1 00:00:12,610 --> 00:00:18,820 So let's start. I would like to welcome you all to the Mathematical Institute for another public lecture. 2 00:00:18,850 --> 00:00:22,870 My name is I don't go really. And I'm in charge of this series of lectures for the department. 3 00:00:23,290 --> 00:00:26,800 So before we start, I have to remind you about the Brexit side. 4 00:00:27,250 --> 00:00:33,940 One, two, three, four, five. It seems the Government cannot quite decide which one is the best to use to leave the building. 5 00:00:35,560 --> 00:00:40,240 We do not plan to have any trouble, but in case of emergency, do not wait for the government. 6 00:00:40,240 --> 00:00:43,700 Just go for the nearest thing. Okay, very good. 7 00:00:43,720 --> 00:00:45,640 So if you. You might have seen. 8 00:00:45,640 --> 00:00:53,950 Now we have nice side now and you might have seen that little extra symbol which looked like a matrix with the sign x x x markets. 9 00:00:54,370 --> 00:01:02,310 It's actually not a mathematical sign, but it's a financial company, X Markets, which is based in London. 10 00:01:02,320 --> 00:01:09,230 It has offices in Singapore and New York, and it's generously supporting not only this lecture but the entire series. 11 00:01:09,240 --> 00:01:17,620 So we're very grateful for the support. So a lot of you have come for a major events to see it tonight, of course. 12 00:01:17,620 --> 00:01:25,090 But we have another major event bringing a lot of eminent mathematician from around the world in this building this week. 13 00:01:25,330 --> 00:01:33,660 It is the 70th anniversary of the birthday of Professor John Bowen that you will see in a minute. 14 00:01:33,670 --> 00:01:42,070 So we wish him very well for according to Wikipedia, his actual birthday is on Saturday from just a couple of days. 15 00:01:44,260 --> 00:01:53,140 So a part of this celebration we have, of course, many, many very high quality, very advanced talks from from different mathematician. 16 00:01:53,470 --> 00:01:56,860 But we thought we would bring something to to the public. 17 00:01:57,430 --> 00:02:01,590 And we we thought that for this special event, we'd try something different. 18 00:02:01,600 --> 00:02:09,190 And that you can see we have a very cosy setting here. And the reason is that tonight's speaker is Michael Atiyah. 19 00:02:09,970 --> 00:02:19,390 And Michael Atiyah, as such an influence is so eminent among mathematics, in modern mathematics, 20 00:02:19,780 --> 00:02:24,310 that it would be completely overwhelming for me to even try to introduce him properly. 21 00:02:24,730 --> 00:02:32,590 So instead of that, my character, Professor Attia, will give a short lecture about certain ideas that he has about numbers. 22 00:02:33,130 --> 00:02:37,959 And after that it will sit and we'll have a nice conversation, 23 00:02:37,960 --> 00:02:45,190 a dialogue with which on board regarding his life, mathematics, their contribution and so on. 24 00:02:45,190 --> 00:02:50,200 So we hope that you will enjoy and I think it will be a very exciting and very enlightening events. 25 00:02:50,710 --> 00:02:54,970 So without further ado, please help me welcome Professor Attia for this. 26 00:03:08,280 --> 00:03:08,770 You also. 27 00:03:11,170 --> 00:03:18,940 Well, thank you very much for the instruction and I'm delighted to see such a large audience in support of mathematics in this famous building. 28 00:03:19,210 --> 00:03:26,200 I spent many, many years in Oxford and although I've not long since retired, it's nice to come back, see so many friends. 29 00:03:26,680 --> 00:03:34,000 Now this lecture the is the title of the lecture is the Titchmarsh lecture used in Oxford 30 00:03:34,270 --> 00:03:40,719 and I represent I'm from the University of Edinburgh and also from Trinity College, 31 00:03:40,720 --> 00:03:47,080 Cambridge. So that's who I am now. I think if I press a button, suddenly something happens. 32 00:03:47,470 --> 00:03:55,370 Let's see. No, it doesn't. Technology support what's happened. 33 00:03:55,620 --> 00:03:59,370 You can always press the button. You don't have to be okay. 34 00:03:59,450 --> 00:04:03,630 Yeah, let's see. See, it doesn't work. 35 00:04:05,340 --> 00:04:08,910 So you can press this mouse button. Such would work. Let's try this one. 36 00:04:10,120 --> 00:04:15,190 No. Let's look ahead. You see, technology is not perfect. 37 00:04:17,040 --> 00:04:21,490 So if you push on any case, you give me the first one. 38 00:04:21,520 --> 00:04:25,400 Yes, this one. No, I want to go. Okay. 39 00:04:26,510 --> 00:04:30,370 Sorry. Small hiccup. Small hiccup. It makes you more exciting. 40 00:04:31,450 --> 00:04:39,280 Okay. So the title of my talk was Numbers are serious, but they're also fun. 41 00:04:40,270 --> 00:04:44,110 If you're a mathematician, you enjoy doing mathematics, whether you're young or old. 42 00:04:44,470 --> 00:04:49,480 And so it's fun. But sometimes you do also play fun games. 43 00:04:49,690 --> 00:04:54,250 You can also get some serious outcomes. And so I want to show you how how that works. 44 00:04:54,590 --> 00:05:00,010 And so let's start very far back in history time with the greatest mathematician of all time. 45 00:05:00,430 --> 00:05:04,930 That was Archimedes. Without question, one of the great geniuses history. 46 00:05:05,020 --> 00:05:12,700 You all heard about Archimedes. He's famous for lots of things, one of which is he jumped out of his bath and ran down the streets shouting Eureka! 47 00:05:13,990 --> 00:05:16,000 In those days, people were more tolerant. 48 00:05:19,510 --> 00:05:25,480 And you may not know this, but he also, by the way, if you didn't know what Archimedes looked like, you can find out. 49 00:05:25,630 --> 00:05:28,390 All you got to do is win a funeral. Read his picture. 50 00:05:29,470 --> 00:05:36,940 So I have a Fields Medal, which I've done in Cambridge, and there is the picture of Archimedes guaranteed by Wikipedia. 51 00:05:37,480 --> 00:05:41,740 Now Archimedes, many, many things. 52 00:05:43,210 --> 00:05:46,690 But one thing in particular, he invented the number of pi. 53 00:05:47,260 --> 00:05:51,040 Now, I think you know what PI is most of you. I know just downstairs. 54 00:05:51,190 --> 00:05:52,930 There's a caveat on the Pi Cafe. 55 00:05:53,320 --> 00:06:02,770 So PI is so famous as a cafe, I buy a number that tells you something about the circumference circle and this very important number. 56 00:06:02,890 --> 00:06:07,570 And there it is, written down a few decimal places, 3.1, four and so on. 57 00:06:07,930 --> 00:06:11,110 So pies is very important number in history. Mathematics. 58 00:06:11,320 --> 00:06:15,430 It was invented by Archimedes. Now. 59 00:06:17,310 --> 00:06:21,000 Second famous mathematician Long Crater. 60 00:06:21,330 --> 00:06:24,330 About 2000 years later, it was Euler. 61 00:06:25,070 --> 00:06:34,440 There's a picture of Euler. He was a remarkable man. He published so much that they still haven't finished editing his works. 62 00:06:35,330 --> 00:06:39,750 He was after he died and later on last part of his life, he was going blind. 63 00:06:39,750 --> 00:06:42,690 But that didn't stop him. He carried on right to the very end. 64 00:06:43,170 --> 00:06:49,380 If he's lost amount of work and almost everything that mathematicians now use is it goes back to Euler. 65 00:06:50,250 --> 00:06:54,149 Now, for example, Euler in invented numbers does like. 66 00:06:54,150 --> 00:06:57,690 Pythagoras invented numbers. Pythagoras invented pi. 67 00:06:57,960 --> 00:07:02,370 Sorry, Archimedes, young Archimedes, even pi. 68 00:07:02,700 --> 00:07:09,050 Euler invented a number called E. E Well, what is he written down there for you? 69 00:07:09,290 --> 00:07:12,920 It's 2.718. And so what is it? 70 00:07:13,670 --> 00:07:22,590 Well, the easiest way to describe you don't know what is is you you go to a friendly bank which offers you, let's say, 100% interest. 71 00:07:22,610 --> 00:07:29,509 Very friendly bank. So you give it £1 at the beginning of the year, then the are in just one. 72 00:07:29,510 --> 00:07:34,520 We end up with £2. Good profit. But suppose you decide to take your money. 73 00:07:35,640 --> 00:07:42,350 And take the first bit out. Six months. And the bank is also friendly enough to give you the same rate if you do compound interest. 74 00:07:42,770 --> 00:07:47,630 And on this, when you come to the second six months, you get not only interest on the whole money, 75 00:07:47,900 --> 00:07:51,440 interest on the interest and then obviously a bit more. 76 00:07:52,430 --> 00:07:56,480 But if you took your interest every quarter and every quarter of quarter. 77 00:07:56,960 --> 00:08:04,730 So the limit, well, how much would you get into what you would get would be so easy, the amount you'd get from a very friendly bank. 78 00:08:06,450 --> 00:08:11,880 Now, of course, fortunately, the formula is such that you can work it out whatever the interest rate is by small change. 79 00:08:12,180 --> 00:08:18,930 E still give you the answer very useful number and you might say, well, I'm not interested in money, but suppose you've got something else. 80 00:08:18,940 --> 00:08:24,060 Suppose you do want to count populations. You have you could you breed rabbits? 81 00:08:24,540 --> 00:08:28,530 Okay. Sorry with two rabbits. Sorry for them it's for you. 82 00:08:28,710 --> 00:08:37,830 And that is called exponential growth. And the world population sometimes suffers an exponential growth and it also come by so is very important. 83 00:08:37,830 --> 00:08:48,930 Number E now is a stands for exponential things that go by multiplication, multiplication and the same formula the Euler e very important number. 84 00:08:49,770 --> 00:08:58,260 Now one of the things that happened between before Euler was people discovered things called complex numbers, 85 00:08:59,130 --> 00:09:07,620 things that don't exist, imaginary numbers. If you squaring number, whether you saw the positive number or negative number, the answer is positive. 86 00:09:08,340 --> 00:09:11,430 So minus one cannot be described any number. 87 00:09:12,180 --> 00:09:15,600 But this aren't put off by things that don't exist. 88 00:09:15,840 --> 00:09:20,790 The less imaginary number you can imagine I and we call it I because I imaginary. 89 00:09:21,180 --> 00:09:26,220 So I gave an imaginary number. There's always doubt it was some scepticism. 90 00:09:26,850 --> 00:09:30,210 You had to use imaginary numbers. Well, yeah, no. Yes or no. 91 00:09:30,420 --> 00:09:39,180 But eventually they find it so useful they allowed it. And so now Euler combined these two together, he took the AI and he says, 92 00:09:39,380 --> 00:09:46,260 You take E and you raise to a power and you raise it to the power using Archimedes. 93 00:09:46,260 --> 00:09:52,860 You were in pi, you write to pi I that was this marvellous collection you find, you get the value one. 94 00:09:53,960 --> 00:10:00,950 And this formula easy to buy who's one is regarded as the most beautiful formula in mathematics? 95 00:10:01,440 --> 00:10:05,210 Anyone who knows you ask them. Almost without exception. 96 00:10:05,420 --> 00:10:08,750 This is the most beautiful formula in mathematics. It's fantastic. 97 00:10:09,020 --> 00:10:13,760 It combines important numbers pi e ai and you get one. 98 00:10:14,330 --> 00:10:24,980 It is staggeringly beautiful and it is so famous, so beautiful that you know this. 99 00:10:25,400 --> 00:10:29,719 If you only want to invent one thing in your life, you can do that and you're famous for that. 100 00:10:29,720 --> 00:10:34,190 But all of the many, many things but this was one I like to explain it to people. 101 00:10:34,340 --> 00:10:42,680 One is like this. If you ask are you a mathematician, by the way, are not illiterate, we can read. 102 00:10:44,090 --> 00:10:53,510 And if you know your hamlet Shakespeare, it is a famous phrase to be or not to be is very beautifully short use. 103 00:10:53,510 --> 00:10:58,400 Only two syllable letters to be is is extremely short. 104 00:10:58,940 --> 00:11:04,969 And yet if you think about this, it's a very deep statement to be or not to be, basically. 105 00:11:04,970 --> 00:11:15,709 Are you going to kill yourself? Yeah. Well, so what could be more important that and so I think Hamlet and Shakespeare to be or not to be, 106 00:11:15,710 --> 00:11:18,800 is the literary equivalent of Euler's formula or other way around. 107 00:11:19,040 --> 00:11:24,380 Euler's formula is a mathematical colon or to be or not to be, they are two perfect gems. 108 00:11:24,800 --> 00:11:28,250 C Remarkably short, succinct, and yet deep. 109 00:11:28,850 --> 00:11:32,660 That is what you aim to achieve in mathematics or nature. 110 00:11:33,080 --> 00:11:38,810 I hope you're convinced now. That was my first slide. 111 00:11:38,990 --> 00:11:43,330 I don't have many slides. I don't believe hundreds of slides, one after the other for the next. 112 00:11:43,330 --> 00:11:51,360 It doesn't work. Now I'm going to spend the next bit talking to my my wife. 113 00:11:51,750 --> 00:11:54,750 Have you don't mind personal. My wife Lily. 114 00:11:56,120 --> 00:12:03,860 Sandy died a few months ago. Well, the mathematician and women mathematicians were rather rare in that time. 115 00:12:04,550 --> 00:12:08,720 And he did his successful life as a mathematician many ways. 116 00:12:09,320 --> 00:12:15,740 And he picture shows here that together we don't eat cakes. 117 00:12:15,740 --> 00:12:20,510 And the photographs of mathematicians, too, the University of Edinburgh, where we are now. 118 00:12:20,840 --> 00:12:27,820 And we open it together. So that was her. And that was her last public appearance in 2040. 119 00:12:29,630 --> 00:12:35,240 And before that, she taught in many places, and she taught in particular. 120 00:12:35,540 --> 00:12:39,260 It's a huge college, Oxford, which you really know down the road. 121 00:12:40,910 --> 00:12:45,980 And so we spent many years in Oxford, and that part of our time was spent there. 122 00:12:46,400 --> 00:12:50,750 And then, of course, another button, I think it was then. Yes. 123 00:12:50,750 --> 00:12:56,060 She also taught at Headington school, which is far up the road, a girls school. 124 00:12:56,330 --> 00:13:05,690 I'm very pleased that Colin Bedford, sitting in the front row here with a fellow teacher of ladies all that time ago, is here for the occasion. 125 00:13:07,040 --> 00:13:10,850 She taught mathematics in heading the school forever, quite a long time. 126 00:13:11,210 --> 00:13:15,950 And since I've been here in Oxford this time I've been told by four different people 127 00:13:16,610 --> 00:13:21,770 that their daughter was taught mathematics by my wife and altered their careers. 128 00:13:22,310 --> 00:13:28,610 So you teach children any age, inspire them, you can alter their lives. 129 00:13:29,060 --> 00:13:31,040 My wife has that ability. 130 00:13:32,150 --> 00:13:40,940 She was a very active in the mathematical association, which involves the whole involvement of teachers teaching mathematics in schools of all kinds. 131 00:13:41,150 --> 00:13:44,120 She was very active in the Mathematical Association here in Oxford. 132 00:13:44,600 --> 00:13:51,380 So I think it's a it's now back in Oxford and we spent 30 years in Oxford together and she passed away a short while ago. 133 00:13:51,800 --> 00:13:54,530 I think I would like to dedicate this lecture to my wife. 134 00:13:58,650 --> 00:14:07,830 So I by the way, I should mention for those who you've been attending and conference on ball and who appear shortly, 135 00:14:08,130 --> 00:14:14,880 it's like miraculous appearance that my wife did it in mathematics. 136 00:14:15,240 --> 00:14:18,030 She worked with Mary Cartwright, the very famous woman mathematician. 137 00:14:18,360 --> 00:14:23,399 And in fact, her work, which is really quite difficult stuff because I didn't really understand what you did. 138 00:14:23,400 --> 00:14:29,280 It is actually turned out to be your reflection, quite closely connected with some of the things we've been hearing about. 139 00:14:29,490 --> 00:14:34,950 It has done both, actually. So she did work of some mathematical importance with her. 140 00:14:35,340 --> 00:14:38,810 Even in the other days I was on her own. 141 00:14:38,820 --> 00:14:43,260 I got my Ph.D., went off to America in those days. 142 00:14:43,560 --> 00:14:47,270 She had to give up her job and follow me. Nowadays, you wouldn't do that. 143 00:14:47,290 --> 00:14:54,209 You send your husband away, say, see you, you come back. But in those days, it was customary to resign your job. 144 00:14:54,210 --> 00:14:58,470 You had a full university job teaching mathematics. Yeah, before me. 145 00:14:58,770 --> 00:15:01,860 And when we got married, she had to leave and go away. 146 00:15:02,430 --> 00:15:05,550 It is sad, but that's how it happened. 147 00:15:06,240 --> 00:15:11,010 Right. So that was my dedication to my wife. I hope you don't mind my little digression. 148 00:15:11,520 --> 00:15:14,730 Now back to the main theme of my lecture. 149 00:15:16,140 --> 00:15:20,250 So we looked to the past Archimedes and Euler. 150 00:15:21,120 --> 00:15:24,630 Great figures. They did marvellous things. Well, how about the future? 151 00:15:25,290 --> 00:15:29,250 Well, somebody in this audience here future of Archimedes. 152 00:15:30,760 --> 00:15:34,300 Any Greeks here? Future Euler? 153 00:15:34,600 --> 00:15:38,200 Actually, we all come from all parts of the world. Doesn't matter where you come from. 154 00:15:38,500 --> 00:15:43,840 Mathematics is absolutely universal. So any way in the world you come, you can try. 155 00:15:44,440 --> 00:15:47,530 So the challenge. Problem of your challenge. 156 00:15:48,640 --> 00:15:53,950 Well, for player numbers like Archimedes Solar and even the new number. 157 00:15:54,610 --> 00:15:58,600 Look, Archimedes Pi. Well, everybody. 158 00:15:59,110 --> 00:16:03,730 And to Pi. Why not try your hand with the new number? 159 00:16:04,120 --> 00:16:09,540 You will become as famous as Archimedes or Euler. You know, only one kind of immortality. 160 00:16:09,790 --> 00:16:13,240 That is the immortality of ideas. Your body passes away. 161 00:16:13,630 --> 00:16:18,700 But any fundamental ideas you create live on. That is real immortality. 162 00:16:19,130 --> 00:16:23,040 So you want to be immortal? Don't buy medicine. 163 00:16:23,370 --> 00:16:27,090 Live longer. Just work hard. Have ideas. 164 00:16:28,840 --> 00:16:35,460 Now I don't want. As I pointed out here, they don't need to jump out of the bath to become famous. 165 00:16:35,610 --> 00:16:47,219 That's extra bonus. But if you look around, you see, when Archimedes found Pi, he it was it being around. 166 00:16:47,220 --> 00:16:52,140 Everybody knew that somehow you have a circle and you had to travel around the circle. 167 00:16:52,350 --> 00:16:59,330 Its length was approximately a bit more than three times. You know, people who know practice everybody roughly speaking, see. 168 00:17:00,240 --> 00:17:05,570 So we know that the shortest distance between two points in a straight line, you got in a curve configuring. 169 00:17:05,670 --> 00:17:10,930 So how much longer? Well, people knew something. So Archimedes made that precise. 170 00:17:11,280 --> 00:17:16,020 He said, Well, I know what it is. And he did it this way. Now you can't say this is the number. 171 00:17:16,170 --> 00:17:21,270 So he was taking some material and actually formalising it, telling you what it was. 172 00:17:21,960 --> 00:17:26,670 So the question is, if you wanted to do something similar to Archimedes now, what would you do? 173 00:17:27,390 --> 00:17:35,490 Well, he'd look around and see what people are doing. What are the common equivalents of the people who are doing primitive agriculture now? 174 00:17:35,520 --> 00:17:39,210 Well, of course, they weren't sophisticated and they might recall physicists. 175 00:17:41,130 --> 00:17:50,100 And if you look around amongst your physics friends, you find that they have a number and the number is actually a name. 176 00:17:50,760 --> 00:17:54,569 It's called the Fine Instructor Conference. I don't need to know anything about what the instructor called. 177 00:17:54,570 --> 00:17:59,760 It is clearly something that has a name like fine structure implies something rather fine. 178 00:18:01,980 --> 00:18:05,400 And it is it is a marvellous thing. Physicists love it. 179 00:18:06,000 --> 00:18:11,129 And actually, whether you talk about the number which is called Alpha, well, you have to think of a letter. 180 00:18:11,130 --> 00:18:16,820 The alphabet first come, first served. Well, Alpha, sometimes people write one over other. 181 00:18:17,160 --> 00:18:20,280 Doesn't matter whether you have a numbers in this, each gives the other. 182 00:18:20,280 --> 00:18:26,100 So they don't prefer the right one over alpha. And this number is known quite well. 183 00:18:26,580 --> 00:18:31,620 Here it is. It's 137.035. 184 00:18:31,710 --> 00:18:34,740 Well, you read it yourself. That number is known. 185 00:18:35,280 --> 00:18:43,379 But what is it? Now, see, people now know a lot more than they did in the early days are quite more advanced. 186 00:18:43,380 --> 00:18:46,440 They have pocket calculators. They don't you think they press a button? 187 00:18:46,740 --> 00:18:50,280 Hopefully. So they know this. But what is it? 188 00:18:50,610 --> 00:18:55,830 Well, let me give you a quotation from a physicist, a very famous physicist. 189 00:18:56,340 --> 00:19:00,810 I'll show you who he was. He was called Richard Feynman. 190 00:19:01,410 --> 00:19:05,370 And there's a picture of Richard Feynman. He was he got a smile on his face. 191 00:19:05,730 --> 00:19:11,760 He was always making jokes, but he was one of the great physicists of the 20th century and unfortunately not dead. 192 00:19:12,300 --> 00:19:15,510 And Richard Feynman said the following thing. 193 00:19:15,900 --> 00:19:22,890 So I agree with you because he's very. But it is visible if I swear is not me. 194 00:19:23,340 --> 00:19:27,770 Feynman swearing. So I hope I'm solved. 195 00:19:28,690 --> 00:19:36,690 And I said, Where does Alpha come from? This number is it related to PI or press E? 196 00:19:37,200 --> 00:19:40,319 He thinks back to Archimedes Euler, his new number. 197 00:19:40,320 --> 00:19:41,820 Well, where did it come from? 198 00:19:41,830 --> 00:19:49,170 It's a number that emerges from physics in some marvellous way, but nobody knows quite about much about it because nobody knows. 199 00:19:49,770 --> 00:19:54,419 This is one of the great damn mysteries of physics. Now you see, it is here. 200 00:19:54,420 --> 00:19:58,980 It's fireman swearing, not me. And a magic number. 201 00:19:59,580 --> 00:20:03,600 Now everybody likes magic, you know, wave in the air, abracadabra. 202 00:20:03,960 --> 00:20:08,040 A magic number that comes to you with no understanding by man. 203 00:20:09,370 --> 00:20:13,420 Where did it come from? You might say the hand of God. 204 00:20:14,440 --> 00:20:19,060 I'm just theological. Well, I didn't know what it means, but. 205 00:20:20,680 --> 00:20:27,070 And we don't. And we don't know how he. That is the capitalist way he pushed his pencil. 206 00:20:27,520 --> 00:20:32,200 So this is what Feynman said. It's a challenge. Can you answer his question? 207 00:20:32,290 --> 00:20:37,720 What do you offer you? You know something about it, but you don't know where it comes from. 208 00:20:38,320 --> 00:20:43,299 Where are you born? Where we belong. Is it part of Israeli supply? 209 00:20:43,300 --> 00:20:46,590 Is it ready? Well, well, well, well, well. 210 00:20:46,960 --> 00:20:50,320 I think the answer is yes. But I better not spoil your fun. 211 00:20:50,650 --> 00:20:53,860 You go away. Anyway, he gets not to come back. 212 00:20:54,340 --> 00:20:57,790 Give it to me. If not, I might leak the secrets privately. 213 00:20:58,690 --> 00:21:03,430 So that is the great problem, is a good example of a challenge. 214 00:21:03,940 --> 00:21:07,990 You look at numbers, play with numbers, but play with interesting numbers. 215 00:21:08,290 --> 00:21:13,329 Play numbers that might be important. This number is not an arbitrary number is number. 216 00:21:13,330 --> 00:21:16,360 It plays a very fundamental role in all of physics. 217 00:21:16,750 --> 00:21:20,710 Everywhere physicists look, this pops up because think about pi. 218 00:21:21,310 --> 00:21:24,520 Pi doesn't just occur in the slums of the circle. 219 00:21:24,760 --> 00:21:28,180 All my physics. I know that PI occurs almost everywhere. 220 00:21:28,660 --> 00:21:33,049 If you look at Gaussian distribution, you find PI. You look at this everywhere. 221 00:21:33,050 --> 00:21:37,990 You look at mathematics. Pi pops up. Why? Well, God only knows. 222 00:21:40,540 --> 00:21:45,910 And this number here is the same is a number that pops up everywhere you look. 223 00:21:46,240 --> 00:21:51,100 You do an experiment with this, that it's there. You do another experiment, something else is there. 224 00:21:51,640 --> 00:21:55,390 Same number and author was there. How does that happen? 225 00:21:56,080 --> 00:22:01,390 Is magic. And magic is really the great beauty of mathematics. 226 00:22:01,750 --> 00:22:05,740 It is fun, enjoyable, yet deeply serious. 227 00:22:06,750 --> 00:22:13,950 We tell us things about the world we didn't understand, and even when you've done it, you stand back and admire the miracle. 228 00:22:13,960 --> 00:22:17,770 So it is really mind bogglingly spectacular. 229 00:22:18,340 --> 00:22:26,500 And so I think if you solve this problem, you know, we really done a lot to increase our understanding of the universe. 230 00:22:26,890 --> 00:22:34,350 And so it is a challenge. And if you have any of you are one of the challenges that it is. 231 00:22:34,360 --> 00:22:43,330 But it's not an easy challenge. I should tell you that this has been around for, let's say, at least 50 years of more so. 232 00:22:43,630 --> 00:22:48,010 And many of you have tried to solve that problem and got nowhere. 233 00:22:48,930 --> 00:22:52,530 So but that's always true of all the great problems of the past. 234 00:22:53,130 --> 00:22:58,980 They've been around sometimes for hundreds of years. Think of Andrew Wiles solving Fermat's Last Theorem in this building. 235 00:22:59,220 --> 00:23:09,540 I mean, the building comes off and so probably it may have been around for 5000 years. 236 00:23:09,900 --> 00:23:12,090 And of course, nowadays things move much faster. 237 00:23:12,270 --> 00:23:19,470 You know, 50 days now with Google and all that is equivalent to several hundred days solving things much quicker. 238 00:23:19,830 --> 00:23:25,980 So you expect after 56 years, this problem would have been solved, but it hasn't. 239 00:23:26,910 --> 00:23:35,309 There's a real challenge. Can you keep up the pressure of advancing mathematics by not just doing little calculations? 240 00:23:35,310 --> 00:23:45,180 That's a dull theology, but solving fundamental questions which have a long history and a great importance and a great beauty. 241 00:23:45,480 --> 00:23:49,800 And of course, you want when you solve this problem, you don't only want understand. 242 00:23:51,350 --> 00:24:00,020 This new number, I'm sure you want to ask, is there some relationship, some analogue or Euler's formula with two fire equals one? 243 00:24:00,800 --> 00:24:08,600 Does this have something to do with that? Because that was the ultimate beautiful formula, the one that I said called to be or not to be. 244 00:24:09,610 --> 00:24:18,760 Well, Shakespeare was a great writer. But there are other great writers who are something else which goes beyond the Shakespearean quotation. 245 00:24:19,210 --> 00:24:22,990 Well, there you see life, mathematics, literature. 246 00:24:23,890 --> 00:24:27,190 Don't stop. There's always room for new things. 247 00:24:27,190 --> 00:24:35,770 And so with an audience full of some young people, some not so young, I don't think there's this challenge. 248 00:24:36,100 --> 00:24:40,510 Can we push the boundaries of what we know little further? 249 00:24:41,300 --> 00:24:45,280 We don't do that. We're just copying our ancestors. 250 00:24:45,720 --> 00:24:50,920 By the way, we had a lot of discussions, some of our meetings about modern computers. 251 00:24:51,250 --> 00:24:54,610 Will the computer replace the human mind? We will. 252 00:24:54,610 --> 00:24:58,390 Artificial intelligence pushes make us all redundant out of work. 253 00:24:59,880 --> 00:25:06,990 People think there's a lot of serious talk these days about replacing the human brain almost entirely by artificial intelligence. 254 00:25:07,770 --> 00:25:11,820 Well, fortunately, I'm a believer in that. You can't do that. 255 00:25:12,420 --> 00:25:22,290 I think artificial intelligence of any kind, however sophisticated or basically has limitations, the human mind does not have those limitations. 256 00:25:22,890 --> 00:25:26,640 And the human mind has evolved over several billion years. 257 00:25:27,030 --> 00:25:33,720 So evolution and no amount of clever manipulation by the scientists is going to catch up. 258 00:25:34,410 --> 00:25:38,100 So they cheer you up. You're not going to be I don't have a job. 259 00:25:39,510 --> 00:25:44,730 Stay with the mathematics and think not just don't don't do routine calculations. 260 00:25:44,910 --> 00:25:50,140 The computer wipe that off the board very fast. That's don't think deeply think imaginatively. 261 00:25:50,370 --> 00:25:54,480 Have brilliant ideas. Think of things that nobody would think of, even a computer. 262 00:25:55,050 --> 00:25:59,760 Then you're ahead. So there's that left message for you. Let's encourage the future. 263 00:25:59,970 --> 00:26:09,210 Don't be depressed. Just remain enjoying doing mathematics, enjoying the fun of it, and realising that the same time you can do something important. 264 00:26:09,630 --> 00:26:14,370 Well, I think I've used up my time and I now. Woman comfortable chair. 265 00:26:26,340 --> 00:26:30,140 If you want to stay this university. Oh, yes. No, no. Sorry. 266 00:26:30,350 --> 00:26:38,910 I was on the side left. So sometimes that goal is useful. 267 00:26:40,050 --> 00:26:43,860 Yes, I should have said this lecture is course called the Titchmarsh lecture. 268 00:26:44,340 --> 00:26:46,110 So I should say something about Titchmarsh. 269 00:26:47,430 --> 00:26:53,280 Well, actually, I shouldn't say much about Titchmarsh because I didn't want him to go for the many very few words. 270 00:26:54,090 --> 00:27:01,230 It is very similar to the famous physicist Paul Dirac, who's also many, very few words, and I'll tell you stories about that. 271 00:27:01,680 --> 00:27:02,910 So they spoke very little. 272 00:27:03,480 --> 00:27:12,720 And so when I came to Oxford, I had to go to my old building, not this grand building here, and I had to get the keys to my office. 273 00:27:13,020 --> 00:27:16,470 That was in 1961, sometime back in the Middle Ages. 274 00:27:17,130 --> 00:27:22,380 And I had to go and see this march because he was the senior officer. 275 00:27:22,920 --> 00:27:26,430 So I went into his office. I sat down. He gave me the key. 276 00:27:27,000 --> 00:27:30,110 I said. And we did. We did. 5 minutes. 277 00:27:30,120 --> 00:27:36,840 Nothing happened. I got up and walked out. He didn't he wasn't the man to wear his words. 278 00:27:39,630 --> 00:27:43,620 And actually, a few years later, he died. And I. I took over his office. 279 00:27:43,620 --> 00:27:50,010 But that's another story. And I tell you about Dirac since I thought I'm talking about people, few words. 280 00:27:50,220 --> 00:27:58,770 Now, Paul Dirac was the most brilliant physicist of the 20th century after Einstein in the hierarchy of physics, Einstein is way up there. 281 00:27:59,130 --> 00:28:05,110 Dirac is just after him and the others. That's modern physics. 282 00:28:05,130 --> 00:28:11,250 I mean, if you go back, if you include Newton and so on. But and Dirac was a memorable man. 283 00:28:11,650 --> 00:28:16,860 Now he had an interesting background. His name was Paul at the Maurice Dirac. 284 00:28:16,860 --> 00:28:26,040 So obviously French origin and his France father, who'd come to Britain from French speaking country, came from Switzerland or Belgium. 285 00:28:26,340 --> 00:28:35,710 Anyway, he was very keen that his son should learn French, so keen that he insisted that at all mealtimes you didn't get any food. 286 00:28:36,510 --> 00:28:42,900 I think he spoke French. Well, if you have any experience with children, you know that he's not very productive. 287 00:28:44,100 --> 00:28:54,509 So the outcome of this was that as soon as Dirac left home and he stopped speaking, his father be sort of speaking French and see he spoke almost. 288 00:28:54,510 --> 00:28:58,470 I was speaking to a man of very few words, and that's true. 289 00:28:58,800 --> 00:29:03,360 He was he really cut his father off completely. And he never spoke French. 290 00:29:04,560 --> 00:29:10,350 I mean, trying to indoctrinate your children by force is counterproductive. 291 00:29:11,550 --> 00:29:15,840 Now, I'll tell you one story and I will stop. Give you an example. 292 00:29:16,290 --> 00:29:24,000 Dirac. Everybody knew he was a man of few words. One occasion he was Fellows and Jones College, Cambridge. 293 00:29:24,630 --> 00:29:29,220 And he went in to lunch one day and sat down. 294 00:29:29,220 --> 00:29:32,490 And a young lady sat down beside him. Hit him. 295 00:29:32,730 --> 00:29:37,110 This is dreck. I've taken the bet that you will say these three words to me. 296 00:29:38,190 --> 00:29:50,260 He didn't do that. He said, You lose. So you see, he was a man of few words. 297 00:29:51,190 --> 00:30:00,970 So I will follow his example announcing that. I think. 298 00:30:03,530 --> 00:30:10,490 Okay. And I think the company I'm sorry, is this is the hot chair. 299 00:30:14,410 --> 00:30:19,540 Right, Don. Nice to meet you. A young 70 year old. 300 00:30:19,870 --> 00:30:25,000 Yes. So thank you so much for this inspiring lecture. 301 00:30:25,370 --> 00:30:34,330 So maybe I could ask you a question. Yes. Yes. Do you think there should be a formula for the fine structure constant or related to Euler's formula? 302 00:30:35,830 --> 00:30:41,770 Yes. I'm a man of few words. 303 00:30:44,200 --> 00:30:47,920 Well, it depends what you mean by a formula. So you've always had the question. 304 00:30:48,220 --> 00:30:52,510 What do you mean by and former the like, you know, format. 305 00:30:52,540 --> 00:31:01,180 Well in PI this isn't really a formula of a by the procedure for carrying by by going some complicated limiting process. 306 00:31:01,750 --> 00:31:10,300 And I claim that this number has all the properties that you think of as PI, but it's a bit more difficult. 307 00:31:11,110 --> 00:31:16,090 Yes. So it is a number with a good ancestry. 308 00:31:16,450 --> 00:31:22,300 Of course, it's a it's a dimensionless number from physics. So you think there are other dimensionless numbers from physics? 309 00:31:22,330 --> 00:31:25,480 Yes, I think that is sort of the same way you see in physics. 310 00:31:25,870 --> 00:31:32,950 Usually you measure things in terms of units, velocities, speed, speed, distance ratio, mass, 311 00:31:33,280 --> 00:31:40,749 every thing the physics depend on the units you use, you take your units metric to balance metres centimetres, 312 00:31:40,750 --> 00:31:46,390 you have to rescale things, but sometimes in a ratio of two things which are the same dimensions, 313 00:31:46,660 --> 00:31:50,740 then they cancel out and they have no dimensions left. So they are not pure numbers. 314 00:31:51,420 --> 00:32:00,010 And by an example, if your circle radius is two pi are not that are you cancel the R and you get pi. 315 00:32:00,040 --> 00:32:05,110 So pi is comes by cancelling all the dimensions and you do that with other quantities. 316 00:32:05,320 --> 00:32:09,700 And this find such a constant is the example dimensionless number. 317 00:32:10,780 --> 00:32:14,650 LeBron. Your number is your number. It comes from mathematics. 318 00:32:14,830 --> 00:32:24,340 How it. So there's a lot of young people here from local schools, I think might be interested. 319 00:32:24,640 --> 00:32:28,620 They might be interested to know how you first got interested in mathematics. 320 00:32:28,630 --> 00:32:34,360 Was it an inspiring teacher, your parents, a book you read, a problem you heard about? 321 00:32:35,350 --> 00:32:38,470 Well, very often people say, yes, somebody inspired me. 322 00:32:38,800 --> 00:32:43,360 And, you know, teachers can be very inspiring. My wonderful teacher, she was so inspiring. 323 00:32:43,810 --> 00:32:48,640 So I think I was well, I was fortunate in a way. 324 00:32:48,970 --> 00:32:53,170 I didn't have to be inspired by a teacher. I was naturally inspired myself. 325 00:32:53,170 --> 00:33:03,010 I mean, and I, I perfectly respectable teachers. 326 00:33:03,430 --> 00:33:07,630 Later on, I got some quite good I had a good, very inspiring teacher rather late in life. 327 00:33:08,620 --> 00:33:13,600 Late in life, meaning when I was 16. I mean, by that time your education's nearly finished. 328 00:33:13,990 --> 00:33:23,380 So when I was 16, I was sent to a school called Manchester Grammar School because they had a very good mathematics, tricked, pretty good university. 329 00:33:23,530 --> 00:33:29,680 The teacher there, it was really inspiring, very old school style person. 330 00:33:29,890 --> 00:33:32,920 He'd been to Oxford, but he thought the best student would go to Cambridge. 331 00:33:32,920 --> 00:33:36,040 So I was trained to go to Cambridge and he was very inspiring. 332 00:33:36,340 --> 00:33:41,530 You made his work very hard. I really worked harder in that year than any time in my life, either before or since. 333 00:33:42,010 --> 00:33:45,250 So he was inspiring, but I already decided the message and before that. 334 00:33:45,580 --> 00:33:48,580 But at that stage he gave me excellent grace. Yes. 335 00:33:49,120 --> 00:33:56,139 So any time in your life you may be inspired, maybe initially or really strong, and inspiration is very helpful. 336 00:33:56,140 --> 00:33:59,730 That inspiration stayed with me. I still think about him. Yes. 337 00:34:00,100 --> 00:34:07,540 You so teachers can have a big effect on your life and good teachers, you know, you can change your life in a minute. 338 00:34:08,170 --> 00:34:11,620 You go and hear good teacher or good lecture and you come away. 339 00:34:12,400 --> 00:34:17,410 Your life is changed and your wife is. You know what inspired her to do mathematics? 340 00:34:18,320 --> 00:34:23,530 Uh, well, my wife, very complicated story, came in very poor background. 341 00:34:23,950 --> 00:34:33,460 Her father works in the dockyards. Nobody. Her family went to technical school, so she found you good at mathematics. 342 00:34:33,730 --> 00:34:41,620 And that was her way out of poverty. And I think what inspires you more than to rise above your roots? 343 00:34:42,040 --> 00:34:48,520 So he pulled us up from nowhere. Ended up by being the best mathematician in a school the best. 344 00:34:48,940 --> 00:34:52,479 Got all the prizes, the university and the, you know, doing very well. 345 00:34:52,480 --> 00:34:58,129 And for me, that was. But no, no. 346 00:34:58,130 --> 00:35:01,640 She pulled herself up entirely by her own existence, her own ability. 347 00:35:02,000 --> 00:35:07,600 And she had the brains. And she was better than no good at English. 348 00:35:07,620 --> 00:35:11,150 She failed all her command in Scotland. So. 349 00:35:13,280 --> 00:35:18,410 And. But. But you always had a good mathematical brain and use it. 350 00:35:19,580 --> 00:35:23,150 So it does help you have a good mathematical brain. You want to do mathematics. 351 00:35:23,390 --> 00:35:26,540 But if you have a good mathematical brain, you enjoy mathematics. 352 00:35:27,140 --> 00:35:31,270 And that sort of feedback, that makes you better. So. 353 00:35:31,340 --> 00:35:38,209 So you're one of the world's most famous mathematicians, and you must have had many great moments, great mathematical moments. 354 00:35:38,210 --> 00:35:46,820 But this is the one moment that you mathematical discovery or moment when you discovered something that stands out among all the others. 355 00:35:47,850 --> 00:35:52,550 Uh, well, yes and no. 356 00:35:53,690 --> 00:36:00,950 All good answers come like this. I worked on something which eventually became called index. 357 00:36:01,130 --> 00:36:06,440 It doesn't matter what it is, but it's. And it wasn't a theorem, but it took me. 358 00:36:06,770 --> 00:36:11,240 It has so many ramifications. Took me 20 years to develop. So it became a theory. 359 00:36:11,990 --> 00:36:15,320 And so that was undoubtedly my best work. 360 00:36:15,740 --> 00:36:19,490 And but it covered that two years I'm the same. 361 00:36:19,500 --> 00:36:23,300 And I am still working on it now. So it takes over your life. 362 00:36:23,930 --> 00:36:27,260 And so in that sense, that's the best thing I've ever done. 363 00:36:27,760 --> 00:36:35,570 But so I will embrace it. It includes other somethings. So that's yes, I think if you done something like that, you you didn't even know it. 364 00:36:36,560 --> 00:36:40,100 You didn't realise that you you know, you found a gold mine. 365 00:36:41,080 --> 00:36:45,879 And you find a gold mine. You know, you go on digging and digging when the gold ran out. 366 00:36:45,880 --> 00:36:48,880 But you so long as it's there, you keep digging. So. 367 00:36:49,120 --> 00:36:53,630 Yes, so I have. Sorry, I rambled a bit. 368 00:36:53,650 --> 00:36:57,129 No, no. But it happened at a precise moment in the afternoon or something. 369 00:36:57,130 --> 00:37:02,120 When you suddenly saw what? Well, there have been occasions like that. 370 00:37:02,350 --> 00:37:11,710 This is, of course, famous bridge story w where Hamilton, the great Irish mathematician who had flights of inspiration as he crossed the bridge. 371 00:37:12,340 --> 00:37:17,710 And you wrote it down there then and now when you cross that bridge, you'll see a black saying here what Hamilton discovered. 372 00:37:18,910 --> 00:37:22,840 And that's very there are many stories of mathematics which are apocryphal. 373 00:37:23,320 --> 00:37:27,010 Archimedes jumping out of his bath with new photographic evidence. 374 00:37:30,160 --> 00:37:34,210 Newton of Apple Tree, where there is an apple tree. But it's not quite clear. 375 00:37:34,240 --> 00:37:43,030 Newton was sitting under it. So, you know, these are stories which are sort of they're really myths. 376 00:37:43,450 --> 00:37:47,650 But good myth is carries a lot of importance, even if it's not actually true. 377 00:37:48,490 --> 00:37:52,690 And so a lot of things are missed. But in the case of Dublin, one is fact. 378 00:37:53,470 --> 00:37:58,360 In my case, I'm trying to think of anything. I've been a few cases in my life. 379 00:37:58,870 --> 00:38:06,430 I remember reading that already. Poincaré, the great French mathematician, used to claim that he got good ideas getting on another bus. 380 00:38:07,480 --> 00:38:12,130 Well, you know, I tried that didn't work. 381 00:38:12,880 --> 00:38:16,540 But I remember very clearly once when going for a long walk. 382 00:38:19,490 --> 00:38:22,960 With. I think my friend says, end of the walk. 383 00:38:23,510 --> 00:38:29,290 We'd solve the problem. And in doing their work, it was a flash of inspiration. 384 00:38:29,570 --> 00:38:38,180 So I remember that clearly now. It was one particular day, something we work on for quite a long time, and we went for a walk and then we walk. 385 00:38:38,700 --> 00:38:42,290 We had that's it. And then we to do other a bit like that. 386 00:38:43,130 --> 00:38:47,060 But within a mile of bus, it could happen anywhere. It could be a bath. 387 00:38:47,060 --> 00:38:53,150 It could be this. And so you get these flashes of inspiration now where they don't know where they come from. 388 00:38:53,750 --> 00:38:58,910 And they crack a problem for you. I think it's a sort of fundamental, difficult something we've been holding up. 389 00:38:59,630 --> 00:39:03,590 And so, yes, I've had that few just not very often, you know. 390 00:39:04,120 --> 00:39:07,220 But I saw it last once. 391 00:39:07,580 --> 00:39:10,760 Yeah. How did these ideas, good ideas come true? He said. 392 00:39:11,030 --> 00:39:15,560 I think I had one good idea, one's modesty, you know. 393 00:39:16,090 --> 00:39:19,400 Now all mathematicians get stuck when they're trying to solve problems. 394 00:39:19,500 --> 00:39:25,100 I feel I'm stuck almost all the time. Yes. So sort of. So what do you do when you're stuck on a problem? 395 00:39:25,310 --> 00:39:32,450 Very good question. Well, after his experience helps, the first time you're stuck on a problem, 396 00:39:32,930 --> 00:39:38,360 you you know, well, it can be devastating and people don't know what to do. 397 00:39:39,080 --> 00:39:42,590 But with a bit of experience, you know, to do things, several things you do. 398 00:39:42,620 --> 00:39:46,300 One is you leave them alone for a while. You forget about it. 399 00:39:46,730 --> 00:39:52,190 Use something else. So you should have a stock of things you can do work on when this problem is stuck. 400 00:39:52,340 --> 00:39:56,330 You work on that problem and that, and then maybe you come back to the person later on. 401 00:39:56,660 --> 00:39:59,899 You have a half a dozen problems and you're stuck on each one. 402 00:39:59,900 --> 00:40:02,970 You shuffle it round. You find you can make progress. 403 00:40:02,990 --> 00:40:06,920 That's one solution. Another solution is that kind of problem. 404 00:40:07,340 --> 00:40:13,400 And you talk to your friends, talk to other people, perhaps have different point of view. 405 00:40:14,300 --> 00:40:20,870 See if you hit a wall, brick wall, you can bang your head against the brick wall till your head breaks. 406 00:40:21,200 --> 00:40:24,210 The wall doesn't break. That's not a good way of making progress. 407 00:40:24,620 --> 00:40:26,870 But it may be that that wall actually is finite. 408 00:40:26,870 --> 00:40:31,820 And you go round the wall and you've got friends telling you they look, why are you banging against the wall? 409 00:40:33,540 --> 00:40:40,400 Yeah, and that happens very often. You don't realise that the obstacle you're hitting is not essential. 410 00:40:40,670 --> 00:40:44,310 There's a way around it and it's another point of view. 411 00:40:44,330 --> 00:40:47,809 Literally perspective can tell you how to do that. 412 00:40:47,810 --> 00:40:51,230 And that happened with me. I'm a gregarious mathematician. 413 00:40:51,620 --> 00:41:00,290 Sorry, good. Gregarious is rather talkative, which means I like to talk to people and I do not like to sit by myself too long. 414 00:41:00,590 --> 00:41:09,230 You've got to balance it in life. You are an alternate, sitting quietly and thinking and then going when talking as a very good form in your life. 415 00:41:09,740 --> 00:41:13,910 Sitting by yourself quietly for a long time that leads to introversion. 416 00:41:14,750 --> 00:41:17,480 Interested is not healthy, is also boring. 417 00:41:19,130 --> 00:41:29,480 It's also like between being thinking hard by yourself, going out with friends, having a good drink or enjoying life and mixing those two together. 418 00:41:29,600 --> 00:41:35,360 And your friends may say, Well, I got an idea about your problem. So you can combine life with that. 419 00:41:35,420 --> 00:41:43,490 That's the way I've tended to work. I tend to be gregarious, talkative, interact with other friends and they give I get that way. 420 00:41:44,030 --> 00:41:51,440 I learn new things. The friends teach you something, you learn something. I mean, you learn technically you just pick up points of view. 421 00:41:52,400 --> 00:41:59,870 But all the rules you've faced for decades, problems that you wanted to solve somehow couldn't. 422 00:42:00,530 --> 00:42:04,580 Yes. I mean, you could say that all my life I've been trying to solve some really hard problem. 423 00:42:04,940 --> 00:42:13,250 And maybe today I solved it, you know, because you don't know until you've got round the wall with no whether there was a wall there. 424 00:42:14,090 --> 00:42:17,149 So it's a very tricky situation. No. 425 00:42:17,150 --> 00:42:22,190 I mean, all your life you're trying to do things and some big things. 426 00:42:22,430 --> 00:42:25,970 You feel the life behind it and you don't quite know what they are. 427 00:42:26,330 --> 00:42:30,860 And, you know, maybe in your life you find out or maybe you don't mind that. 428 00:42:31,400 --> 00:42:37,700 So we always searching for the ultimate big breakthrough, whatever that big breakthrough is. 429 00:42:37,940 --> 00:42:41,060 And I'm 93 and I'm still searching. 430 00:42:41,990 --> 00:42:56,120 I'm not giving up. So in your in your long career, you must have met many, many famous mathematicians, too. 431 00:42:56,210 --> 00:42:59,420 Does any one of them stand out particularly? 432 00:43:00,200 --> 00:43:06,890 I think I bet nearly all the people in my vision of the world, my world almost I. 433 00:43:07,220 --> 00:43:11,790 I met all your fields, medallists. That's a good start. Citing one. And I. 434 00:43:11,820 --> 00:43:15,260 Yes, if you live long enough, you tend to meet more people. 435 00:43:17,210 --> 00:43:20,480 That's a truism. I think I've met everybody. 436 00:43:20,900 --> 00:43:24,800 And what is remarkable is the variety. 437 00:43:25,580 --> 00:43:34,100 Mathematicians come in all shapes and sizes and be outside mathematics. 438 00:43:34,100 --> 00:43:40,130 Think we are all the same. A mathematician is a peculiar character who does like mathematics. 439 00:43:40,520 --> 00:43:45,230 Actually, that's not true at all. We are. We like mathematics, but we are very, very lot. 440 00:43:45,800 --> 00:43:48,320 There are tall people. And so people, in fact, we will be. 441 00:43:48,800 --> 00:43:54,230 And of course, significantly, those who work this kind of mathematical work and that kind of mathematics, 442 00:43:54,530 --> 00:44:00,170 those who work this way or that way, we are a very good, broad cross-section of humanity. 443 00:44:00,620 --> 00:44:08,390 And so that is the diversity of people is actually a very healthy sign. 444 00:44:08,510 --> 00:44:12,530 Mathematics, I think I saw I don't know when I started this one thing going, I keep going. 445 00:44:13,430 --> 00:44:22,220 What was the question? Well. Was there anybody in particular that you remember standing out in some way? 446 00:44:22,250 --> 00:44:32,389 Well, let me say I've met many mathematicians who are obviously Steve said to me in some direction, I think Amanda was much better than me. 447 00:44:32,390 --> 00:44:41,450 In an analysis I let me and I met Jean-Pierre said he was much better than me and number theory and 448 00:44:41,450 --> 00:44:51,890 I met many people who obviously tremendously impressive in the sheer ability to solve our problems. 449 00:44:52,250 --> 00:44:57,110 Doug Milner for example, another man position and I made each one of these I met, I said, Well, 450 00:44:57,110 --> 00:45:02,000 I can't possibly compete with these guys on that score because they're just better than me. 451 00:45:02,750 --> 00:45:09,650 They've got a brain that is very good for this. My brain is of, you know, inferior subsets or different. 452 00:45:10,130 --> 00:45:14,690 So, yes, I've met a lot of people who I consider robots. 453 00:45:14,990 --> 00:45:18,890 Six In Britain, the example of physics is a genius. 454 00:45:19,250 --> 00:45:24,140 So the people who are really good. But every genius had his weak points. 455 00:45:25,700 --> 00:45:34,910 Well, it's Maurice by definition. A genius is somebody is so focussed on doing something that he doesn't notice something else. 456 00:45:35,630 --> 00:45:40,790 Uh, they never knew Ramanujan, but he had his weaknesses too. 457 00:45:41,790 --> 00:45:46,940 Yes. So, I mean, if the one was genius who knew everything very depressing. 458 00:45:48,370 --> 00:45:52,010 I mean, I think was there was one person like that. It was Archimedes. 459 00:45:52,250 --> 00:45:56,090 And fortunately for me, he lived a long time ago and I write his metal. 460 00:45:56,300 --> 00:46:03,800 So I feel, you know, I can. But he would be if I'd been around in Archimedes time, he would have been a daunting figure. 461 00:46:04,580 --> 00:46:12,620 And so but nowadays there are great mathematicians of all kinds and there's lots of them, 462 00:46:12,620 --> 00:46:18,890 and they're all better than me in some particular niche, but they're not all better or in all directions. 463 00:46:19,640 --> 00:46:25,730 So that's what friends. Yeah, but it's, it is interesting that I mean, the same thing is true. 464 00:46:25,730 --> 00:46:30,620 If you're a musician you're very much better at Panenka Jettisons while the musician. 465 00:46:31,010 --> 00:46:39,760 But he's better the the oboe, the violin. And so, you know, there's no single musician who is equally good across the entire slate. 466 00:46:40,190 --> 00:46:46,310 Oh, no, no, no writer. A poet who equally good writing in a large tragedy is more comedies. 467 00:46:46,910 --> 00:46:51,170 Shakespeare got pretty close. And, you know, so people get close. 468 00:46:51,740 --> 00:46:55,370 So this is the real Archimedes Newton. 469 00:46:56,300 --> 00:47:02,510 So they're all very big figures. And in my time, I've got to know quite a lot of mathematicians. 470 00:47:03,260 --> 00:47:12,050 Oh, really? Yes. And it's nice to have them because you get you you learn them, uh, both. 471 00:47:12,830 --> 00:47:20,330 Both the skills and limitations of the human mind. So, uh, well, that's what we do in life. 472 00:47:20,330 --> 00:47:24,680 We learn to live with our limitations and take advantage of our assets. 473 00:47:26,360 --> 00:47:31,060 So as well as being a great mathematician, you became president of the Royal Society. 474 00:47:31,070 --> 00:47:36,160 That was a very different job to do, talking to governments and so on. 475 00:47:36,170 --> 00:47:42,560 So was was that a sort of shock to do that? Did mathematics help you in the in the job? 476 00:47:42,600 --> 00:47:46,580 Well, I'll come clean. I'll tell you exactly. 477 00:47:48,620 --> 00:47:53,680 I was approached. By then President Ross. 478 00:47:53,690 --> 00:47:58,810 I'd say we council decided we'd like to. Oh, but you didn't express it. 479 00:47:59,390 --> 00:48:02,410 I was horrified. It was a good one. I'm not. 480 00:48:03,160 --> 00:48:08,090 I'm not. I had no idea. Reverend Rossetti, you're a real scientist. 481 00:48:08,780 --> 00:48:15,080 And so he said, Well, I'll think about it. So I went back and thought about this. 482 00:48:15,200 --> 00:48:19,410 Talk to my wife, you know, should I take on this job? I'm not I'm not mad. 483 00:48:19,520 --> 00:48:25,520 I'm a scientist, an ordinary mathematician. And I really was very unsure. 484 00:48:26,300 --> 00:48:31,280 And finally, after a lot of hard thinking, I said, perhaps it's my duty to think of my party. 485 00:48:31,280 --> 00:48:35,120 I was influenced by the fact that I'd had all my life. 486 00:48:36,140 --> 00:48:47,480 Fortunately, very early on, I had jobs which allowed me to do my research, which involved a lot of teaching my youth. 487 00:48:47,480 --> 00:48:53,380 But then later on, less and less. And I was really a free man to spend my time doing mathematics. 488 00:48:54,980 --> 00:48:58,460 And I thought, I know. And I by this time I was aged 60. 489 00:48:58,960 --> 00:49:07,130 I thought I'd done my mathematics. Perhaps now it's time for me to repay to society in some other way. 490 00:49:07,280 --> 00:49:11,630 Maybe I. Maybe my days as a creative might be finished. So I take on the job. 491 00:49:12,590 --> 00:49:18,140 They took on the job. There's good sense of public duty because once you take it on, you learn the job. 492 00:49:18,590 --> 00:49:27,920 I learned that running mobilisation, which has its problems and Rosaria was a very old organisation, 493 00:49:28,340 --> 00:49:32,750 had very distinguished people to scientists, but they'd always sometimes mess this up. 494 00:49:33,470 --> 00:49:36,920 And I came to the young radical. I was 60, but so young radical. 495 00:49:38,080 --> 00:49:42,110 And I made a lot of changes. I changed roles. 496 00:49:42,110 --> 00:49:51,620 I mean, in lots of ways. I can tell you privately later on. And I'm glad to see that subsequent presidents that carried on the tradition. 497 00:49:52,010 --> 00:49:56,840 But old institution, you know, lives on in past. 498 00:49:57,350 --> 00:50:01,280 But they had to change the times. I felt the role wasn't changing fast enough. 499 00:50:02,000 --> 00:50:05,600 So I gave you a kick in the pants. That was my contribution. 500 00:50:06,890 --> 00:50:12,410 And after you had done that, did you find it difficult to get back to doing mathematics? 501 00:50:12,740 --> 00:50:17,420 Well, first of all, I didn't do it own. I was simultaneously master of Trinity College, Cambridge. 502 00:50:18,020 --> 00:50:22,159 So I had a double whammy. And so I thought, that's fine. 503 00:50:22,160 --> 00:50:30,020 I'm fully engaged in public service so that that my job as a mathematician, I'm now, you know, good for my duties. 504 00:50:30,020 --> 00:50:33,290 And then I will go in the scrap heap and die quietly. 505 00:50:33,740 --> 00:50:42,710 Unfortunately, things didn't work out like that. When I finished all of this stuff, I said goodbye to all these duties. 506 00:50:43,160 --> 00:50:50,790 Well, what were they going to do? I couldn't possibly keep up with all the young guys who would be doing mathematics in my absence. 507 00:50:52,200 --> 00:50:57,690 So where would I get a new idea? Unfortunately, this is where good fortune strikes you. 508 00:50:58,050 --> 00:51:02,970 I got a letter from my friend Michael Berry, who's a very good physicist. 509 00:51:03,540 --> 00:51:10,500 And when we collaborated, he had John Roberts here. And he said to me, I've come across this following problem in physics. 510 00:51:10,770 --> 00:51:14,430 It is mathematical. It should have solution. 511 00:51:15,330 --> 00:51:20,070 And so he gave me this problem and I found a very good man. 512 00:51:20,410 --> 00:51:24,270 I looked at it worked. Is good problem a solve? 513 00:51:24,300 --> 00:51:27,930 Interesting. I look at it as I looked at it. So what is it, first of all? 514 00:51:27,930 --> 00:51:36,330 Is it true? It is not true. If it's true, it probably state then it is not true. 515 00:51:36,720 --> 00:51:41,400 I looked at it. Nobody done it. There was this beautiful problem sitting around and nobody had done it. 516 00:51:41,970 --> 00:51:48,160 So I was given this free problem. And since and that was my time. 517 00:51:48,720 --> 00:51:57,629 This was 20 years ago. And so over the next ten years or more, I worked on that problem off and on in different ways. 518 00:51:57,630 --> 00:52:01,170 And that's grown and grown. And now that's the centre of my work. 519 00:52:01,860 --> 00:52:09,810 And so it came from responding to a question from a colleague who thought I might be interested and nobody else could contribute. 520 00:52:10,260 --> 00:52:14,460 And yes, that was a gift from God or a gift from Michael Berry. 521 00:52:16,620 --> 00:52:20,309 I mean, God works through an evil, so God has me down. 522 00:52:20,310 --> 00:52:27,300 But now he's a project, he's a problem. And he got mine a very you ask me question and that's how it works. 523 00:52:27,330 --> 00:52:34,500 Yes, that's really true. And I went to Michael Berry, various birthday parties and things, and told him I'd solve this problem. 524 00:52:34,500 --> 00:52:41,160 And it kept me going for 20 years. So you think older people can do mathematics as well as younger people? 525 00:52:41,760 --> 00:52:46,770 Absolutely. I think one of my complaints is that, well, I'll tell you a secret. 526 00:52:48,090 --> 00:52:55,050 Sorry, I have a son, my youngest son. 527 00:52:56,430 --> 00:53:03,510 Some say I told my son good ideas. He said that, look, we all know that mathematicians have their best ideas before they're 40. 528 00:53:04,230 --> 00:53:08,010 You want to get a feel of middle you yet under 40, you're over 80. 529 00:53:08,550 --> 00:53:13,840 It's quite impossible that you have a good idea. If think you've got a good idea, you deluding yourself. 530 00:53:15,150 --> 00:53:16,260 How do I disprove that? 531 00:53:17,040 --> 00:53:26,940 Well, I have been systematically trying to do try to persuade my son that I'm over 80 and I'm not 89, that you can do good stuff. 532 00:53:27,840 --> 00:53:31,920 He's slowly coming around. Maybe I. Maybe I'm right, but not sure yet. 533 00:53:33,030 --> 00:53:39,150 So trying to persuade people that you can good do good work when you're old is extremely hard. 534 00:53:39,750 --> 00:53:43,650 They think you're deleting yourself. And the thought has me alone. 535 00:53:44,010 --> 00:53:54,299 If you look back in history, you'll find that all of great mathematicians or physicists in the later years Einstein then without doubt, 536 00:53:54,300 --> 00:53:59,130 the greatest physicist of the 20th century and famous. 537 00:53:59,850 --> 00:54:05,700 But halfway through his life and done all his fundamental work, people are doing new things. 538 00:54:06,150 --> 00:54:11,010 And he didn't believe in them. He stuck his old roots in the past. 539 00:54:11,140 --> 00:54:14,280 Now he's currently up with the Times. He's passé. 540 00:54:14,280 --> 00:54:19,830 He's old man. You know, he's not keeping up. And so you passed aside, Einstein. 541 00:54:20,910 --> 00:54:24,660 And I think I know a bit about it. I've looked at it. 542 00:54:24,840 --> 00:54:31,620 I think I was right. It was wrong. But they didn't believe him because the old man seems to have drank when he was young. 543 00:54:32,010 --> 00:54:36,750 He had brilliant ideas and was a great man. Nobel Prize five year old one. 544 00:54:37,290 --> 00:54:40,470 He had crazy ideas. So you've gone crazy. Oh, man. 545 00:54:42,570 --> 00:54:45,300 And I think they're actually right. They were wrong. 546 00:54:45,600 --> 00:54:53,130 So is he disregarding what happens with elderly people if they realise they can't keep up the youngsters by running? 547 00:54:54,430 --> 00:54:59,140 You can't keep running the same rate and your 4850 ranks. 548 00:54:59,710 --> 00:55:03,640 But you may have wisdom. You may have instinct. 549 00:55:04,000 --> 00:55:10,180 You may be able to. And you say, well, if I get to contribute now, it's not going to be some trivial calculation. 550 00:55:10,180 --> 00:55:13,840 Anybody can do that. I got to contribute something great. 551 00:55:14,590 --> 00:55:20,649 So you radio stakes, you aim high, and then you tell people, I'm thinking about how you solve the part of the universe. 552 00:55:20,650 --> 00:55:24,010 They say, Oh, you're crazy. But sometimes they're right. 553 00:55:24,880 --> 00:55:27,700 And that's the way old people make big advances. 554 00:55:28,120 --> 00:55:33,970 And the Chinese, like the old people, there's one thing, you know, if you go to China and there was talk before China, 555 00:55:34,480 --> 00:55:39,280 the only thing I like about China or the Orient, they give respect to elderly people. 556 00:55:40,180 --> 00:55:46,330 This is America country for the young, you know, kind of the country with the old. 557 00:55:48,040 --> 00:55:54,310 That's why a lot of Chinese retired to China, because, you know, I think the older and older you get more and more respect. 558 00:55:54,880 --> 00:55:56,590 So finally you disappear under the clouds. 559 00:55:56,630 --> 00:56:08,090 And so I try to end with perhaps I could press you a bit on on something you raised in your lecture about artificial intelligence. 560 00:56:08,120 --> 00:56:14,259 Yes, I remember many years ago, nobody thought that a computer would be able to play good chess. 561 00:56:14,260 --> 00:56:18,430 And now my smartphone can beat me. I trust very easily. 562 00:56:18,850 --> 00:56:25,240 And now computers can check the proofs of theorems and maybe they'll be able to find theorems. 563 00:56:25,720 --> 00:56:28,950 So do you think mathematicians will become redundant now? 564 00:56:29,040 --> 00:56:32,520 No, absolutely not. But for example, chess. 565 00:56:32,960 --> 00:56:36,070 Well, okay. Computer can beat you at chess. But what? 566 00:56:36,070 --> 00:56:39,360 Are you ready? Chess itself. I see. 567 00:56:40,070 --> 00:56:46,050 I mean, we admit the chess society and computers is good getting better, but we lay down the rules. 568 00:56:46,060 --> 00:56:51,250 They just copied us. Okay, that's chess. Remote advancing. Now, you could do much more complicated things. 569 00:56:51,520 --> 00:57:02,380 The same principle. They don't have the imagination do something entirely new, or they have the capacity to do what we do, do much better. 570 00:57:03,430 --> 00:57:10,000 They have the capacity to invent new rules because now computers now will bend new rules, but they will invent rather dull rules. 571 00:57:10,270 --> 00:57:13,080 We won't have the really imaginative ones that go way beyond. 572 00:57:13,090 --> 00:57:20,350 They won't be like Einstein or our Shakespeare or that they will not be like that, because that requires a creative human mind. 573 00:57:20,740 --> 00:57:25,480 And I think the artificial intelligence community has got anywhere near that. 574 00:57:25,510 --> 00:57:31,000 They delude themselves. They are the ones who tell you exist. 575 00:57:31,660 --> 00:57:37,480 So I think and I know the very brilliant man I know by the code, Demis Hassabis, 576 00:57:38,020 --> 00:57:45,840 who runs DeepMind, is the big get the system, which is supported by Google. 577 00:57:46,000 --> 00:57:56,610 And we've done not only report chess but people at go we use a much more difficult game and the is aiming. 578 00:57:57,370 --> 00:58:03,400 I know the Japanese a very brilliant man and he said to me what he's trying to do is to develop machines that 579 00:58:04,030 --> 00:58:10,360 have emotions and you've got a machine as an emotion in principle to be able to tell you this is a good, 580 00:58:10,690 --> 00:58:11,710 beautiful theorem or not. 581 00:58:12,280 --> 00:58:20,160 But I think even that misses the point because we don't understand our own emotions well enough to create a machine that will do something similar. 582 00:58:21,060 --> 00:58:30,600 So I think I'm a firm believer in that the human mind will always be ahead of anything else that's created by machinery. 583 00:58:31,290 --> 00:58:34,490 Well, that's an optimistic note to end with. Thank you very much. 584 00:58:34,500 --> 00:58:40,580 It's been great. I began.