1 00:00:11,290 --> 00:00:15,820 Hello, thank you for that gracious introduction and for leaving your watch behind here. 2 00:00:15,820 --> 00:00:18,730 And it's very, very helpful. Should I stay in time? 3 00:00:18,730 --> 00:00:28,850 And thanks to Darrel Lombard as well for inviting me here, I'm delighted to be a speaker in this exciting programme. 4 00:00:28,850 --> 00:00:37,840 It's particularly good to have the opportunity to talk about a pretty, a pretty simple, all encompassing theme. 5 00:00:37,840 --> 00:00:42,220 The entire universe. That's what we going to be talking about tonight. Ladies and gentlemen, 6 00:00:42,220 --> 00:00:52,150 I want to begin with an observation that Einstein made in a letter to an old undergraduate friend of his three years before Einstein died, 7 00:00:52,150 --> 00:00:57,240 and it concerned what Einstein believed was a central miracle of. 8 00:00:57,240 --> 00:01:06,630 Science, physical science, and that is the fact that we find ourselves in a universe that has a deep underlying order, 9 00:01:06,630 --> 00:01:18,940 that order enables us to understand or have forged an understanding of the universe and do so in a mathematical way. 10 00:01:18,940 --> 00:01:25,240 One hundred and fifty years ago, the peerless thinker about the natural world, 11 00:01:25,240 --> 00:01:29,320 James Clerk Maxwell gave a lecture on the relationship between mathematics and physics. 12 00:01:29,320 --> 00:01:32,890 Broadly speaking, the same topic as I'm talking about tonight. 13 00:01:32,890 --> 00:01:39,970 Now I can't, of course, promise to bring you anything like his depth of depths of thought and experience. 14 00:01:39,970 --> 00:01:43,780 But I would just note that at the beginning of that lecture, 15 00:01:43,780 --> 00:01:51,040 he said that this relationship between the two subjects is far too magnificent for someone of his ability to discuss. 16 00:01:51,040 --> 00:01:59,320 So I hope you feel very sorry for me trying to do justice to this subject from my relatively low, low, low perch on things. 17 00:01:59,320 --> 00:02:10,510 But I will do my best and reflect on some of the things that some of the best thinking, I think is going on on this subject in this institute, 18 00:02:10,510 --> 00:02:22,020 which is you'll, as you'll hear, has played a central role in the story in in the past few decades. 19 00:02:22,020 --> 00:02:30,180 Let me begin by just giving a quick flyover of the of the topics I will be talking about. 20 00:02:30,180 --> 00:02:34,650 You have to start somewhere in a really good place to start on this topic is that person you may have heard 21 00:02:34,650 --> 00:02:45,090 of Isaac Newton and the torch of mathematics that he and others helped to shine on the natural world. 22 00:02:45,090 --> 00:02:50,160 Theories of gravity, electricity, magnetism, atomic forces are based on mathematics, 23 00:02:50,160 --> 00:02:57,450 and we'll be talking about the great successes that that arose from that observation. 24 00:02:57,450 --> 00:03:03,630 But the path between physics and mathematics, the relationship with them hasn't always run smoothly. 25 00:03:03,630 --> 00:03:12,690 And there was a what has been rather graphically noted by Freeman Dyson, a divorce between the subjects directly after World War Two. 26 00:03:12,690 --> 00:03:18,570 But they did get back together. As you'll hear, Oxford has a lot to do with that, 27 00:03:18,570 --> 00:03:25,350 and I'm going to be talking about the roles of the two foundational theories of the 20th century physics, 28 00:03:25,350 --> 00:03:34,740 quantum mechanics and the basic theory of relativity as the basis of the engine, so to speak of that close relationship. 29 00:03:34,740 --> 00:03:42,900 And I shall be asking whether it really is true that mathematics is today, broadly speaking, 30 00:03:42,900 --> 00:03:48,810 leading physics astray, as many, many comets or several commentators have have argued. 31 00:03:48,810 --> 00:03:52,020 And finally, just to embarrass myself and give you some amusement. 32 00:03:52,020 --> 00:03:58,080 I'm going to I'm going to leave hostages to fortune by looking to the future of the subject. 33 00:03:58,080 --> 00:04:02,220 And as you know, all predictions on about the future of science, 34 00:04:02,220 --> 00:04:07,890 like the future of British politics, are completely worthless, but it's entertaining nonetheless. 35 00:04:07,890 --> 00:04:11,840 All right. Let's begin with. 36 00:04:11,840 --> 00:04:22,430 The event that happened on an unremarkable, otherwise unremarkable summer's day in sixteen eighty seven, the fifth of July. 37 00:04:22,430 --> 00:04:27,140 Check the weather reports upon an ordinary day, nothing particularly going on. It was a Saturday. 38 00:04:27,140 --> 00:04:35,060 And on that day in London, a three volume book was published for the first time. 39 00:04:35,060 --> 00:04:44,500 And this was the book. The the mathematical principles of natural philosophy. 40 00:04:44,500 --> 00:04:49,750 Now this book is quite famous, now we call it Newton's Principia. 41 00:04:49,750 --> 00:04:56,620 It sold reasonably well. Never, actually. They actually tried. It was quite a difficult job to actually get to sell these books. 42 00:04:56,620 --> 00:04:57,110 But it was. 43 00:04:57,110 --> 00:05:11,950 Now many of you will know this has a status as the beginning of the mathematical approach to physical science, and it was written by Isaac Newton, 44 00:05:11,950 --> 00:05:23,200 Cambridge professor, who who was if I may use the word genius once he is the presiding genius of this subject. 45 00:05:23,200 --> 00:05:30,130 He was, by his own description, a natural philosopher. Remember what physicists did not? 46 00:05:30,130 --> 00:05:36,520 He would never have used that word about himself. He was a natural philosopher thinker about the natural world. 47 00:05:36,520 --> 00:05:43,240 The natural natural philosophy at that time was thought of as the rational study of God's creation. 48 00:05:43,240 --> 00:05:48,520 Very important that God is in there as your Oxford historian Rob. 49 00:05:48,520 --> 00:05:57,130 I live in his classic book Priest of Nature has demonstrated Newton regard himself more than anything else as a as a, 50 00:05:57,130 --> 00:06:04,720 as a a man of God to use a term that would have he would have he would have used. 51 00:06:04,720 --> 00:06:13,730 He was also a mathematician. Very important. And just to underline his his variety of skills, he was not just a great experiment, 52 00:06:13,730 --> 00:06:23,670 he was a great thinker about the natural world and a mathematician. So he really was blessed with with with a terrific, we would now say, skill set. 53 00:06:23,670 --> 00:06:32,130 In that book, he set out what we now pretty well, all of us, even even those who are not not versed in this subject, 54 00:06:32,130 --> 00:06:37,230 know is the way you do mathematical science at a very basic level. 55 00:06:37,230 --> 00:06:46,200 You have a basic mathematical structure. You make predictions about the natural world and you check that those predictions 56 00:06:46,200 --> 00:06:53,040 against the most accurate observations one has if if the if they disagree, 57 00:06:53,040 --> 00:06:56,520 then you feed back, you modify the theory and then put it back to nature. 58 00:06:56,520 --> 00:07:07,530 You're trying to account for that order, so to speak, in the universe around us and in this monumental book, not easy to read. 59 00:07:07,530 --> 00:07:12,840 Let's be clear, this was not. This was not J.K. Rowling. This was a tough read. 60 00:07:12,840 --> 00:07:21,540 It was in. There was the law of gravity, which don't need to say what it is in detailed a mathematical description of the force between two masses, 61 00:07:21,540 --> 00:07:35,840 any two masses at any distance apart, and also the laws of nature that that that that mathematically describe motion. 62 00:07:35,840 --> 00:07:39,800 It worked. I don't need to go into the details for the point, the point of view of this talk. 63 00:07:39,800 --> 00:07:50,270 It worked supremely well. You'll know great and justly celebrated observation perception that the force that pulls a piece of chalk or an apple 64 00:07:50,270 --> 00:07:56,360 to the ground or here on Earth is exactly the same force as the force that holds the Moon in the Earth's orbit. 65 00:07:56,360 --> 00:08:06,000 They all are a result of this of this law that is pervasive everywhere and maybe throughout all time. 66 00:08:06,000 --> 00:08:15,690 Very important to notice, nonetheless, that although this was a a an absolutely astonishing achievement to have achieved that intellectual framework, 67 00:08:15,690 --> 00:08:22,200 first of all, he didn't do it on his own. He was standing, as he said on the shoulder of giants Galileo, you're Kepler's, 68 00:08:22,200 --> 00:08:26,250 right, the way back to the ancient Greeks, whom he revered more than anybody else. 69 00:08:26,250 --> 00:08:33,630 But Newton, I think it's fair to say he was a great synthesiser, as well as a great original, original thinker. 70 00:08:33,630 --> 00:08:40,710 Now it's it's the fate of anyone in the field of science that their work is never finished. 71 00:08:40,710 --> 00:08:46,530 Newton For all the tremendous success that his work had, he didn't completely finish that work. 72 00:08:46,530 --> 00:08:52,680 It was still things he couldn't quite account for within the scope of his theoretical structure. 73 00:08:52,680 --> 00:08:56,700 And it's very important to notice that, particularly on the continent, 74 00:08:56,700 --> 00:09:02,100 people were very unhappy with his conception of gravity because he didn't give a mechanical origin for it. 75 00:09:02,100 --> 00:09:05,880 What causes it? He didn't say. He said he he didn't know what it was. 76 00:09:05,880 --> 00:09:12,870 He didn't feel it necessary to specify it. So on the continent, particularly in France, Newton was regarded as a great mathematician. 77 00:09:12,870 --> 00:09:19,320 True enough. But as a thinker about nature, extremely eccentric. 78 00:09:19,320 --> 00:09:24,000 And he finished his. He finished his life. 79 00:09:24,000 --> 00:09:25,020 Poor, poor man. 80 00:09:25,020 --> 00:09:36,150 Tortured by gout and not in the best state, but certainly revered by in Britain as the greatest natural philosopher the world had ever seen. 81 00:09:36,150 --> 00:09:37,590 But he knew his work was unfinished. 82 00:09:37,590 --> 00:09:43,860 He could not complete these calculations on the stability of the universe, aspects of putting planetary motion and what have you. 83 00:09:43,860 --> 00:09:50,280 This is not in any way to to diminish his achievement, but just to say science is something that really doesn't have a, 84 00:09:50,280 --> 00:09:55,890 you know, you don't go into science because you're going to solve everything you you set out to achieve. 85 00:09:55,890 --> 00:10:01,530 What he certainly had done was to demonstrate in the words of his great rival, 86 00:10:01,530 --> 00:10:06,330 LoopNet, that mathematics was a torch that you could shine on to nature. 87 00:10:06,330 --> 00:10:19,050 It was a it was. It was. It was something that the abstract complex of ideas could be used to actually shed light on the world around us. 88 00:10:19,050 --> 00:10:27,570 But it was it was something that was beyond the great Newton's can, for example, to give a description of electricity and indeed of magnetism. 89 00:10:27,570 --> 00:10:30,990 That's one of many examples that needed to be sorted out. 90 00:10:30,990 --> 00:10:41,320 And he was unable to do that with the tools at his command. 91 00:10:41,320 --> 00:10:48,760 The Newtonian project was more or less completed, not in Britain, but on the continent, in particular in France, 92 00:10:48,760 --> 00:10:58,570 and this is my candidate for the most important person in that completion, Seymour Le Plus, known as the French Newton, especially in France. 93 00:10:58,570 --> 00:11:04,810 And he this gentleman was a superb mathematician, a devotee of Newton, 94 00:11:04,810 --> 00:11:14,200 someone who who was not part of the naysayers that thought was not was not a deep thinker about the natural world, merely a mathematician. 95 00:11:14,200 --> 00:11:22,300 And he with the person who was what we would now say supervisor and bear and all the continental mathematicians. 96 00:11:22,300 --> 00:11:26,470 Claire, who the newly look Raj and others. 97 00:11:26,470 --> 00:11:36,970 They collectively developed the the schema that Newton developed a whole new bunch of mathematical techniques 98 00:11:36,970 --> 00:11:47,270 that that developed what we would now call the classical account of of mechanics and in cosmology. 99 00:11:47,270 --> 00:11:54,210 Now. One of one of The Flash's achievements, and there were many is not nearly what enough known in our country, 100 00:11:54,210 --> 00:12:01,120 in my opinion, was to write up in a multi volume masterpiece called Celestial Mechanics. 101 00:12:01,120 --> 00:12:09,480 The the mathematical completion of Newton's account of of of the cosmos deployed with enormous 102 00:12:09,480 --> 00:12:17,430 mathematical power that the place had one of those volumes was dedicated to his great friend and sponsor, 103 00:12:17,430 --> 00:12:29,400 so to speak. Napoleon, who was a was a was a tremendously beneficial force, not for French science, in particular the study of of electricity. 104 00:12:29,400 --> 00:12:33,570 Now such was the activity in in France that a take home message. 105 00:12:33,570 --> 00:12:41,700 It's a bit rough and ready, but it will do it. Sometime said by historians that physics, as we now know it, broadly speaking, 106 00:12:41,700 --> 00:12:46,810 is pretty much a French invention that took place in the early 19th century. 107 00:12:46,810 --> 00:12:54,330 Now what do we mean by that? We mean but what we now regard as something that physicists do, the topics that they study? 108 00:12:54,330 --> 00:13:03,780 They started to come into a sharp focus in and around the orbit of the planet at the turn of the 19th century. 109 00:13:03,780 --> 00:13:10,180 The thing started to take shape before other other topics were allied to even psychology and things like that. 110 00:13:10,180 --> 00:13:18,700 But the topic that we now talk about is physics that started to take shape in France in the early 19th century. 111 00:13:18,700 --> 00:13:28,660 And the first school of mathematical physics was run by this gentleman here in his mansion in actually which doesn't exist anymore. 112 00:13:28,660 --> 00:13:34,510 I'm afraid it south of Paris. And he had around him. 113 00:13:34,510 --> 00:13:41,800 You held court with various students and other acolytes guiding their their 114 00:13:41,800 --> 00:13:46,390 development of what we what we would we would regard as a Newtonian programme. 115 00:13:46,390 --> 00:13:56,050 But it was a it was a more advanced programme mathematically. And in its range, people like bio ampere and others were there. 116 00:13:56,050 --> 00:14:05,830 Now the very important to me totally revered Newton, but he moved things ahead of he developed the science that Newton had. 117 00:14:05,830 --> 00:14:11,380 For one thing, particularly important is this this gentleman here was godless. 118 00:14:11,380 --> 00:14:20,500 You may know the story about about Napoleon asking the place why God has no place in his books, and he said, I have no need of that hypothesis. 119 00:14:20,500 --> 00:14:29,260 So he was not a natural philosopher in the mould of Newton, and he believed that in a deterministic universe with the present, 120 00:14:29,260 --> 00:14:34,960 if you if you knew everything about the present, you could predict the future and go back to the past. 121 00:14:34,960 --> 00:14:43,750 He was a chilly rationalist who believed he had great faith in the existence of natural laws that could describe the universe. 122 00:14:43,750 --> 00:14:53,900 So we have shaping a quite a modern view of science. You go to his system of the world and you see that he's talking about phenomena all over 123 00:14:53,900 --> 00:14:58,880 the map in physics and believing that you could talk about interactions between particles, 124 00:14:58,880 --> 00:15:03,890 a more basic view of physics from which you could derive the results of experiments. 125 00:15:03,890 --> 00:15:08,510 Again, that Newtonian insistence that you have to use your theories if you can call it that 126 00:15:08,510 --> 00:15:15,140 and make predictions about the natural world that will be tested against nature. 127 00:15:15,140 --> 00:15:27,260 So this this this man here was enormously influential set up, as I said, a standard way of doing physics at his his country mansion. 128 00:15:27,260 --> 00:15:35,660 But by the time of the Battle of Waterloo in 1815, his trajectory fell. 129 00:15:35,660 --> 00:15:42,620 But nonetheless, the French science continued to to flourish, although with different emphases. 130 00:15:42,620 --> 00:15:48,950 And he's the author. Authoritarian way of running physics fell by the by the wayside. 131 00:15:48,950 --> 00:15:59,070 One of the things that he and his way of doing looking at the natural world couldn't do was to describe electricity and magnetism. 132 00:15:59,070 --> 00:16:07,940 The the the person who we now know most effectively shone the torch of mathematics onto that subject was this gentleman here, 133 00:16:07,940 --> 00:16:16,520 James Clerk Maxwell, whom I mentioned at the beginning. Now he was my favourite Scot ever. 134 00:16:16,520 --> 00:16:28,640 A wonderful, wonderful person. Very lovable human being, a Cambridge trained mathematician and a natural philosopher to his fingertips. 135 00:16:28,640 --> 00:16:36,830 Early in the mid-19th century when he was being educated in in natural philosophy and in mathematics, 136 00:16:36,830 --> 00:16:43,040 by then, physics really had taken shape and there were people studying optics, 137 00:16:43,040 --> 00:16:51,320 material structures, heat engines, gases, the sort of things that we now study in school and in early, early years of of of college. 138 00:16:51,320 --> 00:17:00,710 And everybody knew that what you aspired to with mathematical laws that could describe these various parts of of nature. 139 00:17:00,710 --> 00:17:09,260 What he decided to do and he wrote to one of his two of a very famous thinker at the time, 140 00:17:09,260 --> 00:17:14,270 William Thomson, that he was going straight after he got his undergraduate degree at Cambridge. 141 00:17:14,270 --> 00:17:18,950 He was going to attack electricity. That's the word he used in his in his letter. 142 00:17:18,950 --> 00:17:27,230 Now, this showed the extent of his ambition because many of the best thinkers about the natural world working on exactly that topic, 143 00:17:27,230 --> 00:17:39,140 particularly on the continent. So what Maxwell decided decided to do was to study the relationship between electricity, magnetism and the Aether. 144 00:17:39,140 --> 00:17:44,480 He just saw those as the package, right? No, it wasn't something he thought was a some kind of expressions. 145 00:17:44,480 --> 00:17:53,780 It was central to his thinking. The really brilliant one of the really brilliant things that he did was he didn't start thinking 146 00:17:53,780 --> 00:18:00,800 about it until he really had become acquainted with the best experimental work on that subject, 147 00:18:00,800 --> 00:18:04,160 which was done by his hero, Michael Faraday, 148 00:18:04,160 --> 00:18:15,410 a self-taught natural philosopher working in the basement of the royal institution who done some incredibly clever and thoughtful experiments there. 149 00:18:15,410 --> 00:18:19,730 In addition to all the other things he did, one of the greatest scientists ever produced on should say, 150 00:18:19,730 --> 00:18:25,870 scientists, natural philosophers on on on these shores. And it was. 151 00:18:25,870 --> 00:18:29,230 Faraday, who was absolutely not a mathematician, 152 00:18:29,230 --> 00:18:35,710 it's sometimes said that the most advanced mathematics Faraday ever did was balancing the books of the royal institution. 153 00:18:35,710 --> 00:18:41,080 He was not a mathematician, but he came up with the absolutely central idea, right? 154 00:18:41,080 --> 00:18:45,610 Which was one that we will learn about more less a junior school. 155 00:18:45,610 --> 00:18:50,650 The idea of a magnet, for example, sitting there and it has a magnetic field around it, 156 00:18:50,650 --> 00:18:56,170 a field that the space around is not completely empty, but is in some sense activity. 157 00:18:56,170 --> 00:19:00,430 Some it could be acted upon by that, by that magnet. 158 00:19:00,430 --> 00:19:05,680 And from that, the accounts see the English language now gravitational field, electric field. 159 00:19:05,680 --> 00:19:11,440 That idea was born in a modern sense in the mind of Michael Faraday and the 160 00:19:11,440 --> 00:19:16,540 much more mathematically sophisticated Maxwell picked up on that studied it. 161 00:19:16,540 --> 00:19:24,910 And in the course of several years, amongst other things, he was a very, very but he was very, very versatile thinker. 162 00:19:24,910 --> 00:19:33,790 He in the early 1850s came up with this theory of the electric electrons interaction with electricity, magnetism and the Aether, 163 00:19:33,790 --> 00:19:43,930 and came up as a as a quite glorious prediction that out of the equations that he he principles that he used, 164 00:19:43,930 --> 00:19:54,790 the theory that he predicted that light was was an electromagnetic disturbance, something that was only later verified. 165 00:19:54,790 --> 00:20:03,820 Something that I want to stress very important about Maxwell is not only did he have the completely peerless feel for the way nature works, 166 00:20:03,820 --> 00:20:08,770 it's very difficult to say what that means, incidentally. But there are some thinkers who just have this field. 167 00:20:08,770 --> 00:20:15,580 They have very limited describe. They somehow have a feel for the way nature is built, and Maxwell really did have that. 168 00:20:15,580 --> 00:20:20,050 But he also was a very good mathematician. Scrappy. 169 00:20:20,050 --> 00:20:28,060 Yes. Not particularly rigorous, yes. But he was very interested in ideas right at the forefront of mathematics. 170 00:20:28,060 --> 00:20:31,440 The theory of knots when you tie knots in your shoelaces. 171 00:20:31,440 --> 00:20:37,780 That's the very primitive version of the thing that mathematicians now study in a very rarified way called knot theory. 172 00:20:37,780 --> 00:20:43,360 The branch of geometry called projective geometry and in a mathematical object called Kotoni. 173 00:20:43,360 --> 00:20:46,510 These were frontiers of mathematics in Maxwell's time, 174 00:20:46,510 --> 00:20:54,280 and he was fascinated by them because he thought that those mathematical ideas could be used to shine a torch onto nature. 175 00:20:54,280 --> 00:21:01,000 And in his great treatise on electromagnetism in 1873, you'll see references to that modern mathematics. 176 00:21:01,000 --> 00:21:06,980 In there he was. He had become a very, very mathematical thinker, not always popular. 177 00:21:06,980 --> 00:21:17,060 His friend and admirer William Thompson, was was distasteful of of of this Maxwell in inclination to mathematics. 178 00:21:17,060 --> 00:21:25,510 Thompson described mathematics as the aethereal ization of common sense and was very insistent that mathematics should be the servant of physics, 179 00:21:25,510 --> 00:21:40,030 not its guide. So Maxwell stood out and was, I say again a a a a a thinker of considerable depth on this relationship between physics and mathematics. 180 00:21:40,030 --> 00:21:44,140 He died in 1879, far too young. 181 00:21:44,140 --> 00:21:49,330 I think he was forty eight years old, not knowing whether that theory of electric magnetism was the right one. 182 00:21:49,330 --> 00:21:56,920 There were other competitors on the continent, but his field theory of electron electromagnetism held out and is now seen, 183 00:21:56,920 --> 00:22:02,270 in my opinion, quite right as the crowning glory of 19th century physics. 184 00:22:02,270 --> 00:22:14,110 And by the time Maxwell was on his deathbed in Cambridge in 1879, that had flourished amongst all the specialisations in science, 185 00:22:14,110 --> 00:22:19,600 a branch of science called theoretical physics, particularly in Germany, 186 00:22:19,600 --> 00:22:28,510 where you had for the first time people who actually paid to do not to get their hands dirty on doing experiments, 187 00:22:28,510 --> 00:22:41,660 but actually to think using mathematics about the natural world and to try to develop our understanding of the most basic laws of of nature. 188 00:22:41,660 --> 00:22:47,690 They started very small, but this was the this was the discipline. 189 00:22:47,690 --> 00:22:55,940 Who's who's most famous representative was was to be born a generation later. 190 00:22:55,940 --> 00:23:01,050 This gentleman is the person I'm talking about Albert Einstein. 191 00:23:01,050 --> 00:23:07,020 Einstein always described himself as a theoretical physicist, but as I shall argue, in my opinion, 192 00:23:07,020 --> 00:23:12,030 he was about 50 percent a natural philosopher as well, which I do not mean in pejorative terms at all. 193 00:23:12,030 --> 00:23:22,830 He was most definitely a philosophical thinker about the natural world, as well as a peerless theoretical physicist. 194 00:23:22,830 --> 00:23:26,820 Contrary to popular myth, he was a bright child. 195 00:23:26,820 --> 00:23:32,760 Inquisitive alright may not have been an outstanding genius when he was a young boy, but he was certainly very, very bright. 196 00:23:32,760 --> 00:23:38,700 He was headstrong, very independent minded and intensely curious. 197 00:23:38,700 --> 00:23:52,410 By the time he went to college, he was absorbed very much in the Maxwell's theory, which he which he said had the most impact on him. 198 00:23:52,410 --> 00:23:54,840 That's a very important point. He saw this. 199 00:23:54,840 --> 00:24:04,650 He had what you might call taste as a physicist, even as a young young student, and was skipping lectures, most particularly on mathematics. 200 00:24:04,650 --> 00:24:09,120 He he really thought, and this is clearly on the record for people that spoke to him at the time, 201 00:24:09,120 --> 00:24:14,460 that physics was essentially a subject that you needed only very basic mathematics to do. 202 00:24:14,460 --> 00:24:22,500 You don't need to go into the pure maths department and study fancy structures that the real professionals are doing. 203 00:24:22,500 --> 00:24:29,490 So when Einstein had his great year, his mirabilis that is justly celebrated. 204 00:24:29,490 --> 00:24:38,250 If you look at those papers about the nature of light on the news, a modification of Newton's ideas on space and time, 205 00:24:38,250 --> 00:24:43,470 which was which was the special theory of relativity and in Syria, Brownian motion. 206 00:24:43,470 --> 00:24:49,590 You look at those simply wonderful papers and you will see that the mathematics that Einstein uses. 207 00:24:49,590 --> 00:24:57,270 All right. It might be beyond most of us, but it was. It was certainly not especially advanced by the standards of professional mathematician. 208 00:24:57,270 --> 00:25:03,570 And I would I would just make the point that Laplace, if he were looking down from heaven or wherever right, 209 00:25:03,570 --> 00:25:07,590 would have had absolutely no problem understanding that mathematics. 210 00:25:07,590 --> 00:25:14,400 So Einstein was someone who I think it's fair to say, disdained advanced mathematics. 211 00:25:14,400 --> 00:25:19,410 All this changed, and it changed quite quickly at around this picture of time. 212 00:25:19,410 --> 00:25:26,910 This picture was taken in 1912. By then, he was thinking deeply and he did. 213 00:25:26,910 --> 00:25:28,770 I don't think he thought in any other way. 214 00:25:28,770 --> 00:25:42,360 He was thinking about gravity and the need to is he saw it to set up a new understanding of the of of Newton's theory of gravity, 215 00:25:42,360 --> 00:25:51,600 which could not account for a very small number of observations, for example, on the motion of of of Mercury. 216 00:25:51,600 --> 00:25:59,190 He believed on theoretical grounds that that that theory of Newton's had to be superseded. 217 00:25:59,190 --> 00:26:06,810 And he came up with a new principle of principle of equivalence on which he based is based his thinking. 218 00:26:06,810 --> 00:26:18,510 But he found it extremely difficult to realise that in mathematical terms, using his assumption that everything would be simple and straightforward, 219 00:26:18,510 --> 00:26:33,210 it was only when he spoke to close friends in in mathematician friends in in Switzerland in 1912 that he started to see that the clue, 220 00:26:33,210 --> 00:26:40,200 the clue to solving the problem of actually setting out that theory was to use something called differential geometry, 221 00:26:40,200 --> 00:26:45,060 which almost certainly he'd skipped as an undergraduate. 222 00:26:45,060 --> 00:26:50,550 And he then saw it was it was experience that never left him. 223 00:26:50,550 --> 00:27:01,230 He saw that in that advanced mathematics was that was the key to solving his problem of finding a successor to Newton's law of gravity. 224 00:27:01,230 --> 00:27:06,390 This was extraordinary. Let me just come up with an analogy. 225 00:27:06,390 --> 00:27:11,670 Whenever a physicist or anybody else goes into a new field, write it. 226 00:27:11,670 --> 00:27:15,360 It's because they do not really know where they're going. 227 00:27:15,360 --> 00:27:20,920 They have a sense vaguely what they're trying to do, and they don't know how to solve the problem. 228 00:27:20,920 --> 00:27:26,100 It's this is a tough field to be in. This is like heading out into the desert, right? 229 00:27:26,100 --> 00:27:34,620 Not a not knowing how you're going to make it to the next oasis and then finding on the side the perfect survival kit. 230 00:27:34,620 --> 00:27:39,450 Jeanette, just engineered for you. That's what differential geometry did for him. 231 00:27:39,450 --> 00:27:49,020 It was sitting there waiting for him and was perfectly suited for the development of his new theory of gravity. 232 00:27:49,020 --> 00:27:58,440 He delivered that that theory in November 1915, having nearly been given the biggest shock of his life. 233 00:27:58,440 --> 00:28:06,670 Why? Because he found it an enormous struggle to complete that theory, but not just the mathematics, but the interpretation. 234 00:28:06,670 --> 00:28:12,460 It was it was an extremely difficult problem, and he found it very, very difficult to finish off. 235 00:28:12,460 --> 00:28:17,080 He actually came very close to the answer about the time we took this picture, but he couldn't finish it off. 236 00:28:17,080 --> 00:28:24,580 And he very bravely, I think, went down to Göttingen and spoke to the mathematicians there about his incomplete theory. 237 00:28:24,580 --> 00:28:28,750 And the great mathematician David Hilbert, who was then past his best as a mathematician, 238 00:28:28,750 --> 00:28:37,930 saw that this Einstein was was a tyro in mathematics and was right on his tail breathing hot breath down Einstein's neck. 239 00:28:37,930 --> 00:28:51,790 He was literally days behind him, and Einstein did finally beat Hilbert to the to the goal and set out that new law of gravity in November 1915. 240 00:28:51,790 --> 00:28:58,900 Now what is important here is that Einstein, by his recollection, got to that goal. 241 00:28:58,900 --> 00:29:09,280 Guided by mathematics that when he found the right natural structure, then he then the problems he'd been wrestling with fell away, 242 00:29:09,280 --> 00:29:15,190 and this became the most important guide to him about the way to do theoretical physics. 243 00:29:15,190 --> 00:29:19,600 You trust mathematics to deliver it for you. 244 00:29:19,600 --> 00:29:25,330 Very important to say that excellent scholars Juergen Ren and his colleagues have looked at 245 00:29:25,330 --> 00:29:30,970 Einstein's notes on this and shown that that is a very partial way of looking at that research. 246 00:29:30,970 --> 00:29:39,550 In fact, he was looking at both what what we call a two pronged strategy looking at the experimental side, 247 00:29:39,550 --> 00:29:44,050 the need to be consistent with Newton's law and what have you and the mathematics alternately? 248 00:29:44,050 --> 00:29:49,930 Right? Whereas Einstein had a very partial recollection of this, that it was the mathematics that delivered. 249 00:29:49,930 --> 00:29:53,380 Now Einstein was the only person there, I guess. Right. 250 00:29:53,380 --> 00:30:02,860 But he this became his credo. Right. That mathematics would lead you to develop your your your theories. 251 00:30:02,860 --> 00:30:12,280 Him having had this colossal success of producing a brand new theory of gravity, and let's face it, 252 00:30:12,280 --> 00:30:21,490 you have Newton's gravity that almost everything and you produce a successor that reproduce everything Newton did and had made additional predictions. 253 00:30:21,490 --> 00:30:30,370 Einstein wanted to go one step further. He wanted to take that theory of gravity and extend it so that it included electricity and magnetism. 254 00:30:30,370 --> 00:30:35,500 Now, how do you do that? What most people would do is look for experimental clues. 255 00:30:35,500 --> 00:30:39,580 That's the Orthodox way of doing it. Art experiment to give you a guide. 256 00:30:39,580 --> 00:30:46,780 Now, Einstein's view taking that philosophy that I just spoke to you about was not to do that because there weren't any clues, 257 00:30:46,780 --> 00:30:54,320 but instead to generalise the mathematics of his theory to focus on the mathematics. 258 00:30:54,320 --> 00:30:59,060 This was seen as a very eccentric way of proceeding. 259 00:30:59,060 --> 00:31:10,250 Let's be clear, there were very few people that took this seriously, and he was ridiculed by his frenemy, Wolfgang Paoli, for full, as he put it. 260 00:31:10,250 --> 00:31:19,580 Moving over to pure mathematics of playing with what he called a completely squeezed out lemon, which was the general theory of relativity, 261 00:31:19,580 --> 00:31:23,900 it was seen as a completely foolhardy activity, 262 00:31:23,900 --> 00:31:32,270 and he didn't actually really go public with his philosophy of this mathematical philosophy for some years. 263 00:31:32,270 --> 00:31:41,050 He finally did so. In Oxford at Rhodes House, a nice building now. 264 00:31:41,050 --> 00:31:46,300 I think it's a very good wedding venue. But but theoretical physicists, but ones that know about Einstein, 265 00:31:46,300 --> 00:31:54,490 think of this is where Einstein actually went public with his, his philosophy, his way of doing theoretical physics. 266 00:31:54,490 --> 00:32:01,150 And this was in 1933. Saturday, the 10th of June, just after or around exam time. 267 00:32:01,150 --> 00:32:04,240 This was a societal highlight of the season. 268 00:32:04,240 --> 00:32:15,250 Einstein about to flee to the United States of America, his life having been made impossible by the rise of the Nazis. 269 00:32:15,250 --> 00:32:24,580 He was staying in Christchurch, and this was to be the first lecture that Einstein gave purely in English, and he was seeking accessibility. 270 00:32:24,580 --> 00:32:30,370 He knew that there'd be people in that audience who didn't know anything about relativity or atoms or anything like that. 271 00:32:30,370 --> 00:32:38,830 So he wanted to speak in plain English, and he gave a talk there that a title, even the title is significant. 272 00:32:38,830 --> 00:32:44,770 The method of theoretical physics note is not a method, not my method, the method. 273 00:32:44,770 --> 00:32:55,280 And it was a method almost nobody else was using. This is fake news. 274 00:32:55,280 --> 00:32:59,150 This is a mocked up picture of Einstein in Rhodes House. 275 00:32:59,150 --> 00:33:04,190 All right. Pretty much what those people would have seen when Einstein was giving that lecture 276 00:33:04,190 --> 00:33:09,050 thanks to people to the my friends at Rhodes House for allowing me to take that picture. 277 00:33:09,050 --> 00:33:14,870 He was. He presented in a very friendly way to to his audience. 278 00:33:14,870 --> 00:33:19,100 I don't think there's a single mathematical symbol in the lecture about his project 279 00:33:19,100 --> 00:33:25,040 of generalising his theory of gravity so that it included electricity and magnetism. 280 00:33:25,040 --> 00:33:34,700 And as I said, not focussing on experimental clues but focussing on mathematical structure, he said in the crucial line of that lecture, 281 00:33:34,700 --> 00:33:38,360 and I've had it multiply translated by German scholars, 282 00:33:38,360 --> 00:33:45,230 and they all say the same thing that the creative principle of the theory is in the mathematics. 283 00:33:45,230 --> 00:33:49,220 He went, he was that strong. He believed that's where the creativity lied. 284 00:33:49,220 --> 00:33:56,000 I say again very, very controversial and singular way of looking at developing theories. 285 00:33:56,000 --> 00:33:59,930 The embarrassing thing was, and I again, I'd be very respectful when I say this. 286 00:33:59,930 --> 00:34:06,050 This had got him nowhere. He was making very little progress on on on, on this subject. 287 00:34:06,050 --> 00:34:13,790 One of the reasons why was because the new discovery of quantum mechanics, which was the theory of motion on the atomic scale, 288 00:34:13,790 --> 00:34:28,290 showed that nature was was granular and had these discontinuities at a small distances that he's think what Einstein is thinking could not encompass. 289 00:34:28,290 --> 00:34:33,840 So Einstein at that Einstein was not going to be deflected. 290 00:34:33,840 --> 00:34:40,290 He was extremely stubborn person. I'm sure he'd be very proud to hear him describe like that because that's what he that's what he was. 291 00:34:40,290 --> 00:34:44,400 But he knew that the new generation was coming up and the new kids on the 292 00:34:44,400 --> 00:34:50,670 block who were taking over from him as the pre-eminent physicist at the time. 293 00:34:50,670 --> 00:34:58,500 And these people were almost all the new, the young quantum theorists. 294 00:34:58,500 --> 00:35:02,310 This is a famous picture of the Solvay conference in 1927, 295 00:35:02,310 --> 00:35:11,930 where many of the pioneers of of quantum mechanics are sitting round the the person who knew his place in their businesses, 296 00:35:11,930 --> 00:35:15,420 in the community, Einstein sitting front and centre. 297 00:35:15,420 --> 00:35:26,220 And there are many of the pioneers of this most revolutionary theory of the 20th century, much more revolutionary to the general theory of relativity. 298 00:35:26,220 --> 00:35:33,150 Why? Well, Einstein always said that the general theory of relativity was meant to be a generalisation of the Newton theory. 299 00:35:33,150 --> 00:35:40,800 He did not see it as revolutionary. He said that more than once, quantum theory was was seemed to be a sharp break with the theory that went before 300 00:35:40,800 --> 00:35:48,510 it in order to understand this bizarre behaviour of matter on the atomic scale. 301 00:35:48,510 --> 00:35:54,480 Now, the wall I want to concentrate on is the person who was quite proud to have his picture taken here. 302 00:35:54,480 --> 00:36:01,740 And this gentleman's name is Paul Dirac. And you could see him there sitting on Einstein's right shoulder now. 303 00:36:01,740 --> 00:36:05,170 Dirac was very modest person. Right, right. 304 00:36:05,170 --> 00:36:10,470 But Mike, he was not too proud to send a copy of that picture to a school. 305 00:36:10,470 --> 00:36:19,920 He was very proud of sitting right behind his hero, someone who turned him on to theoretical physics when he was a teenager. 306 00:36:19,920 --> 00:36:24,180 Now, the Iraq did not invent quantum mechanics on his own. By any means he was. 307 00:36:24,180 --> 00:36:28,440 It was two other people Heisenberg and Schrodinger, who got the ball rolling. 308 00:36:28,440 --> 00:36:33,780 Dirac then moved in and became one of the pioneers of the subject. 309 00:36:33,780 --> 00:36:42,330 But what distinguished Dirac was his particularly mathematical approach to the subject, and that's why he interest us in this lecture. 310 00:36:42,330 --> 00:36:49,160 Particularly Dirac had come as an outsider into theoretical physics. 311 00:36:49,160 --> 00:36:52,920 He he'd been he'd done an undergraduate degree in engineering, 312 00:36:52,920 --> 00:36:57,240 learning how to fill in tax forms, learning about aircraft, motor cars and what have you. 313 00:36:57,240 --> 00:37:03,810 He then did a degree in mathematics, both in Bristol, and then he went to do a Ph.D. in Cambridge. 314 00:37:03,810 --> 00:37:10,470 Right. Having having had no formal training in theoretical physics. 315 00:37:10,470 --> 00:37:22,150 When he read Heisenberg's paper, he was brought into that field and then shot to the to the front line and became a peer of those people. 316 00:37:22,150 --> 00:37:27,280 Durack had this knack of taking projects in quantum mechanics, 317 00:37:27,280 --> 00:37:33,730 a study of this motion at the atomic level and finding and linking it to modern mathematics, 318 00:37:33,730 --> 00:37:39,670 I might say not doing it on purpose, but he found himself doing modern mathematics. 319 00:37:39,670 --> 00:37:41,170 Give you an example of that. 320 00:37:41,170 --> 00:37:49,600 When he read that first Heisenberg paper in his parents house in Bristol, he saw something at just a line you can go home and read tonight, 321 00:37:49,600 --> 00:37:53,290 whereby in Heisenberg's way of looking at motion, 322 00:37:53,290 --> 00:38:01,030 you take to observe objects and be and when you multiply them together, the order of multiplication matters. 323 00:38:01,030 --> 00:38:07,090 Everyone here knows it. Six times nine is the same as nine times six. That 10 times four is the same as four times 10. 324 00:38:07,090 --> 00:38:11,680 In quantum mechanics, you take these two operators and the order actually matters. 325 00:38:11,680 --> 00:38:17,410 Now, the horrible word direct, unfortunately coined for this, was long called mutation. 326 00:38:17,410 --> 00:38:25,810 It means the order of multiplication matters. Heisenberg, by his own admission, said, Well, this is probably this looks a bit embarrassing. 327 00:38:25,810 --> 00:38:33,460 We'll sort this out. Dirac saw that as key non-call mutation is a key theme of 20th century mathematics and 328 00:38:33,460 --> 00:38:41,560 was absolutely central to the way that Dirac developed his his version of that subject. 329 00:38:41,560 --> 00:38:49,480 What the Iraqis most famous for in his is coming up for coming up with an equation for the first fundamental particle to 330 00:38:49,480 --> 00:38:57,940 be discovered the electron and combining special relativity and quantum mechanics into a description of the electron. 331 00:38:57,940 --> 00:39:03,670 And it brought him into the mathematics of spinners that describe the behaviour of the electron spinners. 332 00:39:03,670 --> 00:39:14,200 We discovered a few decades before in Germany describing the motion of a spinning top, and Dirac was a hit on that and hit on spin a geometry, 333 00:39:14,200 --> 00:39:21,700 which is a very important theme in 20th century mathematics and in his for my money, there's hardly a personal thing. 334 00:39:21,700 --> 00:39:29,230 His greatest paper, which is on how quantum theory leads naturally to a theory of a magnetic monopole. 335 00:39:29,230 --> 00:39:37,420 Everyone knows that magnets come in north and south. But in quantum mechanics, it's quite natural to have a monopole, a north alone or south alone. 336 00:39:37,420 --> 00:39:43,510 And in doing that, he was driven to be doing creative research in the field of topology, 337 00:39:43,510 --> 00:39:55,330 which is about the properties of shapely shape things that don't change when they're stretched or not torn, but otherwise distorted. 338 00:39:55,330 --> 00:39:59,410 So Dirac, those are three good examples. 339 00:39:59,410 --> 00:40:03,730 There are others. He kept finding that physics took him to mathematics, 340 00:40:03,730 --> 00:40:11,800 and the mathematics then guided him in his approach to physics in a wonderful phrase that he coined in nineteen seventy five. 341 00:40:11,800 --> 00:40:22,450 But it's a very resonant one is that mathematics will lead you by the hand and take you to new paths, a new territory where you can take stock. 342 00:40:22,450 --> 00:40:25,450 Now that's a critical phrase, ladies and gentlemen, right? 343 00:40:25,450 --> 00:40:32,740 He's saying that if you trust in mathematics, it will take you to places that will enable you to make progress. 344 00:40:32,740 --> 00:40:37,540 Now, one thing that even his worst enemy wouldn't say about Dirac, right? 345 00:40:37,540 --> 00:40:44,500 No one would ever call him a philosopher. He was an A. philosopher. So he must have been quite surprised at the end of nineteen thirty eight. 346 00:40:44,500 --> 00:40:50,950 This is what 12 years after this picture was taken to be invited in Edinburgh to give a talk on the philosophy of physics. 347 00:40:50,950 --> 00:40:54,010 This is something that Dirac had no interest there at all in. 348 00:40:54,010 --> 00:41:04,000 But he decided to take up the topic and gave a talk on the relationship between mathematics and physics, 349 00:41:04,000 --> 00:41:08,410 which was a topic remember that Maxwell spoke about in 1870 to remember. 350 00:41:08,410 --> 00:41:17,170 This is one of the great lectures of of of direct oeuvre and indeed one of the great lectures, in my opinion, public lectures in theoretical physics. 351 00:41:17,170 --> 00:41:23,170 You can go and read it online. Anyone can read it. It contains no mathematical symbols at all, too far as I can recall. 352 00:41:23,170 --> 00:41:33,520 This is more fake news. This is another mock up of Dirac standing outside the Royal Society of Edinburgh in central Edinburgh. 353 00:41:33,520 --> 00:41:36,100 And this is what it might have looked like on the sick. 354 00:41:36,100 --> 00:41:50,170 The February 1939 storm clouds gathering very close to the beginning of World War Two and Dirac gave a lecture that lasted an hour and. 355 00:41:50,170 --> 00:41:57,970 He reviewed right from the most basic level, the cleaner in that organisation could have listened to the opening of that lecture. 356 00:41:57,970 --> 00:42:04,690 Right. He talked about how the universe or the world around us has a mathematical quality 357 00:42:04,690 --> 00:42:09,160 that is not obvious to people until they begin to study it right at that level. 358 00:42:09,160 --> 00:42:15,490 And then he goes right up to the application of quantum theory relativity, no using no mathematics, 359 00:42:15,490 --> 00:42:21,310 but thinking about how we could develop or how he and his peers could develop their thinking about the subject. 360 00:42:21,310 --> 00:42:25,360 It's most famous amongst his amongst many people today, 361 00:42:25,360 --> 00:42:32,650 being the place where he coined his principle of mathematical beauty, which is the statement of extremely bold. 362 00:42:32,650 --> 00:42:36,940 Some people would say overly bold and perhaps even foolish, 363 00:42:36,940 --> 00:42:46,030 statement that physics advances fundamental advances from one theory to the next or the next. 364 00:42:46,030 --> 00:42:51,520 Through increasing mathematical beauty, you start off with something that is relatively ugly, 365 00:42:51,520 --> 00:42:55,000 and the theories gradually become more mathematically beautiful. 366 00:42:55,000 --> 00:43:01,330 Now, even if you're not a professionally trained philosopher, you don't need to see there's a big hole in this argument, right? 367 00:43:01,330 --> 00:43:04,960 I mean, without being disrespectful to direct. How do you define what beauty is? 368 00:43:04,960 --> 00:43:08,560 People have different views on this. Dirac had no time for that at all. 369 00:43:08,560 --> 00:43:13,660 He was. He was concerned in mathematics. You really don't do know. But what beauty is? 370 00:43:13,660 --> 00:43:19,810 And he stuck by his, his guns. And it was, as he said, in later life, almost a religion. 371 00:43:19,810 --> 00:43:31,000 He believed that mathematics beautiful mathematics would take you to to the correctly to the next stage. 372 00:43:31,000 --> 00:43:37,690 Now these are three statements that I just want you to look at and their statements that where I wish people, 373 00:43:37,690 --> 00:43:46,630 people of direct stature could all write like this with with, in my opinion, truths of great beauty themselves that are very, very simple. 374 00:43:46,630 --> 00:43:52,750 Look at that. Look at this for a statement. The mathematician plays a game in which he himself, sorry about the sexism, 375 00:43:52,750 --> 00:43:59,170 invents the rules while the physicist plays the game in which the rules are provided by nature. 376 00:43:59,170 --> 00:44:03,550 That's it, in a nutshell, that's why physics and mathematics are different. 377 00:44:03,550 --> 00:44:09,280 They are not the same thing. Very important to realise that this is even more germane. 378 00:44:09,280 --> 00:44:17,650 In my opinion, the rules that the mathematician finds interesting are the same as those that nature has chosen. 379 00:44:17,650 --> 00:44:22,240 Now, that's not obvious. Why should it be right that that. 380 00:44:22,240 --> 00:44:27,430 But mathematician pure mathematicians looking at these patterns of ideas are finding themselves 381 00:44:27,430 --> 00:44:32,920 on the same territory that state of the art theoretical physicists are working on as well. 382 00:44:32,920 --> 00:44:37,780 That is not at all obvious, and in this is this is almost wild. 383 00:44:37,780 --> 00:44:43,030 This lecture at certain points. I mean, Dirac, a very reserved, very quiet spoken person. 384 00:44:43,030 --> 00:44:52,420 He wild in the sense of he really does talk in very bold sense about the future of the subject makes one observation, which I love, 385 00:44:52,420 --> 00:44:57,460 which he was saying that philosophically, the most interesting thing about theoretical physics was not quantum theory of relativity. 386 00:44:57,460 --> 00:45:03,370 It was cosmology. I wasn't expecting to see that. Now, today that looks extremely modern, right? 387 00:45:03,370 --> 00:45:12,360 That's what he says in passing in this lecture. It's an amazing lecture. And he also says possibly mathematics and physics will one day unify. 388 00:45:12,360 --> 00:45:17,370 Now, that's also a very bold, bold statement, but one it is coming back into fashion may not be correct, 389 00:45:17,370 --> 00:45:21,840 but it's something that's starting to look very modern, as will will. 390 00:45:21,840 --> 00:45:27,390 We'll talk about now that unity certainly didn't come after the Second World War, 391 00:45:27,390 --> 00:45:34,330 as Freeman Dyson has explained in his many talks with me at the Institute for Advanced Study. 392 00:45:34,330 --> 00:45:41,190 Freeman began life as a as a I think it's fair to say, a mathematical prodigy, 393 00:45:41,190 --> 00:45:46,470 a number theorist trained at the feet of G.H. Hardy at Cambridge University. 394 00:45:46,470 --> 00:45:52,170 And by Freeman's account, although he was a totally gifted mathematician, 395 00:45:52,170 --> 00:46:00,180 he found that the mathematics he was doing at Cambridge was not the stuff that was really cutting edge at the time he was there, 396 00:46:00,180 --> 00:46:08,610 which is in the Second World War. And just and shortly afterwards, the pace setters were known as Bourbaki, 397 00:46:08,610 --> 00:46:15,320 which is an organisation of French mathematicians and anonymously grouped up under that name of Bach. 398 00:46:15,320 --> 00:46:21,510 You first met in 1934 with the ambition to rewrite the whole of mathematics set out 399 00:46:21,510 --> 00:46:28,500 of all of those axioms to make plain the unity and logical structure of mathematics. 400 00:46:28,500 --> 00:46:35,650 The one thing it wasn't interested in was applications to the real world had no interest to them at all. 401 00:46:35,650 --> 00:46:42,990 Philip Freeman told me that he heard the big, bulky agenda at Cambridge referred to as a French disease. 402 00:46:42,990 --> 00:46:49,740 I didn't know that was a synonym for syphilis, but it is. They certainly had no time for Bourbaki at all. 403 00:46:49,740 --> 00:46:55,230 Freeman chose to concentrate on problem solving, 404 00:46:55,230 --> 00:47:04,500 and that's what led him to his triumph in in in in setting out a quantum theory of electricity and light. 405 00:47:04,500 --> 00:47:09,000 But his observation that he ran home to me many times is that at that time after the war, 406 00:47:09,000 --> 00:47:16,050 there was a divorce between physics and mathematics, where the two went their own separate ways. 407 00:47:16,050 --> 00:47:24,330 Something that was confirmed by a Princeton colleague, Karen Allen Beck, winner of the Abel Prise this year, 408 00:47:24,330 --> 00:47:29,430 who had exactly the same experience or very similar experience 20 years later. 409 00:47:29,430 --> 00:47:43,110 And where that where where the gradual coming together of physics and mathematics was reviewed was viewed as something to be as deeply suspicious. 410 00:47:43,110 --> 00:47:45,420 Now, I'm afraid I don't have to go through that far too quickly. 411 00:47:45,420 --> 00:47:57,600 The second part of my talk here, but you'll forgive me if I go quite a gallop here where I come in as a spear carrier was in this era 1970, right? 412 00:47:57,600 --> 00:48:03,720 And this is when I became a student. Now this, of course, is the sexier side of that time. 413 00:48:03,720 --> 00:48:06,060 In fact, it was pretty a miserable time. 414 00:48:06,060 --> 00:48:13,110 As I remember these wars in Southeast Asia and the Middle East, a UK economy plummeting, known then as a sick man of Europe. 415 00:48:13,110 --> 00:48:20,130 Nothing much changed there then. But for me and for far more eminent people than I could ever aspire to be. 416 00:48:20,130 --> 00:48:28,770 This was a time of huge excitement and that the reason for that was because of the activity in understanding the subatomic world, 417 00:48:28,770 --> 00:48:36,750 the subject of particle physics and also on the macroscopic scale Astro Astrophysics. 418 00:48:36,750 --> 00:48:40,020 And I must admit that not being particularly mathematically inclined myself, 419 00:48:40,020 --> 00:48:45,360 I was very suspicious to see these incursions of mathematics made at that time 420 00:48:45,360 --> 00:48:51,540 when it seemed to me that the real action was in accounting for experiments. 421 00:48:51,540 --> 00:48:54,480 Now, with the benefit of hindsight, 422 00:48:54,480 --> 00:49:02,520 that the critical thing that was that was starting to take shape now then and I urge this is the take home message tonight, 423 00:49:02,520 --> 00:49:09,630 because it's still true today, is that the theories that that if you want to produce a fundamental theory, 424 00:49:09,630 --> 00:49:17,340 then as Dirac had alluded to in that lecture, those theories must be consistent with the special theory of relativity theory 425 00:49:17,340 --> 00:49:22,740 of motion that Einstein and others had put out in 1995 and quantum mechanics. 426 00:49:22,740 --> 00:49:28,530 Nobody has ever found not done an experiment that has contradicted those two theories. 427 00:49:28,530 --> 00:49:31,920 So it's an incredibly strong empirical base. 428 00:49:31,920 --> 00:49:39,450 And what physicists have done much of what they have done in basic physics has been jamming those two theories together. 429 00:49:39,450 --> 00:49:46,230 Now it's worse. It really is worth stressing that that is extremely difficult to do. 430 00:49:46,230 --> 00:49:48,330 Einstein thought that he was not alone. 431 00:49:48,330 --> 00:49:54,450 It was impossible to take theories that look so different with such different mathematics and find a way of jamming them together, 432 00:49:54,450 --> 00:50:01,920 such that they produce just about a theory that works. And it did because it produced the first theory of what we call quantum electrodynamics, 433 00:50:01,920 --> 00:50:08,100 which is possibly the best verified physical theory in in nature. 434 00:50:08,100 --> 00:50:12,680 And it also triumphed in astrophysics as well. 435 00:50:12,680 --> 00:50:20,060 I remember when I was a twenty five year old graduate student going to a lecture, not here, of course, but in Oxford, 436 00:50:20,060 --> 00:50:28,370 given by the great Dennis Sharma when he was talking about the way Stephen Hawking had had shocked his community 437 00:50:28,370 --> 00:50:33,830 by putting forward this idea that you could actually bring in quantum mechanics to the study of black holes, 438 00:50:33,830 --> 00:50:42,200 which is a classical subject, and come up with this physical notion that black holes ain't so black but actually continually emit radiation. 439 00:50:42,200 --> 00:50:46,130 Something that was, I saw people saying, is completely nuts at the time. 440 00:50:46,130 --> 00:50:56,060 Now it's part of the textbooks. But he did it with a tour de force calculation that did not combine the rigorous rigorously in one fell swoop, 441 00:50:56,060 --> 00:51:01,880 but brilliantly brought the theories together in a way that made the calculation extremely robust. 442 00:51:01,880 --> 00:51:10,250 I still remember that talk of still remember Dennis's admiration and excitement for the people in the audience with whom I was one. 443 00:51:10,250 --> 00:51:15,470 What we were seeing was a different jamming together of quantum mechanics and relativity, 444 00:51:15,470 --> 00:51:21,620 the theory at the gauge theories of the forces that govern the atom. 445 00:51:21,620 --> 00:51:31,070 Now this theory was we now call quantum field theory governing the basic interactions all together the nucleus and the atom. 446 00:51:31,070 --> 00:51:35,180 I say again, it's a it's amazing that the theory even exists, right? 447 00:51:35,180 --> 00:51:42,410 But it does. Right. And like very careful study of the symmetries we leading theoretical physicists found what we 448 00:51:42,410 --> 00:51:49,190 now call the standard model that has had nothing but takes for nature from nature for decades. 449 00:51:49,190 --> 00:51:57,560 So this is an extremely powerful way of doing theoretical theoretical physics. 450 00:51:57,560 --> 00:52:06,620 The I want to illustrate one particular meeting that really brought in my opinion, and it's central to my book here. 451 00:52:06,620 --> 00:52:09,260 That was the central moment, I think, 452 00:52:09,260 --> 00:52:20,150 when a central moment where mathematics and physics really did start to come together and the divorce was became a thing of the past. 453 00:52:20,150 --> 00:52:32,030 It was the meeting between the great mathematician for many years here at Oxford, Michael Attia and below Edward Witten, the American mathematician. 454 00:52:32,030 --> 00:52:37,190 Attia was a great geometry without question one of the great mathematicians of the 20th century. 455 00:52:37,190 --> 00:52:44,750 And he had become interested in these gauge theories that govern atomic atomic physics that, as I described. 456 00:52:44,750 --> 00:52:52,790 And he and in the early 1970s, he and his he described to me, he began to morph into a quasar. 457 00:52:52,790 --> 00:52:59,060 A physicist and the person who he was most close to was Edward Witten. 458 00:52:59,060 --> 00:53:04,190 Many years his junior, a complete singularity, an outsider like Dirac, 459 00:53:04,190 --> 00:53:08,990 an undergraduate in modern languages and history, and briefly studied economics. 460 00:53:08,990 --> 00:53:18,200 And by by the time he switched, I think it was the twenty three he switched into into theoretical physics. 461 00:53:18,200 --> 00:53:26,780 And they met in the fall of nineteen seventy six in the in an office in the Massachusetts Institute of Technology. 462 00:53:26,780 --> 00:53:31,070 Microsoft has described that meeting to me a dozen times. He was there. 463 00:53:31,070 --> 00:53:34,970 There was about twelve people sitting around a small office in that there, 464 00:53:34,970 --> 00:53:43,940 and he said one person knew more than everybody else put together, and that was the recently graduated Ph.D., Edward Witten. 465 00:53:43,940 --> 00:53:47,960 Together they were. 466 00:53:47,960 --> 00:53:52,050 Edward was had begun work just but not just. I shouldn't use that word. 467 00:53:52,050 --> 00:53:56,210 We were looking at data closely looking at what one could derive from it. 468 00:53:56,210 --> 00:54:01,910 But with encouraged by a TIA and with an enormous mathematical ability of his own, 469 00:54:01,910 --> 00:54:12,740 they started to bring those two subjects together and analysed ever more closely the mathematical structures of those gauge theories. 470 00:54:12,740 --> 00:54:22,850 I can't resist it is a tribute to Michael, who died a few months ago, his favourite image that it was like having two intersecting tunnels, 471 00:54:22,850 --> 00:54:28,490 one being dug by gauge theories, the other way being dug by mathematicians. 472 00:54:28,490 --> 00:54:36,020 They were oblivious of what each others were doing, and at a certain point they intersected and found they were working on each other. 473 00:54:36,020 --> 00:54:43,580 Subjects that intersection, ladies and gentlemen, took place at the Mathematical Institute of the University of Oxford. 474 00:54:43,580 --> 00:54:52,280 That is when I would say those two things intersected. And Frank Yang, who also has a claim for being part of this, that is where it took place. 475 00:54:52,280 --> 00:54:58,370 And in 1977, seven A and several other very eminent scientists, 476 00:54:58,370 --> 00:55:05,960 West were working on that common territory between pure mathematics and theoretical physics. 477 00:55:05,960 --> 00:55:11,660 Stunning monopoles things called instant ones, which are events in space and time and a plot. 478 00:55:11,660 --> 00:55:19,770 Beginning to apply it to other subjects as well. Luckily, we now know the physics of solids I saw to my dismay, 479 00:55:19,770 --> 00:55:26,180 I have to say because I was I wasn't anything like a sophisticated mathematically as I what needed to be. 480 00:55:26,180 --> 00:55:31,130 I thought this would go away. I thought that nature couldn't be that complicated, right? 481 00:55:31,130 --> 00:55:37,670 But it has stayed the subject. Mathematical complexion has endured, 482 00:55:37,670 --> 00:55:46,070 and particularly through the next generalisation of quantum mechanics and relativity coming together in something called string theory, 483 00:55:46,070 --> 00:56:01,220 which is witness, said wisely, My view is the only interesting idea that is a development of both general relativity and the gauge theories of atoms. 484 00:56:01,220 --> 00:56:08,330 String theory began to take shape properly in in the summer of 1984, 485 00:56:08,330 --> 00:56:18,830 when we had a viable account of of not just gravity, but the the the three fundamental forces that hold together atoms. 486 00:56:18,830 --> 00:56:24,080 And for the first time ever, it gave a reason why gravity must exist, Witten said. 487 00:56:24,080 --> 00:56:31,460 To me, that is the main reason why he was interested in string theory, and it became, this is a key point for us. 488 00:56:31,460 --> 00:56:36,380 This became a Klondike for mathematicians. Even today as we speak. 489 00:56:36,380 --> 00:56:40,640 I think it fair to say that if that string theory has above all, 490 00:56:40,640 --> 00:56:48,050 been of enormous benefit to two mathematicians and there been other developments of two by physicists, 491 00:56:48,050 --> 00:56:55,880 the something called end theory, which is a generalisation I further development of string theory and two years later, 492 00:56:55,880 --> 00:57:01,820 one male to same is linking between string theory and gauge theory. 493 00:57:01,820 --> 00:57:10,040 It appears to people working in this field that these mathematical connexions demonstrate that physics is on the right track. 494 00:57:10,040 --> 00:57:17,360 It is. It would be idle to pretend that there aren't people who oppose that view, and they are calling card. 495 00:57:17,360 --> 00:57:23,750 Mainly the biggest one is that string theory has yet to make a direct connexion with experiment by 496 00:57:23,750 --> 00:57:30,020 by virtue of a new prediction that can be that could be tested in laboratory that cannot be denied. 497 00:57:30,020 --> 00:57:36,170 That hasn't happened, but string theory libs it has applied, which most naturally applies at very, very high energies. 498 00:57:36,170 --> 00:57:43,100 So it's going to be very difficult to test, which is not to say it's impossible, but nobody has actually contradicted it. 499 00:57:43,100 --> 00:57:49,160 But there are without doubt there's reasons to be concerned about about the interpretation of it. 500 00:57:49,160 --> 00:57:53,360 And I might say as well it has its connexion with ordinary space. 501 00:57:53,360 --> 00:57:57,920 The one that we live in is also problematic. That cannot be denied. 502 00:57:57,920 --> 00:58:08,870 But what I would like to say is that the application of string theory by it is such 503 00:58:08,870 --> 00:58:16,010 that people who the top the best experts see that still as the most promising theory, 504 00:58:16,010 --> 00:58:20,570 they'll all people who disagree with that. It's a free country. They could work on those other topics. 505 00:58:20,570 --> 00:58:27,340 But I think it's fair and reasonable to say that these other competitors a minority sport. 506 00:58:27,340 --> 00:58:31,030 They may disagree. Of course, they're free to do that. 507 00:58:31,030 --> 00:58:41,050 So let me just look, if I may, to the to the to what we now call the doubly unreasonable effectiveness. 508 00:58:41,050 --> 00:58:45,760 Mathematics, of course, is incredibly on a credibly effective in physics. 509 00:58:45,760 --> 00:58:51,700 But physics now we know more than ever is extremely effective in mathematics. 510 00:58:51,700 --> 00:58:57,460 And I've given several examples of here which are on and I'm not going because of time. 511 00:58:57,460 --> 00:59:02,080 I'm not going to go through them, forgive me, but I covered them in detail in my book. 512 00:59:02,080 --> 00:59:10,480 There is absolutely no doubt that that physics and mathematics are joined at the hip in fundamental physics today. 513 00:59:10,480 --> 00:59:16,390 So what do I what's my view of looking to the future? 514 00:59:16,390 --> 00:59:22,450 Well, my view is that there is good reason to believe that we are on the right track, 515 00:59:22,450 --> 00:59:30,400 guided by quantum mechanics and special relativity, but that we definitely need to be patient. 516 00:59:30,400 --> 00:59:34,810 My generation, if I can call it that was used to the results coming every few years. 517 00:59:34,810 --> 00:59:40,600 Major new major new results that were rich pickings from from from Mother Nature. 518 00:59:40,600 --> 00:59:45,470 Today they come much more slowly. And I think we're going to have to be in physics. 519 00:59:45,470 --> 00:59:52,330 We're going to have to get used to the mathematical timescale where things are done much more, much more slowly. 520 00:59:52,330 --> 00:59:58,720 This is these are my predictions all silly, right? Well, they're not intended to be silly, but they probably will. 521 00:59:58,720 --> 01:00:05,530 But I want to show why. I think this is how I think this what we're aspiring to here. 522 01:00:05,530 --> 01:00:11,380 First of all, I predict that the quantum field theories that are now used to describe atoms which 523 01:00:11,380 --> 01:00:16,870 are extremely difficult to calculate that is ripe for a completely new understanding. 524 01:00:16,870 --> 01:00:23,230 Quantum field theory will be reformulated in a way where these horrendous calculations will be much simplified. 525 01:00:23,230 --> 01:00:27,610 There are already evidence to get us started on that. I predict that will happen. 526 01:00:27,610 --> 01:00:35,890 I also predict that string theory. Yes, I'm sure there are things that need to be radically revised in the theory. 527 01:00:35,890 --> 01:00:38,320 I'm sure that maybe even revolutions around the corner. 528 01:00:38,320 --> 01:00:49,590 But I believe that this is not wasted effort that this is this will be seen as a perfectly worthy step on the on on the path to the future. 529 01:00:49,590 --> 01:00:58,470 They understand the understanding that the senior gave us of gravity in terms of a equivalence between a string theory and gauge theory, 530 01:00:58,470 --> 01:01:05,700 I believe will be seen to be that B b be applicable to the real world. 531 01:01:05,700 --> 01:01:09,480 Most important, this is a particularly big thing that I can't explain in detail, 532 01:01:09,480 --> 01:01:17,640 but I talk about in my book and you can read elsewhere space time developed most famously by Einstein that is going to be superseded. 533 01:01:17,640 --> 01:01:26,790 I don't know of any leading theoretical physicist now who believes that the Einstein in view of time is is it is complete, 534 01:01:26,790 --> 01:01:30,120 it is going to be superseded and we're being guided on that track. 535 01:01:30,120 --> 01:01:34,170 I say again by quantum mechanics and special relativity, 536 01:01:34,170 --> 01:01:39,750 and we're seeing I think this is very heartening a trend towards unity, particle physics, cosmology, 537 01:01:39,750 --> 01:01:48,750 condensed matter that solids information theory where there is a coming together of all areas, all across fundamental physics, 538 01:01:48,750 --> 01:01:56,370 with mathematics being the glue between them and mathematics providing a guide to help us understand those relationships. 539 01:01:56,370 --> 01:02:02,880 So I think we're going to have to get used to something that surprising new insights 540 01:02:02,880 --> 01:02:08,070 from experiments and observations will start to become few and far between, 541 01:02:08,070 --> 01:02:11,440 right? I know it's a bit depressing, but they're not going to come every few years. 542 01:02:11,440 --> 01:02:16,200 Nature is getting harder and harder to question constructively about these things. 543 01:02:16,200 --> 01:02:24,420 So I think physics tells us that it's going to be a long, a longer term thing that it seemed when I was starting out during those slow decades. 544 01:02:24,420 --> 01:02:26,760 And I think we're in one now. 545 01:02:26,760 --> 01:02:35,790 We will physicists will have to focus, I think, on mathematics and and do, as Einstein said and Dirac said and others are separate those two. 546 01:02:35,790 --> 01:02:40,110 I think the point is that by looking at the mathematical content, 547 01:02:40,110 --> 01:02:46,620 you will be able to advance the subject so that it's ready for the next generation of of experimenters. 548 01:02:46,620 --> 01:02:54,060 Now it seems a harsh thing to say, but I believe we're going to have to take this. 549 01:02:54,060 --> 01:03:03,090 While it's difficult to get clues out of nature, we can console ourselves that nature doesn't speak to us just in terms of observations. 550 01:03:03,090 --> 01:03:30,487 It also speaks to us in numbers. Thank you very much.