00:19:20,400 Right. And really see how do you see looking back what what were the ingredients that made that place special of the time? 176 00:19:22,230 --> 00:19:28,430 Well, it was a nice it was a small department. So it was a kind of family atmosphere. 177 00:19:28,440 --> 00:19:31,460 But I think it was it wasn't in some sense locks. 178 00:19:31,740 --> 00:19:37,620 Stephan Mueller, for example, he came on a while doing his undergraduate degree. 179 00:19:37,860 --> 00:19:47,350 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. 180 00:19:47,370 --> 00:19:54,689 And Vladimir Sharrock, he came, he was interested in work at dawn and first ability, 181 00:19:54,690 --> 00:19:59,489 and he'd done some wonderful stuff on invisibility and he came for that. 182 00:19:59,490 --> 00:20:01,830 So I think it was just in some sense luck. 183 00:20:01,950 --> 00:20:11,100 You know, you, you, it has to be like serendipity and you cannot try to recreate it in that way or who writes it. 184 00:20:12,420 --> 00:20:19,380 But it always depends. I mean, I've seen that in a few, few places, and usually it depends on a few individual, right? 185 00:20:19,590 --> 00:20:23,850 One is not enough, but you have two or three that are like minded and truly change. 186 00:20:24,420 --> 00:20:26,670 So that's where there Robin was. There was there. 187 00:20:26,670 --> 00:20:36,600 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. 188 00:20:36,610 --> 00:20:43,280 I looked at our policy and many people Marshall Slemrod, Gerry Marsden and. 189 00:20:45,560 --> 00:20:51,170 So it was an exciting time, but it was a small place that I think that's interesting because now big, it's beautiful. 190 00:20:51,410 --> 00:20:59,629 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. 191 00:20:59,630 --> 00:21:08,690 But well, these people's careers were not damaged by being in this small place with maybe not very good library facilities. 192 00:21:08,720 --> 00:21:18,440 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. 193 00:21:19,400 --> 00:21:23,389 So it is I mean, you spend 23 years in area. 194 00:21:23,390 --> 00:21:31,520 To what? So you went through the rank. At some point it's you became professor, is it the professorship was professorship of apply. 195 00:21:31,520 --> 00:21:34,910 And that is is that a title you chose for yourself? I think so. 196 00:21:35,480 --> 00:21:39,379 Where you the first you think? I think you could choose your own. 197 00:21:39,380 --> 00:21:48,650 Yeah, I think I want to know what was behind you is that is defining you feel or I'm 198 00:21:48,650 --> 00:21:53,020 not sure with I think that phrase was used at the time so it was just a natural. 199 00:21:53,060 --> 00:21:57,799 I probably didn't think about it very much because there was a chance. 200 00:21:57,800 --> 00:22:03,020 You know, you mentioned all the people you brought into the centre or what brought in the UK. 201 00:22:03,440 --> 00:22:11,920 There were it was not the typical UK applied mathematics or even mathematics in general. 202 00:22:11,930 --> 00:22:22,460 You were bringing something different, right? It's the that place was a seat for the rest of the UK as time went by. 203 00:22:23,260 --> 00:22:28,500 I remember getting one person who gave a lot of support was Jemmy Wales from Warwick. 204 00:22:28,510 --> 00:22:32,319 I think that he saw that that was something interesting happening. 205 00:22:32,320 --> 00:22:39,300 So that was, you know, just odd comments like that are kind of good for one's morale actually. 206 00:22:39,310 --> 00:22:43,600 But but episode was SIRC. 207 00:22:43,660 --> 00:22:52,840 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. 208 00:22:52,840 --> 00:22:58,600 So it was it was good. And at the time there was the Applied Mathematics Community in the UK, 209 00:22:58,600 --> 00:23:06,070 but there is also the mathematics in the UK which increasingly recognised that as an important part of mathematics. 210 00:23:06,100 --> 00:23:09,309 Is that the case? Yes, I think so. 211 00:23:09,310 --> 00:23:13,150 I, I think it I mean, there was there were other factors. 212 00:23:13,150 --> 00:23:20,350 There was some point there was an influx of Russians to doing sort of differential equations in the UK. 213 00:23:20,350 --> 00:23:25,690 They were working on maybe things I'm not myself so interested in spectral theory and so on. 214 00:23:25,690 --> 00:23:36,580 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. 215 00:23:39,660 --> 00:23:43,370 But but but we didn't have so many students. 216 00:23:43,380 --> 00:23:52,620 I mean, people like John Toland and myself didn't have so many students that populated universities. 217 00:23:52,620 --> 00:23:57,030 Most. Most of the people, I think, came from outside. I think that's still still the case. 218 00:23:58,990 --> 00:24:02,830 So when when you look back at his years at Earth, what's I mean? 219 00:24:04,150 --> 00:24:12,340 There's a great number of distinct work or branches of your work that you've that initiated at that point. 220 00:24:12,340 --> 00:24:24,040 Wright's work on dynamical systems, methods for elasticity, work on the ensemble of function interpretability and things like that. 221 00:24:24,640 --> 00:24:32,299 So when you look back at it, was it did you see it as the most productive part of your academic life, 222 00:24:32,300 --> 00:24:36,400 full of maybe the most productive for the study, the ones to come? 223 00:24:38,740 --> 00:24:45,399 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. 224 00:24:45,400 --> 00:24:48,880 But of course, other people, they think think differently. 225 00:24:49,360 --> 00:24:54,910 Just when I look at the number of single author papers that you produce, they're indifferent. 226 00:24:54,970 --> 00:25:04,450 You know, big papers sitting in very clear terms in theory, in a given field that become the first work, the reference work. 227 00:25:04,450 --> 00:25:11,650 You know, you work on cavitation only at the reference work and you can trace all of the work that came after. 228 00:25:12,560 --> 00:25:18,940 The same is true for a number of on the order of the topics that you started that you started at the time. 229 00:25:19,600 --> 00:25:23,589 So was it a productive? It certainly was a productive time. 230 00:25:23,590 --> 00:25:26,680 But how do you see it or do you remember it? That's what I remember. 231 00:25:27,040 --> 00:25:30,820 I mean, one thing I remember is somebody we haven't mentioned is Jack Carr. 232 00:25:30,880 --> 00:25:38,800 Yes. So I was just you know, it was Memorial Memorial meeting and Edinburgh and we're very good friends and we 233 00:25:38,800 --> 00:25:43,810 would often go to sort of football games together and talk about mathematics. 234 00:25:43,810 --> 00:25:48,550 And and we worked together with Oliver Penrose, who was another important influence. 235 00:25:48,730 --> 00:25:55,420 So he came from the open university. And so that developed a new a new topic. 236 00:25:55,420 --> 00:25:59,100 And that's the work on the cognitive fragmentation equations. 237 00:25:59,120 --> 00:25:59,499 That's right. 238 00:25:59,500 --> 00:26:14,380 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, 239 00:26:14,740 --> 00:26:20,110 even though apparently they might be denied by statistical physics. 240 00:26:20,110 --> 00:26:24,960 But since he was statistical physicist, this was a big reassurance. 241 00:26:25,330 --> 00:26:31,180 And is that what opened the doors to you work on phase transition that came later with Dick James. 242 00:26:31,180 --> 00:26:36,159 Well Dick was visit Dick was a visitor to Heriot-watt on one of these grants. 243 00:26:36,160 --> 00:26:45,639 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. 244 00:26:45,640 --> 00:26:48,879 He he said. He asked me someday. 245 00:26:48,880 --> 00:26:52,390 Well, but what would I? 246 00:26:52,690 --> 00:26:58,690 A minimising sequence for energy looked like that didn't converge to a minimise. 247 00:26:59,620 --> 00:27:01,220 And so it was interesting. 248 00:27:01,270 --> 00:27:08,610 So I drew some kind of half space and some consonant gradient below there and then some kind of sequence like that, like this. 249 00:27:08,620 --> 00:27:15,610 And he said, That reminds me of something. And the next day he came back and he said, That's an Austin Mountainside interface. 250 00:27:16,930 --> 00:27:24,339 So this is how it happened. I'm not under the moment where you can you can trace the spark. 251 00:27:24,340 --> 00:27:30,060 That wasn't the one discussion that made the other one or the other. 252 00:27:30,070 --> 00:27:35,500 You came about the problem of cavitation your long standing interest in singularities right now? 253 00:27:35,500 --> 00:27:38,650 I'm not sure. I'm not sure how. 254 00:27:42,300 --> 00:27:47,880 I think it probably came from these growth conditions and seeing I mean, so what what could happen if. 255 00:27:49,090 --> 00:27:57,610 The growth conditions were not sufficiently strong and I began to realise that maybe an ex of a little max was something. 256 00:27:57,610 --> 00:28:03,370 And then I thought maybe of holes and I see because the growth condition is infinity, 257 00:28:03,370 --> 00:28:08,379 I realise of the opening the cavity right the stretched the divergence. 258 00:28:08,380 --> 00:28:13,780 So you have, you don't have to go to infinity to realise that it's there. 259 00:28:14,650 --> 00:28:23,350 So actually my, my, my paper on cavitation was communicated by Brooke Benjamin and I, Brooke was a great expert in cavitation. 260 00:28:23,350 --> 00:28:29,469 His thesis was on cavitation interference and, and he told me a lot about these things. 261 00:28:29,470 --> 00:28:39,070 And so at that time, I think you could maybe have more influence on the publication process than you can now. 262 00:28:39,080 --> 00:28:48,489 So this paper got a got a pretty negative referee's report, I think it was from Rodney Hill, actually. 263 00:28:48,490 --> 00:28:52,360 So maybe it was not so not negative as I read it. 264 00:28:53,020 --> 00:28:57,759 Anyway, I remember Brook taking very forceful action to get it to get this paper accepted. 265 00:28:57,760 --> 00:29:01,410 So I have to thank him for that. 266 00:29:03,850 --> 00:29:07,569 So here we are, two what's 23 years? 267 00:29:07,570 --> 00:29:10,750 And so what was your next step after that come about? 268 00:29:11,170 --> 00:29:14,440 Was that special connection with Brooke Benjamin? Well. 269 00:29:16,230 --> 00:29:23,070 I was very happy with her and I was really well treated as I have been in Oxford, that I should say. 270 00:29:23,070 --> 00:29:32,450 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. 271 00:29:33,140 --> 00:29:39,020 So if I was going to move from Heriot-watt, which seemed eventually to be a good idea, 272 00:29:40,280 --> 00:29:50,509 just on general sort of grounds, it was probably to Oxford or Cambridge and and then this chair came up in Oxford. 273 00:29:50,510 --> 00:29:54,889 And so quite suddenly, quite suddenly I suddenly, of course. 274 00:29:54,890 --> 00:29:59,000 And. Yes. 275 00:29:59,000 --> 00:30:04,440 And so. So. Well, I didn't apply for it, actually, at that time. 276 00:30:04,940 --> 00:30:09,080 It was it was almost that if you applied for a chair at Oxford, you would. 277 00:30:09,170 --> 00:30:12,440 You would not get it. So. So I didn't. 278 00:30:12,440 --> 00:30:18,260 I didn't apply. Eventually, I got some kind of feeler from somebody saying, well, might I want to apply? 279 00:30:19,370 --> 00:30:22,430 And eventually I sort of did it did apply at some level. 280 00:30:23,750 --> 00:30:27,140 And then I was offered it. And then it was a long kind of. 281 00:30:28,550 --> 00:30:29,870 Negotiation period. 282 00:30:31,730 --> 00:30:41,809 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. 283 00:30:41,810 --> 00:30:46,760 And I was really mad about this. And so I was negotiating on this. 284 00:30:47,330 --> 00:30:57,049 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, 285 00:30:57,050 --> 00:31:04,360 maybe if one chose a different college, I could maybe get at least twice my salary. 286 00:31:05,120 --> 00:31:08,960 So that was market. Then I was told that this would require an act of parliament. 287 00:31:10,910 --> 00:31:14,719 So this idea was was scotched. 288 00:31:14,720 --> 00:31:21,610 And but eventually I eventually I accepted and swallowed my pride. 289 00:31:21,620 --> 00:31:28,130 So the chair of Natural Philosophy, the oldest science chair, and go with going back to the 17th century. 290 00:31:29,930 --> 00:31:33,640 Is there any other chair of natural philosophy that still exists that you know of? 291 00:31:33,650 --> 00:31:41,150 Well, that was the nuclear case Lucasian chair and Cambridge, of course, which was once held by Newton. 292 00:31:41,150 --> 00:31:49,670 But. And so there is I always feel that there is something special about the name natural philosophy 293 00:31:49,670 --> 00:31:56,150 so that it does it fits you you view of science and mathematics and the unification of both. 294 00:31:58,260 --> 00:32:07,860 Yeah, perhaps. I think its main effect was that I get all this public publication stuff on books, in philosophy. 295 00:32:08,370 --> 00:32:11,390 I think by mistake, I think. 296 00:32:13,950 --> 00:32:18,149 But it's a it's a suit that fit fitted you in a way. 297 00:32:18,150 --> 00:32:21,360 Right, since it's coming in being professor of Metro. 298 00:32:21,600 --> 00:32:24,959 Yes. No, no, I was I was very happy to come here. 299 00:32:24,960 --> 00:32:28,560 And it's been a wonderful experience. 300 00:32:29,040 --> 00:32:33,059 So you come in Oxfords and you start developing around. 301 00:32:33,060 --> 00:32:38,940 You have a group mostly known in our partial differential equation. 302 00:32:38,940 --> 00:32:46,380 Right. You've been an advocate trying to push let's get to the UK, which to start with it was very slow actually. 303 00:32:46,740 --> 00:32:47,729 There was a sort of one. 304 00:32:47,730 --> 00:32:58,980 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. 305 00:33:00,060 --> 00:33:05,490 So and he didn't stay such a long time. 306 00:33:05,490 --> 00:33:08,970 And then it was several years before things started to expand. 307 00:33:09,900 --> 00:33:20,030 No, we had a lot of support from from successive chairs of the department, liquid house, some house. 308 00:33:20,070 --> 00:33:33,330 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. 309 00:33:33,330 --> 00:33:40,010 So. So. So then it became a, you know, a group with critical mass. 310 00:33:40,180 --> 00:33:43,630 But for several years, it was quite sort of delicate, actually. 311 00:33:44,410 --> 00:33:55,170 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? 312 00:33:55,180 --> 00:34:04,129 Or is it. Well, I think I mean, Oxford has a unified department of pure and applied mass, 313 00:34:04,130 --> 00:34:10,820 which is one reason why I felt it had a sort of big advantage to Cambridge. 314 00:34:11,330 --> 00:34:18,110 But but still within it's a very big department. And of course, there are people in it who have different views about what. 315 00:34:19,230 --> 00:34:23,200 Applied maths means. And so those two are certainly tensions. 316 00:34:23,490 --> 00:34:25,530 That's correct I think. But. 317 00:34:27,060 --> 00:34:36,810 I suppose slowly they may have dissipated, but a bigger factor was probably support from the top within the department, I think. 318 00:34:37,920 --> 00:34:42,030 But at the same time, by by the time you came to Oxford, of course, 319 00:34:42,030 --> 00:34:48,570 you work had been recognised both nationally and internationally, so you came with a certain way. 320 00:34:48,720 --> 00:34:52,370 So yes, I think my friends in the fields, you know. 321 00:34:52,770 --> 00:34:56,910 But you know, a lot. Nobody has so much influence in our. 322 00:35:02,010 --> 00:35:13,260 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. 323 00:35:13,860 --> 00:35:19,830 And he said, Well, don't raise your blood pressure by thinking you can change Oxford overnight. 324 00:35:21,120 --> 00:35:24,150 He was he was certainly correct with advice. 325 00:35:25,680 --> 00:35:35,030 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. 326 00:35:36,850 --> 00:35:40,589 Yeah, I think it was it was a continuation. 327 00:35:40,590 --> 00:35:46,770 Of course, it was possible here to recruit, if you like. 328 00:35:48,760 --> 00:35:56,560 High quality faculty, which would not have been so easy, whatever it was, probably, even though there were very good people there. 329 00:35:57,640 --> 00:36:03,010 So in some sense, everybody wants to come to Oxford or at least well, think with think of coming to Oxford. 330 00:36:03,010 --> 00:36:08,080 So that was a big, big plus about being here. 331 00:36:10,060 --> 00:36:14,799 I had good students here, but I wouldn't say they would necessarily. But the students I had before. 332 00:36:14,800 --> 00:36:17,880 But I have I've had wonderful students and post-docs after. 333 00:36:20,710 --> 00:36:24,370 I think it was a it was an it was a natural progression, of course. 334 00:36:24,670 --> 00:36:31,659 And I was involved in some European networks. These were important influence on Trend Network. 335 00:36:31,660 --> 00:36:41,230 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. 336 00:36:43,690 --> 00:36:49,960 I see. So you had a number of very, very well-known research student in your life. 337 00:36:50,260 --> 00:36:58,020 So what's what's your general philosophy? How do you deal with students about giving them problem or letting them come with problems? 338 00:36:58,060 --> 00:37:05,020 You have a general approach or advice. I think it depends on the quality of the student. 339 00:37:05,030 --> 00:37:11,140 And actually, I'm much less sort of worried about the. 340 00:37:12,370 --> 00:37:15,459 Ability of the student and some other people. 341 00:37:15,460 --> 00:37:19,780 I. What's important to me is that well-motivated. 342 00:37:20,640 --> 00:37:31,010 And so but I think how I treat students depends on some kind of assessment I have of their current background or qualities. 343 00:37:31,010 --> 00:37:37,190 So maybe I might be more directive for a student who I think needs more direction. 344 00:37:38,480 --> 00:37:41,600 And of course, sometimes you have a problem which you really think, Well, 345 00:37:41,600 --> 00:37:46,399 I really would like to see somebody work on this or work with somebody on this. 346 00:37:46,400 --> 00:37:51,139 And and at other times, maybe you don't have such natural problems, 347 00:37:51,140 --> 00:37:58,190 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. 348 00:37:59,570 --> 00:38:05,510 With with somebody, which I think is this has worked quite well in some cases anyway. 349 00:38:06,990 --> 00:38:16,170 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. 350 00:38:16,680 --> 00:38:22,470 You see the truth that says us as long as as long as they're ready to work hard. 351 00:38:22,500 --> 00:38:27,020 You should be giving them time. But if they're not, they should be scorned. 352 00:38:27,450 --> 00:38:35,700 If they don't remember that I've tried not to scold students, but as you say it, it doesn't matter. 353 00:38:35,700 --> 00:38:38,720 But the ability, it's the attitude. I think so. I think so. 354 00:38:38,730 --> 00:38:42,809 And it's amazing how people can develop their produce. 355 00:38:42,810 --> 00:38:47,460 And then we should be looking at the test course so closely. 356 00:38:47,640 --> 00:38:56,910 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. 357 00:38:56,910 --> 00:39:05,850 I mean, so I, I know many, many of the world's best mathematicians and so in some sense and. 358 00:39:07,230 --> 00:39:10,650 And I know you know how quickly some people think. 359 00:39:10,740 --> 00:39:17,190 I know, I think much more slowly than this. But then then there are for researchers, something different. 360 00:39:17,220 --> 00:39:20,370 You know, it's it's a question of what you work on. 361 00:39:20,370 --> 00:39:22,670 And the timescales are completely different. 362 00:39:22,680 --> 00:39:31,530 And there are different kind of qualities that can be successful, which are not tested in three hour examinations. 363 00:39:32,100 --> 00:39:33,820 So thinking faster process, 364 00:39:33,840 --> 00:39:43,829 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. 365 00:39:43,830 --> 00:39:50,640 You've as you said, you've you've met a lot of mathematician, maybe most of the top mathematicians in the world. 366 00:39:50,940 --> 00:39:56,520 Is there anybody who really stands out that you have memories of that's, you know, the natural. 367 00:39:59,080 --> 00:40:06,280 Well, I just came back from Oregon, where I met Jerry Erickson, who's now 94. 368 00:40:06,280 --> 00:40:10,970 So he's one of my. Scientific heroes, I think. 369 00:40:11,030 --> 00:40:15,959 And you know well the really great figures in mechanics. 370 00:40:15,960 --> 00:40:22,710 So he he was very important to me and and we had some correspondence. 371 00:40:22,710 --> 00:40:31,130 So at that time, people actually wrote letters, handwritten letters, and we had some very interesting discussions. 372 00:40:31,130 --> 00:40:34,600 And he certainly put me right on a number of things. 373 00:40:34,610 --> 00:40:41,660 Yes. And which is interesting. Right. Because Erikson was not one to collaborate, but he was. 374 00:40:42,410 --> 00:40:46,720 But he was ready to potatoes. But he was exciting. He was very interactive. 375 00:40:47,090 --> 00:40:52,850 Very interactive. And of course, when whenever you asked him a question, he would ask you a question. 376 00:40:53,090 --> 00:40:56,140 And it was. And he still does. 377 00:40:56,360 --> 00:41:08,839 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. 378 00:41:08,840 --> 00:41:18,499 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. 379 00:41:18,500 --> 00:41:28,879 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? 380 00:41:28,880 --> 00:41:37,920 What's the balance there? Well, it's it's something that suits some people and doesn't suit others, I think. 381 00:41:39,330 --> 00:41:41,670 I suppose I. I'm not sure how I. 382 00:41:43,240 --> 00:41:56,440 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. 383 00:41:57,770 --> 00:42:02,629 I said once I get interested in it, become informed by it and know some people. 384 00:42:02,630 --> 00:42:06,020 And I suppose it kind of grew from there. 385 00:42:09,320 --> 00:42:13,340 Yes. Obviously, some people are more natural. 386 00:42:14,090 --> 00:42:22,760 If you like I say administrators, but. More natural for such positions than others and and at top. 387 00:42:22,790 --> 00:42:25,820 But that's just just the way it is. 388 00:42:25,840 --> 00:42:29,440 I've been very lucky to have these positions. 389 00:42:29,440 --> 00:42:37,030 I've enjoyed them immensely. And so you get to the I am you and you sit as a president. 390 00:42:37,030 --> 00:42:43,540 You said you you've made some change. I mean, the Fields Medal is something of a bit of a. 391 00:42:45,030 --> 00:42:50,040 Mystery, shrouded in great secrecy for various reasons. 392 00:42:51,270 --> 00:42:58,020 So maybe you can give us some insight since you've seen the process from from from the inside. 393 00:42:58,320 --> 00:43:04,680 Well, I was twice on the Fields Medal Committee once as a member, and then when I was president, 394 00:43:05,610 --> 00:43:09,780 it always used to be the tradition that the president chaired the Fields Medal Committee. 395 00:43:09,780 --> 00:43:19,709 But when Jackie Williams was president, his son Pierre-Louis, was a potential candidate. 396 00:43:19,710 --> 00:43:24,530 So he felt he couldn't chair the committee. And and I think it was a did. 397 00:43:24,570 --> 00:43:27,930 And then for a couple of cycles this continued. 398 00:43:27,930 --> 00:43:33,509 But we reverted to the president chairing chairing the committee, 399 00:43:33,510 --> 00:43:41,880 which I think is important because there are guidelines for the Fields Medal that have not always been followed. 400 00:43:42,810 --> 00:43:53,680 So for example, two important guidelines are that you can award from 2 to 4 medals with a strong preference for four. 401 00:43:54,230 --> 00:44:00,090 And another is that it should respect a diversity of fields. 402 00:44:00,960 --> 00:44:04,170 But in some cases, this is didn't didn't happen. 403 00:44:04,650 --> 00:44:10,110 And I think this was one of the reasons why we, if you like, took back control of the process. 404 00:44:11,730 --> 00:44:17,340 So you feel you your contribution was to make sure that guidelines were followed? 405 00:44:18,510 --> 00:44:22,320 Well, yes. And well, that was that was maybe something I was so. 406 00:44:23,930 --> 00:44:29,800 There was also the question of the age limit, which was kind of interesting that you have to be under 40. 407 00:44:29,810 --> 00:44:34,790 So there was a question about exactly what under 40 means. 408 00:44:35,120 --> 00:44:42,710 So if you go to the Army website, you can read what I wrote, which defines precisely what 40 to 40 means. 409 00:44:43,340 --> 00:44:48,570 Very good. Including the latitude. And that's okay. 410 00:44:48,680 --> 00:44:54,049 Very good. But at the time there was a singular event also that in terms of the Fields 411 00:44:54,050 --> 00:45:00,080 medal is that's one of the nominees for the Fields medal was Grigory Perelman's. 412 00:45:00,740 --> 00:45:04,100 It was he was awarded the medal. 413 00:45:04,520 --> 00:45:08,240 And the question knowing him was whether or not he would accept it. 414 00:45:09,320 --> 00:45:18,310 Can you can you tell us about that? Yes. So. Well, Paramount proved the Poincaré conjecture, 415 00:45:18,400 --> 00:45:27,100 but at the time when the Fields Medal Committee had to make its decision, it was not completely clear that. 416 00:45:28,960 --> 00:45:32,020 Everything had been proved. This was one problem. 417 00:45:32,020 --> 00:45:40,990 But earlier than that it was more or less clear that whether or not he had proved the correct conjecture ahead, 418 00:45:41,740 --> 00:45:47,140 he was a very likely candidate for a Fields medal and was this kind of past history. 419 00:45:48,190 --> 00:45:52,570 So the executive committee of I am you considered. 420 00:45:53,640 --> 00:46:00,960 What would happen were he to be. Awarded the Fields medal and declined to. 421 00:46:02,010 --> 00:46:02,630 Accept it. 422 00:46:03,360 --> 00:46:12,120 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. 423 00:46:12,120 --> 00:46:19,349 And that was his business. Because if you think about the other alternatives, they were not tenable actually. 424 00:46:19,350 --> 00:46:25,079 I mean, you couldn't just say award three medals and not name who the fourth person was. 425 00:46:25,080 --> 00:46:31,500 This would just be ridiculous. And and also we felt that it was important to. 426 00:46:32,810 --> 00:46:42,440 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. 427 00:46:43,400 --> 00:46:51,170 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. 428 00:46:51,230 --> 00:47:00,200 And. And then we, we, we decided to award my fields medal and. 429 00:47:01,190 --> 00:47:07,370 Well, it was it's a tremendous story that you can read about in in Wikipedia, which is which is pretty accurate, actually. 430 00:47:07,370 --> 00:47:15,920 But at some point I. Called him up and said, Well, would you accept the Fields medal? 431 00:47:15,950 --> 00:47:24,700 And he said, No, I wouldn't. And I said, Well, can I come to Saint Petersburg to so I can understand the reason? 432 00:47:24,700 --> 00:47:30,400 He says, Yes, you can come. Okay, so and so you had to do it without anybody really knowing. 433 00:47:30,610 --> 00:47:33,270 Otherwise he would revealed. Yes, that's right. 434 00:47:33,280 --> 00:47:42,490 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. 435 00:47:43,100 --> 00:47:54,610 So so, in fact, the day that I went to Saint Petersburg, England, were playing, I think Paraguay and the World Cup. 436 00:47:54,610 --> 00:48:02,200 So I went straight from the airport to some Russian baths to watch, to watch, to watch this game. 437 00:48:02,200 --> 00:48:11,200 But then I spent a couple of days talking to Powerman and he well, he maintained his his position and. 438 00:48:13,500 --> 00:48:18,570 So it was a very interesting time. We walked a lot around St Petersburg and. 439 00:48:21,120 --> 00:48:27,870 And then there was, well, various other strands to the to the story. 440 00:48:27,870 --> 00:48:34,700 But but one was the article written in The New Yorker by Silvana Sau, who mentioned your trip was. 441 00:48:35,220 --> 00:48:43,200 Well, yes and no. It said it was controversial because because some prominent mathematician from Harvard didn't go. 442 00:48:43,830 --> 00:48:48,210 Yes, well, i11 thing that I was lucky that I had that I did. 443 00:48:48,420 --> 00:48:52,709 Prudent, if you like, was that I talked to Marcus de Soto beforehand. 444 00:48:52,710 --> 00:48:56,070 So I knew that this was going to be some kind of. 445 00:48:57,940 --> 00:49:06,669 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. 446 00:49:06,670 --> 00:49:12,160 You know, you can you can say if you say this is off the record, they cannot quite anything at all. 447 00:49:12,170 --> 00:49:18,790 So most of the time I was saying that was off the record or it could be non attributable or something. 448 00:49:18,790 --> 00:49:29,349 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, 449 00:49:29,350 --> 00:49:37,270 what terrified me was that they were going to publish this article with the night with the fact that Paramount had a 450 00:49:37,270 --> 00:49:43,659 Fields medal before the International Congress because the Fields medals are announced at the International Congress. 451 00:49:43,660 --> 00:49:55,120 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. 452 00:49:56,770 --> 00:50:05,560 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. 453 00:50:05,710 --> 00:50:08,830 It must have been by the time a more or less open secret. 454 00:50:09,520 --> 00:50:14,170 Oh, well, you know, there are people who know the people who don't know, of course. 455 00:50:15,250 --> 00:50:18,580 But it was obviously not likely to be the case. 456 00:50:18,730 --> 00:50:24,170 But but at the time at the time, we still didn't know that he had proved the point. 457 00:50:24,250 --> 00:50:28,480 Correct. Conjecture. When did that come? Which is. Well, I mean, that would have been. 458 00:50:29,900 --> 00:50:37,160 A few months later, if you look at the citation for the Fields medal, it does not give credit for for freedom. 459 00:50:37,250 --> 00:50:43,790 Yes, we were pretty sure. Yeah. But there were these different groups and that was the story about the plagiarism. 460 00:50:43,790 --> 00:50:47,720 And it was it's a really interesting story. 461 00:50:47,860 --> 00:50:54,649 It's not every day you have affairs or scandal in the world of mathematics and maybe the biggest in recent time, 462 00:50:54,650 --> 00:50:59,000 but it's also one of the biggest results to prove it. But it touched it. 463 00:50:59,130 --> 00:51:04,280 See, I thought that Perelman would get a bad press for. 464 00:51:05,610 --> 00:51:09,210 Seeming to be ungracious. Yeah, right. 465 00:51:09,500 --> 00:51:16,290 It's very opposite. He. He became some kind of popular hero of somebody with integrity, you know, 466 00:51:16,290 --> 00:51:23,420 turning down a prize in the process because he also got the, you know, the Millennium Awards or the cliff. 467 00:51:23,630 --> 00:51:27,300 And then that that really was turning down money. And he turned down $1,000,000. 468 00:51:27,380 --> 00:51:33,459 Yes. So just for my own, this was in around 2006. 469 00:51:33,460 --> 00:51:36,630 So it's almost 15, 12 years ago. 470 00:51:37,020 --> 00:51:40,710 What's the situation now with Paramount? Yes, with Paramount. 471 00:51:41,670 --> 00:51:47,370 Well, I don't know. I don't think anybody knows. But the assumption is that he's not doing mathematics. 472 00:51:47,370 --> 00:51:51,720 But who knows? But for the iyamu, he has a Fields medal. 473 00:51:52,020 --> 00:51:56,550 Yes, he has a Fields medal. He could come and get it. And I think for the foundation, the money is there. 474 00:51:56,910 --> 00:52:01,950 No, no. That money was handed over to the institute or a banker. 475 00:52:02,190 --> 00:52:07,710 Uh huh. Yeah, that is at his request. So it's probably not at his request. 476 00:52:10,030 --> 00:52:19,440 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, 477 00:52:20,000 --> 00:52:29,010 you have interests motivated by science and you have but as you wrote in your thesis, you want to do rigorous mathematics. 478 00:52:29,550 --> 00:52:37,890 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? 479 00:52:38,100 --> 00:52:41,909 What's what is your view about that? 480 00:52:41,910 --> 00:52:45,640 Which is. Well, I think. 481 00:52:47,060 --> 00:52:52,610 One thing is you should take responsibility for the model that you're working on. 482 00:52:53,360 --> 00:52:56,480 You shouldn't just say that. Well, 483 00:52:56,780 --> 00:53:01,159 some physicists have told me that this is the right equation and then you just 484 00:53:01,160 --> 00:53:06,580 work on them on the mathematics of this and don't try and understand the physics. 485 00:53:06,590 --> 00:53:17,659 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, 486 00:53:17,660 --> 00:53:22,340 you have to interact with with people who ideally do experiments. 487 00:53:22,340 --> 00:53:29,960 I think I think if you talking directly to experimentalists is very valuable, then you you cut out. 488 00:53:31,090 --> 00:53:40,870 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. 489 00:53:41,320 --> 00:53:51,580 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. 490 00:53:51,580 --> 00:53:55,870 But it's it takes a lot of time to learn some of this language. 491 00:53:55,870 --> 00:53:58,900 And then you have to have this kind of mixture of. 492 00:54:01,420 --> 00:54:06,370 Confidence that you can say something about this particular field. 493 00:54:08,690 --> 00:54:18,019 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. 494 00:54:18,020 --> 00:54:22,100 So it's it's a kind of difficult but interesting process, I think. 495 00:54:22,640 --> 00:54:31,760 And I hope you experience reception from the material science community or do they see your work in general? 496 00:54:31,760 --> 00:54:35,380 In general, it's been. It's been. Very good. 497 00:54:35,920 --> 00:54:38,440 It's a slightly. I mean, so I've worked twice. 498 00:54:40,410 --> 00:54:48,780 On sort of these modern static phase transformations which was interacting with material science and also more recently on liquid crystals. 499 00:54:49,170 --> 00:54:55,350 So I think the liquid crystal community is perhaps more traditionally receptive of mathematics. 500 00:54:55,350 --> 00:55:02,730 So there was really no pushback at all. But for material science, there was a bit of a pushback. 501 00:55:03,510 --> 00:55:06,630 You know that you know what you're you're ignoring. 502 00:55:07,680 --> 00:55:12,300 You know, you're taking this idealised model and doing this, you're ignoring this, that and the other, 503 00:55:12,330 --> 00:55:18,510 you know, because materials are, in fact, a complex that's just unbelievably complex. 504 00:55:19,590 --> 00:55:24,270 So you mentioned liquid crystal. You came about you started working about ten years ago. 505 00:55:24,270 --> 00:55:28,500 And I guess all of you come about that as a topic of interest, 506 00:55:28,740 --> 00:55:38,430 because I was asked to be external examiner of a polymer diamond as a thesis and Bristol and so. 507 00:55:40,190 --> 00:55:52,040 So I'd heard many talks in liquid crystals over the years from from Frank Leslie, in particular in Scotland and and Gerry Eriksson. 508 00:55:52,040 --> 00:55:56,920 So. And of course, it was in some sense similar to elasticity. 509 00:55:57,050 --> 00:56:01,340 So it's a multi-dimensional directional problem, at least in statics. 510 00:56:02,510 --> 00:56:09,760 And so I. It was not such a difficult thing to sell in the cities, but it made me think about. 511 00:56:14,190 --> 00:56:16,560 This problem in a way I've not thought about before. 512 00:56:16,920 --> 00:56:22,420 And it's just, you know, one little detail and you start thinking about one little detail and then it turns into. 513 00:56:23,520 --> 00:56:26,790 Which underlines the importance of doing service. 514 00:56:26,790 --> 00:56:32,340 Things like examining things that made people die seem like a drag on your research. 515 00:56:32,400 --> 00:56:36,150 Let's, let's let's you. You remained open to other things. 516 00:56:36,330 --> 00:56:43,950 The stimulus. So is how would you say what time you main research areas right now. 517 00:56:45,990 --> 00:56:57,660 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. 518 00:56:57,660 --> 00:57:08,309 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 519 00:57:08,310 --> 00:57:13,970 organisers of Newton Institute program on image processing and service organising workshop and 520 00:57:13,980 --> 00:57:19,379 you could you give it it was like in the old days when you were assigned a topic to talk on which 521 00:57:19,380 --> 00:57:25,500 was elasticity and image processing of which which I think I know a little bit about elasticity, 522 00:57:25,500 --> 00:57:27,149 but nothing about image processing. 523 00:57:27,150 --> 00:57:33,650 So, so now I've got quite interested in this because there really is a connection between elasticity and image processing, 524 00:57:33,660 --> 00:57:36,720 or at least there are some elasticity based methods. Yeah, sure. 525 00:57:37,050 --> 00:57:40,560 So maybe this is a new area now just starting. 526 00:57:41,220 --> 00:57:47,549 And that's I mean, image processing is becoming increasingly important and it's naturally related to 527 00:57:47,550 --> 00:57:54,750 a lot of the big data fashion that we see is what's what I you've you would say, 528 00:57:54,750 --> 00:57:55,490 you know, 529 00:57:55,500 --> 00:58:05,969 people from outside would say you're a traditional mathematician because it's mostly theory improving and maybe working with people doing computation, 530 00:58:05,970 --> 00:58:09,750 but doing forward computation based on model of the universe. 531 00:58:09,930 --> 00:58:15,150 So how do you see that's the new era of mathematics or science? 532 00:58:15,300 --> 00:58:19,709 Well, I think there's something genuinely exciting that is happening. 533 00:58:19,710 --> 00:58:26,540 On the one hand, of course, it's maybe. Like many sort of new things, hyped a little. 534 00:58:27,260 --> 00:58:31,240 What's striking to me is, is the the. 535 00:58:32,540 --> 00:58:38,930 It's as if traditional science and some of these machine learning methods are working in parallel universes. 536 00:58:39,620 --> 00:58:53,440 So, I mean, for example, if you. If you gave some machine learning program to the data for planets moving in the solar system. 537 00:58:54,040 --> 00:58:57,489 Right, which of course, historically, this is what happened. 538 00:58:57,490 --> 00:59:03,250 You know, people had the data for and and well, would such a program, you know, 539 00:59:03,280 --> 00:59:09,630 get you Newton's laws of gravitation and Newton's laws of motion or so? 540 00:59:09,780 --> 00:59:15,729 So there are and well, it will probably do a very good job in predicting planetary paths, unless, 541 00:59:15,730 --> 00:59:23,350 of course, it reached some kind of instability, which would not which was not there in the original data. 542 00:59:24,130 --> 00:59:29,830 So I think I think I think that there's a big challenge now to in some sense, 543 00:59:30,370 --> 00:59:36,580 bridge the gap between traditional science and these these these new methods. 544 00:59:36,850 --> 00:59:48,310 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. 545 00:59:49,750 --> 00:59:55,180 But nevertheless, it can help us make maybe we haven't learned to ask the right question, 546 00:59:55,190 --> 01:00:01,900 some of the right questions, but there's certainly an exciting and exciting time, I think. 547 01:00:02,410 --> 01:00:08,050 Of course, it's, I suppose, a little worrying as a mathematician to. 548 01:00:08,960 --> 01:00:16,250 To see these developments and that. So computers will. 549 01:00:17,740 --> 01:00:24,090 Well, I increasingly able to check proofs and when they check proofs, oh, no doubt be able to find proofs. 550 01:00:24,100 --> 01:00:34,720 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. 551 01:00:34,750 --> 01:00:44,950 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. 552 01:00:44,950 --> 01:00:51,820 It will change really, really dramatically. Probably, yes. 553 01:00:53,170 --> 01:01:01,149 So one thinks that often mathematicians do as part of the natural evolution process, 554 01:01:01,150 --> 01:01:06,640 is that they're turning to either historian of science or philosophy of science in general. 555 01:01:07,120 --> 01:01:12,490 That's, you know, and I wouldn't say they pontificate, but they reflect on the entire field. 556 01:01:13,300 --> 01:01:22,270 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. 557 01:01:23,200 --> 01:01:26,290 It's not new kind of things in general. 558 01:01:26,440 --> 01:01:36,370 You have natural philosophy in your title, but you resist philosophy of a role that would be I do resisted. 559 01:01:36,370 --> 01:01:41,830 I mean, I I'm actually I've always liked looking at old papers. 560 01:01:44,330 --> 01:01:50,030 It's amazing when you read papers that analysts at the beginning of the 20th century and 561 01:01:50,150 --> 01:01:57,100 how clearly they're written in prose descriptions of lumbago while something like this. 562 01:01:57,140 --> 01:02:03,920 It's it's really great to read to read these papers so I'm interested in the history of science. 563 01:02:03,920 --> 01:02:10,370 And I think it's very important for people to sometimes go back to read to read some of these papers. 564 01:02:10,370 --> 01:02:19,859 But I've not felt. The urge to write things on the history of Silence of Trouble is like so many unwritten papers, 565 01:02:19,860 --> 01:02:29,969 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, 566 01:02:29,970 --> 01:02:33,690 I think it would turn probably into writing. 567 01:02:33,690 --> 01:02:42,210 And this book I've been writing with Dick James for four years, that's probably more likely to be written for it. 568 01:02:43,110 --> 01:02:50,010 So apart from your role in being a good citizen of mathematics and science and promoting in various society, 569 01:02:50,370 --> 01:03:00,180 you've also been very active and I was always very impressed in helping developing countries scientifically or in the mathematics level. 570 01:03:00,360 --> 01:03:04,170 You describe your activities there and what what you do think it's important? 571 01:03:06,210 --> 01:03:16,140 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. 572 01:03:17,760 --> 01:03:20,129 Well well, when when I became president of. I am. 573 01:03:20,130 --> 01:03:29,520 You know, one of the things that struck me was that the budget for helping developing countries was was just pathetic compared to the. 574 01:03:30,870 --> 01:03:41,760 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. 575 01:03:42,480 --> 01:03:50,220 Now, if you've got a. You've got a decent Internet connection, which of course not everybody has. 576 01:03:50,730 --> 01:03:58,260 Then you can access anything, you know, Sai Hub, you can get any, any paper sign up. 577 01:03:59,880 --> 01:04:03,930 So it's but of course, accessing the information is not is not enough. 578 01:04:03,960 --> 01:04:07,830 You need to know what to do with the information. 579 01:04:08,150 --> 01:04:15,720 Right. I mean, I so I think the story I told you about when student one suggested this problem shows how, you know, unless, 580 01:04:15,900 --> 01:04:23,459 you know, personal contact from somebody who knows how to do it and it was done it themselves is absolutely essential. 581 01:04:23,460 --> 01:04:26,610 So especially with the amount of information. 582 01:04:26,850 --> 01:04:31,210 Yes. Yes. Where to look. Exactly. And so. 583 01:04:32,130 --> 01:04:37,900 So which are one of the projects I'm involved with is this mentoring African research for mathematics. 584 01:04:37,920 --> 01:04:48,810 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. 585 01:04:50,040 --> 01:04:54,990 But, you know, it's a question of maximising the pool of human talent. 586 01:04:56,280 --> 01:04:58,680 So it's good for everybody. 587 01:04:59,790 --> 01:05:09,820 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. 588 01:05:11,070 --> 01:05:17,040 But you also done things at a lower level before research and all that with Tibet. 589 01:05:18,180 --> 01:05:23,490 Yes. Well, you tell us a little bit about this activity. Well, my wife is is is from Tibet and. 590 01:05:24,990 --> 01:05:34,620 And so I visited three times. Each time I think also taking in the University of Leicester and my. 591 01:05:35,640 --> 01:05:40,380 My research student. By saying sorry. 592 01:05:41,020 --> 01:05:53,860 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. 593 01:05:54,640 --> 01:06:01,430 So you you've mentioned a few times you mentioned again to your wife of an award. 594 01:06:01,450 --> 01:06:02,650 You mentioned your family. 595 01:06:04,700 --> 01:06:13,820 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. 596 01:06:14,210 --> 01:06:20,480 So can you tell us what is what's the role of you family within within your own work or within your own lives? 597 01:06:22,940 --> 01:06:26,540 Well, I mean, you've you've met Cyrus, you know that. 598 01:06:26,540 --> 01:06:29,959 She's a very interesting. 599 01:06:29,960 --> 01:06:34,370 And I've been so happy to. Be married to her. 600 01:06:35,420 --> 01:06:40,639 But we're very different. We're very different people with different, different views on life often. 601 01:06:40,640 --> 01:06:44,060 And and our children. Yes. 602 01:06:44,060 --> 01:06:48,290 It's it's it's it's of course, the great experience of life having children. 603 01:06:49,590 --> 01:06:52,640 But it's not always, not always easy. 604 01:06:54,560 --> 01:06:59,510 But that's how you like. But we but we we just like for the important thing is we all talk to each other. 605 01:06:59,550 --> 01:07:04,520 We're all good friends. So if we would like mathematics to be easy, you know what? 606 01:07:04,730 --> 01:07:09,470 You want it to be interesting. Just like your family life. I guess this cannot be interesting. 607 01:07:10,850 --> 01:07:19,910 Yes. When? The last time you mentioned that to a very different person, I think I said I said, oh, you have? 608 01:07:20,660 --> 01:07:28,970 Yes, I agree with you on that one. So what would be you know, we always being pulled in different direction. 609 01:07:29,240 --> 01:07:34,370 That's and have to do a number of things every day. 610 01:07:34,910 --> 01:07:38,300 But what would be your perfect day if you could choose? It's you know. 611 01:07:43,010 --> 01:07:47,760 That's a difficult that really is a difficult question as well. 612 01:07:47,990 --> 01:07:55,790 I mean, sort of mathematically, of course, it's when you finally solved the problem you've been worrying about for two years. 613 01:07:56,690 --> 01:08:02,690 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. 614 01:08:02,690 --> 01:08:06,229 It is not it doesn't last as long as you might think. 615 01:08:06,230 --> 01:08:12,620 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. 616 01:08:12,920 --> 01:08:16,310 Stop right there and go enjoy it. Because it might not last. 617 01:08:17,270 --> 01:08:21,860 Well, it might, too, because that's what I thought. That's another point, of course, that often that often that happens. 618 01:08:22,340 --> 01:08:32,290 Yes. So you should enjoy the way it lasts. Well, thank you very much, John, for for taking this time. 619 01:08:32,300 --> 01:08:37,670 Is there any other memories you would like to recall? I think we've probably gone through it all through enough. 620 01:08:38,510 --> 01:08:39,680 Thank you. Thank you again.