Paul Dirac and the religion of mathematical beauty

Paul Dirac and the religion of mathematical beauty

So welcome to the Royal Society’s Centre for the History of Science. I’m Uta Frith, and I’m the Chair of the Library Committee, and therefore I feel very privileged also to be part of the events that are being put on, and in fact I want to particularly thank Felicity Henderson, who probably is still standing outside, for organising this really fascinating series of events that happen on a Friday. And of course, today’s speaker, Graham Farmelo, will be a special treat for us. I should say that this talk will be podcast, which has some implications for switching mobile phones off, that sort of thing. I’m sure you would do that anyway. And I’ll just say a very few words about Graham. I have of course, his book here, which maybe many of you have read and he will talk to us about Paul Dirac. It is very interesting that Graham trained as a theoretical physicist himself, so he has, of course, extremely privileged access to the mind of Dirac. He has been a scientist at the Science Museum. He has now taken up a Fellowship at Churchill College, Cambridge and he spends his summers at the advanced, the Institute for Advanced Study in Princeton. He has become a full-time writer, because he’s obviously immensely gifted as one of the really new breed of science communicators, whose books really win prizes, and of course, Graham’s books have also all got wonderful awards. So I’m now giving you to Graham Farmelo, to speak to us about Paul Dirac and the religion of mathematical beauty. Thank you very much. Well thank you for that gracious introduction, It’s a great pleasure to be here at the Royal Society – humbling for someone like myself to talk in this environment. I’d like to thank Felicity and Peter for the introduction. Here he is – Paul Dirac, arguably the most illustrious scientist elected to the Fellowship here in the 20th century. He is most famous for co-inventing the most revolutionary theory of the past 150 years – the theory of quantum mechanics, fundamental theory of atoms and molecules, matter on the very small scale. His reputation, if anything, has increased since he did his best work in the ’20s and ’30s, and now it’s a by-word to hear him referred to among theoretical physicists as ‘the theoretician’s theoretician’ or the first truly modern theoretical physicist. Around the time this picture was taken, he was described by CP Snow as the greatest living Englishman – a bit of a surprise, because hardly any English people had actually heard of him when that was actually said. But that was the way Dirac wanted it. His anonymity is the price we pay for his great modesty and taciturnity. At the end of his life, one thing struck me when researching his biography: namely, his complete obsession with the role of mathematical beauty in physics – the idea that if a theory is mathematically beautiful, then that is a candidate for a fundamental theory of what is going on in nature at the most fundamental level. He was also – and this amazed his friend, Robert Oppenheimer – fundamentally a geometric thinker. Oppenheimer, like most other people, thought of Dirac as an algebraic thinker, an algebraic practitioner of steam-hammer power, but that is not how Dirac saw himself at all. He saw himself fundamentally as someone who thought of things in geometrical, in a spatial way. Now what I want to do in this talk today is to look at this abiding obsession that he had, certainly in his old age, with this concept of mathematical beauty, and also take a look at his extraordinary character. Those of you who are physicists will know that part of the rite of passage of any physicist is to know at least one half-original Dirac story – a story which illustrates his extraordinary personality. As every physicist knows, Dirac was, in the words of Niels Bohr, “the strangest man of quantum mechanics” – someone deeply private, of very, very few words, rectilinear in thinking, virtually, apparently devoid of empathy with other, other human beings, always an outsider. Here he is – a picture taken in Cambridge when he was in his pomp, shortly before he was elected to the Fellowship of the Royal Society, a year or two before, and it’s not a coincidence – taken right next to a tree, because he used to love climbing trees at lunchtime, in his professorial garb, in this suit here bought from the Co-op in Bristol – of course, notably, 2 inches too short in every dimension. Apart from being an outsider, there were two characteristics that mark Dirac as different from the theoreticians who were co-inventing this revolutionary theory. First of all, he was very strongly anti-philosophical. You wouldn’t see him discussing with Niels Bohr, for example, the philosophical niceties of quantum mechanics – not interested. The other point is, he was deeply anti-religious. His acquaintance, Wolfgang Pauli, was once heard to say after hearing an uncharacteristic rant from Dirac about the concept of God, Pauli said, “There is no God and Dirac is his prophet.” So anti-religious and anti-philosopher. What was most striking to people who didn’t know any physics and just came across this remarkable man was his extreme taciturnity, and it was that that he always said in later life that was caused by his upbringing in Bristol. He was born in 1902. This picture was taken shortly before Paul Dirac went to school – that was in 1907. Looks like a pretty happy family. His father is Swiss, fled an unhappy childhood in Switzerland; mother from Cornwall; Dirac’s elder brother, Felix, and his sister, Betty. Looks like a pretty ordinary family – in fact, according to Dirac’s testimony – and I won’t say that again, but all of this comes from his own testimony – it was an appalling childhood. In fact, he said, “I never had a childhood.” The reason for that was that they never had visitors – almost never had visitors. In fact his father said, “We don’t need this at all.” They were driven to study the whole time, and in particular, they had an extraordinary linguistic regime. Every mealtime, the family would split into two, with Dirac and his father in the front room and his mother and other siblings in the kitchen. In the kitchen, they’d be speaking only English; he would speak only French. He’s told a reporter in the 1930s that when he was a boy, he thought that men spoke French and women spoke English. This was not funny to him, because he saw every mealtime as a trial. His father, a very strict disciplinarian – his strategy was to speak only in French to his children and to punish at the dinner table any error of any kind with denying the young Dirac his next wish. Dirac, from a young age, had very bad stomach problems, often needed to be sick – like anybody else, as a child, he needed to go to the toilet. He would be denied those wishes. If that sounds extreme, you go to the Bodleian Library, you will see that Dirac’s wife records these disasters – which of course they would be for a child – happening every day. I personally don’t believe that, but that is what she said, and he told her. One thing he never denied was that he had a superb education – just around the corner from their house in Monk Road, North Bristol, where he was born, was this school, Bishop Road School – still stands. And he had a very good practical education. Go back and see the school reports – you can see all the school inspectors said that all the teachers were very good at giving the children a balanced, practical education. From some testimonies there, we know that Dirac was exceptionally quiet. The only thing that would draw him into speech would be a teacher making an error, and his hand would shoot up and it would be politely corrected. Among the children he didn’t speak to were Cary Grant – Cary Grant, who lived about 200 yards up the road. Both Cary Grant and Paul Dirac had an excellent education in technical drawing. Now, this is important, because this is where – in my judgement, this is where Dirac got his first schooling in the geometrical way of thinking about things. Remember, he was doing algebra and doing geometry at school, in elementary fashion, but thanks to the Great Exhibition of 1851, the school syllabus was changed, and this syllabus was definitely changed that way by Sir Henry Cole, inventor of the Christmas card, first director of the V and A. He and others like Lyon Playfair got technical drawing brought in from the Continent to chivvy up the school education for boys – the girls were sent off and told to do needlework. So they were split up in those ways, and Dirac studied technical drawing – wait for it – for nine consecutive years. So he really, really had a very strong education in depicting things geometrically – artificial objects like this here, but also doing the fancy tricks of cycloids and things that I did at school and maybe you did too. So he was doing well at school – not brilliantly, we’re not looking at genius stuff, but he did increasingly well at junior school – he kept all his reports. By 1914, opening of the First World War, he went to another superb school – one of the best public-funded schools in the country – the Merchant Venturers’ Technical College. There, the most notorious master was one Charles Dirac, his father, known as ‘Dedder’ – the most notorious disciplinarian in the school, so you can imagine what it must have been like for Felix and for Paul in that playground, to know that their father, who was as I said, the toughest, but also arguably the most effective teacher there – he was teaching modern languages. Notice – no old-fashioned languages here – this was a resolutely practically-minded school. So they did French, they did German, they did Spanish – Charles Dirac allegedly learnt a new language every summer. This is where Dirac took off. He did well at the beginning, and two years into his school education, he was doing extremely well. Teachers were having real difficulties in giving him problems that he could, that would challenge him. He was even given by his maths teacher a textbook on Riemannian geometry when he was 13 years old, just to try and keep him occupied. He said – and this is his own testimony and I’ve no reason to disbelieve it – that even at school, he was 13 years old, he was going into his bedroom at home and thinking about the nature of space and time. This is extraordinary – not unbelievable – remember, HG Wells was writing about that kind of thing at that time – but still remarkable for a boy of that age to be thinking like that. He was very close to his brother at that time. This is Felix – a stouter young boy – not nearly as clever, not nearly as clever as Paul Dirac, but did decently well at school. His father bullied him, according to Paul’s account, into not being a doctor, which is what Felix desperately wanted to do – I’ve seen the records that showed he wanted to join the St John’s Ambulance – and he made him go and study engineering so that he could get a job. The Dirac brothers were the children of HG Wells – people who wanted to get a – not literally – but wanted to get a job in engineering. That was the prevailing philosophy at the time there. And Felix here was struggling along in his engineering degree and his brother followed him. Paul Dirac followed his brother into the Merchant Venturers’ College, as it was then called, and did a degree in engineering, having seen, as I say, his father bully his brother into that career. Dirac is typically remembered, known as the most austere of thinkers, the most head-in-the-clouds, nothing to do with experiment. This is how he spent his time, ladies and gentlemen, as an undergraduate – he was visiting factories, he was building model aeroplanes, he was building cars, he was learning how to fill in tax forms. And on 11 March 1919, standing here looking like, with a kind of – look at him – look, he’s straight into the camera there, like James Dean – he was visiting an automobile factory. So let’s get one thing right – he was a very practically-minded person, completely different, as I said, from the image that he has among most theoretical physicists. A few months after this was taken, in November 1919, Dirac had an epiphany, and that epiphany was caused by an event that was stage-managed by some of Britain’s leading astronomers and scientists – partly at this institution and partly the Royal Astronomical Society. They arranged for Einstein to be made a global superstar – he was already famous among physicists, but virtually unknown outside – and they arranged, at a special meeting at the Royal Astronomical Society, to have a Newton vs Einstein, head-to-head clash over the results of the recent solar eclipse experiment, which Einstein would win – and he did. But overnight, following an article in ‘The Times’, Einstein became an international celebrity. Eventually, as you may know, the ‘Time’ magazine ‘Person of the century’. That was all launched by a campaign as cynical or hard-bitten – whatever you want to say – as anything you might see in the media today, to propel an obvious genius into the place in public life that he deserved, after the horrors of the First World War. Dirac started to read about this and was entranced – this was a key event, ladies and gentlemen, because this is where he found his first love – not in flesh, but in the equations of physics. He discovered the concept of theoretical physics – a new science, only begun in the 1850s in Germany. He realised that there was this thing that you could study where you could imagine your way into the heart of nature through a combination of mathematics and through interpreting data. So Dirac started to aspire to this condition of being a theoretical physicist, while being a first-rate engineering student whose only real flaw was his hopeless inability as an experimenter. He got his only really terrible report in a placement at Rugby, at an engineering works, where he was basically told – ‘You’re a very smart guy, Paul, but don’t please get a job in a factory.’ It was in Rugby that we learn, according to Dirac’s testimony, that relations with his brother had really got terribly bad. They were actually walking on different sides of the streets to avoid each other. We don’t know the exact origin of this – Dirac, Paul Dirac said that he speculated that his brother was depressed, having been pushed into the wrong career. Dirac might not have been the most forthcoming, loving of brothers – one doesn’t know. But whatever else one says about it, they were effectively completely separate human beings, not communicating at the time that he was in Rugby. So in 1921, we have the most successful engineering graduate Britain produced in the 20th century, with the value of hindsight. This is Paul Dirac, and he was rewarded with a certificate of unemployment. He tried to get a job – I don’t think he was the most exciting interviewee. Also, it has to be said, he was being interviewed at the worst recession this country has seen until the one we have been in now – we’re probably still in it, actually, except for the economists that deny it. But that’s how serious this was – he could not get a job. And this was the first of these instances that I want to draw attention to here, where Dirac had the benefit of a great, great teacher and a kind person who came in on his behalf – and there are several instances like this, you’re going to hear in this talk. His instructor in the electrical engineering lab, David Roberts – who used to zoom around the laboratory in his wheelchair – saw that the feckless Dirac was doing these ridiculous stroboscopic experiments and said, “You don’t want to do that.” He got him onto a maths degree and he was able to freeload on that degree for two years – that was an extremely wise and generous thing to do, and Dirac duly got his degree in mathematics, so he came equipped with an engineering degree and a maths degree. During that maths degree, he met the teacher he regarded as “the best teacher [he] ever had” – the name of that teacher was Peter Fraser. I spent about a month of my life in the course of writing this book trying to find out things about Peter Fraser and found nothing. He didn’t produce a single research paper. All he did in life was to be a teacher, but he was a brilliant teacher – and for Dirac to say so, he must have been damn good. One thing we know about him, he was obsessed with one thing – mathematical beauty. He taught something called projective geometry, a type of geometry where, about lines and planes where there are very few equations, in the most elementary books, at least, and it links completely with the technical drawing that Dirac had done at school. In France, they’re taught in the same lessons – or they were, anyway. Technical drawing and projective geometry had the same origins by Monge and people like that in France in the previous century. So you have that very, very strong visual link being brought out there. So just after this, you have Dirac coming out now as a very strong student, and the person who was pushing him to move on was his father, his hated father, quoted from Dirac, many, many times – loathed and detested his father. Behind the scenes, his father was trying to get him to Cambridge, and he did. In 1923, shortly after his 21st birthday, the young Paul Dirac joins up on a PhD course here in Cambridge. This is St John’s College, which talent-scouted him in Bristol and got him up there. Now, Dirac was given a supervisor by the name of Ralph Fowler – international quality physicist, but he was actually – Dirac wanted to study relativity, he was very miffed about this – he was put onto quantum theory – he didn’t want to do that, that was a horrible subject, he thought. So he’s here as a quantum theory student with a very fine supervisor. Ralph Fowler was a Henry VIII figure – big, burly, bone-crushing handshake – very adept at giving good problems to people – soluble problems that they could solve. Dirac started to stand out here. I’m remind you – he would not have got in as an undergraduate to Cambridge – he didn’t have Latin or Greek. He joined this thing and stood out immediately. Well, the first thing is – what a weird character! He came there with a maths degree, an engineering degree from a place whose degrees were not even recognised – are not even recognised still officially by Cambridge – but brought with him a phenomenal performance in the scholarship exam. He stood out immediately as a first class student. He was doing brilliantly up until March 1925 – five papers, absolute rock-solid certainty for a PhD. He walked across on 8 March 1925 the quadrangle just behind this picture here, and all that came to an end when he went into his pigeonhole, opened a letter from his Aunty Nell, and that letter asked him to brace himself, because his brother had killed himself. No record of what Dirac said – I’ll just jump ahead 40 years and say that Dirac – this is the one topic Dirac would not discuss with his family. He apparently was too traumatised to even show his children a picture of his brother when they were younger. Dirac productivity plummeted for several months. Right out of the blue, when Dirac returned in the summer of 1925, his grieving family in Bristol – Ralph Fowler got this paper and sent it, very generously – it’s the only copy of this paper in Britain – and he sent it to his most brilliant student, Paul Dirac. This is the paper – it was, we now know, the first paper on quantum mechanics. It was the proof of Heisenberg’s paper on quantum mechanics that – I want just to say it’s very important to recognise this was not recognised as a masterpiece then. Now we know it is, but then, Dirac looked at this and Dirac said, “Nature can’t be this complicated,” and put it aside. If you look at the paper, it contains in there one statement that Heisenberg made, that if you have position and momentum in this new scheme, where you represent variables according to matrices, not numbers – what a bizarre thing to do, incidentally – then the numbers, the order in which you multiply these things matters – position x momentum is not the same thing as momentum x position. The order matters. Heisenberg said – ‘We’ll clear this up.’ Dirac had seen that in his studies of projective geometry. He took that single thread and he wove it into the golden tapestry that became the fundamental equations of quantum mechanics – his first great paper, the only paper in early quantum mechanics you can now read, and it still reads like a modern paper. Thus began, ladies and gentlemen, the longest creative streak, longest and deepest creative streak of any theoretical physicist in the 20th century, apart from Einstein. Dirac co-invented quantum mechanics in that streak, and in the words of the great Freeman Dyson, Dirac’s papers, unlike anyone else in the field, they were “perfectly carved marble statues falling from the sky”. You can still read them today. They still look fresh, they still look accurate, they still are written in a modern language. I’m not going to be discussing the details of the articles – we could spend weeks, we could have whole summer schools on this if we wanted to. I want to concentrate on the themes that I’ve outlined earlier on. But I can’t resist saying that he stood out. Look at this picture. This was a year or two after he’d got his PhD, and he visited the centre that he was competing with as a kind of one-man show in Cambridge with the might of the mathematicians and theoretical physicists in Göttingen, led by Max Born here. Look at Dirac here. There’s always one – not interested in talking to the photographer – he’s reading a paper. I fantasise that he was reading about the thing that he came into contact with in Göttingen, that would trouble him for the rest of his life. One of the things that Dirac had done a few months before was to relate the two different types of quantum theory that were around at the time: the matrix theory of Heisenberg and the wave theory of Schrödinger. He showed how they can be switched from one to the other. He called that paper “my darling” – he loved it, it was his favourite paper. He then, three weeks later, co-invented field theory – the way in which the language of small fundamental particles are now discussed. When he did a calculation on the interaction between an electron and a photon – it couldn’t be a simpler calculation – he found he got infinity out for the energy of that system. And he wrote, “This is obviously wrong, but we can get rid of this.” What he’d seen there was the seeds of something, as I said, that troubled him for the rest of his life, and he may just have been reading about that in this rather evocative picture taken in Planckstrasse in Göttingen. The truth is – and we triumphalist physicists like to think that there are these great people that do all these majestic things and they’re all heroes and what-have-you – the truth is that this subject was being invented by many people largely at the same time, and Dirac was, although a pre-eminent mathematician and an outstanding practitioner, he was doing stuff that other people were doing similarly at the same time. He did – he was outstandingly good, but he wasn’t someone who you’d say was a mighty figure – until in late 1927, he did something that some 20 people of Nobel stature, later of Nobel stature, were seeking to do. They took that ordinary quantum theory and combined it with the special theory of relativity to produce the first union between those theories in describing the electron. He married those theories and came up with what we now call the Dirac equation – the only equation in Westminster Abbey – you can go and check it yourself if you want, just down the road. This equation called by Frank Wilczek “achingly beautiful”, quite rightly. He had achieved his aim – just like Einstein had written the achingly beautiful equations of general relativity, Dirac was one of the very, very few people who’d sought to take after his hero and done it. He’d produced a wonderfully rich mathematical structure that not only described the electron in the way he wanted, but explained the recently observed phenomenon of electron spin and why the electron has magnetism. He was the star of the year 1928. It was seen, as Heisenberg said to one of his students – “There’s this English guy – if he tackles a problem, it’s not worth going anywhere near, frankly. Because he’s so smart, it’s just not worth competing with him.” He really had arrived then, was seen as the leading master of quantum mechanics. It’s very tempting for me now to go into a kind of operatic aria now about his great papers, and there are innumerable great papers that I could come back and talk about, one after the other. But I did want – I just want to mention one thing that he squeezed out of this equation that will have his name written in the history of our species for however long it lasts. He used this equation to predict the existence of the anti-electron. The electron has a certain mass, it has an electrical charge. He predicted that there should exist, on the basis of the beauty of that equation, a particle has identical mass but the exact opposite electrical charge. This was not taken seriously. His most fervent apostles did not even mention this in their talks – I’ve seen them. It was regarded as too wild to take any notice of. But on 2 August 1932, when the Los Angeles Olympics were being held, the first example of the anti-electron was detected at the California Institute of Technology. Seven months later – that’s how long it took – 2 and 2 were put together to show that Anderson had detected the first example of anti-matter. What Dirac had done – and his friend and competitor Heisenberg said it was probably the biggest of all steps taken in 20th century physics – was to open up this world of anti-matter which, I stress again, he got from not experiment – there were no clues – he’d got it from mathematical thinking that led him to this beautiful equation, and by taking that equation seriously. Let me just say one way of looking at this. Dirac began his life, as I did, in a terraced house, modest terraced house, modest family. Within 27 years of doing that, he had done something special. In cosmology, you may know that we now teach in every classroom, right back to schools, that the very beginning of the universe, half of it consisted of anti-matter – the other half of matter. So Dirac conceived half the early universe in his head, from those humble beginnings. This is the scale of imagination we’re talking about. But I would say one thing that’s very striking – I’ve read every single one of his papers with great pleasure and great profit – not one of them mentions beauty. Not one. He mentions it in a couple of lectures and in one experimental paper – yes, he was an experimentalist too – he wrote papers on experimental physics, which he did in Rutherford’s laboratory – he does mention it once there, but not in his papers. Well, here you have a Fellow of the Royal Society, Fellow of St John’s, Nobel Prize, salary of £250,000 a year by today’s money, and I think that’s pretty much what he’d get today, isn’t it? All he wanted as a heterosexual man was a woman. And he got one – or rather, she got him. This was “Wigner’s sister”, as he called her. He met her on 1 October 1934 and then she set about pursuing him – it’s quite clear that that is not a sexist thing to say – you can read the correspondence, six-line letters from him, 24-page letters from her. Did he write in equations? No, no equations, but in one of them, in one she got absolutely furious, saying, “Well, why don’t you answer any of my questions?” And he sent her back a table with an enumerated list of letters, unanswered questions and answers. And then he did it again. This is that extraordinary person. She used to call him – remember, we’re talking about a serious guy here – he’s almost a religion to people in physics – but you know what she used to call him? “My little Mickey Mouse”, because Mickey Mouse was his favourite film character. Dirac had two children, and this is a picture taken in their front garden in Cambridge with Mary, who died recently, and this is him reading from ‘The Wizard of Oz’ – apparently being murdered now by Andrew Lloyd Webber, as we speak in the West End at the moment. But this is him reading from the book, and here he’s working on a nuclear bomb, incidentally. He was working on the neutron flux calculations in his back garden. By this time, his falling-out over quantum theory was so serious, he had come to detest that theory – the theory of quantum field theory that I mentioned earlier on. He was asked at that time by Max Born, then a refugee physicist with tenure at the University of Edinburgh, to give a talk on the philosophical aspects of physics. I would have expected Dirac to turn that down, but in fact he accepted it, and he gave a talk in February 1939 called ‘The relation between mathematics and physics’ – ladies and gentlemen, it is a complete masterpiece. How many abstract mathematical variables are in that paper? None. You could read it to anyone. It’s got some absolutely gorgeous lines in it, like – listen to this for a non-fussy, non-philosophical statement – “Mathematics is a game where mathematicians invent the rules. Physics is a game where the rules are given to us by nature. What is interesting is that the rules of nature appear to be in the same mathematical rules as the mathematicians have concocted.” No fancy words, just complete, devastating insight, and it goes on for ten pages. Absolutely amazing – you can get it on the web. In this paper, he introduces what he calls “the principle of mathematical beauty”, which says – it’s never actually stated per se – but the implication is very clear: that fundamental physics advances by successively more beautiful theories – he has now staked his colours to the mast of beauty as being the criterion. He thought the thing about quantum field theory was it was so damned ugly – it could not be right – and he lifted that to a criterion in physics, one that he never turned away from. He really hated that theory and hated the ugliness that he saw at its heart, that offended his aesthetic sensibilities. After the war, “quantum field theory was tidied up”, and they are the words used by Richard Feynman, who with other people tidied up the quantum field theory of the electron and made it such that you could always calculate observables in photons and electrons and move those infinities away such that they’re not part of the calculation. Dirac thought that was an abomination, but it worked. It won Feynman and others a Nobel Prize. This picture here is Feynman desperately and unsuccessfully failing to get anything out of Dirac. It was taken in 1962 in Warsaw. My friend, Freeman Dyson, who first showed that that theory was renormalisable, which means that that process works, that you can take those infinities and move them away from the field, so to speak, so you could always have a finite prediction – he was, as he put it – and he described this to me many times – he was so proud of himself. He went up to Dirac and said, “What do you think about the theory of quantum electrodynamics, Dirac?” And Dirac looked at him and he said, “I would like it, if it were not so ugly.” And he said he felt about this big. Dirac said, and I quote – that for him “beauty was like a religion”. He simply could not believe that although that theory was right to one part in a trillion, if shown to experimenters and verified, that that was a true, acceptable theory of nature. It simply was unacceptable. The year after this picture was taken, he actually started slumming it and writing a popular article. He actually wrote a popular article – or probably it was written for him – on the history of theoretical physics – not an academic history, but what it focused on – yeah – was on the concept of beauty in theoretical physics, and he came up with a statement, now widely quoted and intensely irritating to many experimenters – that it was “more important to have beauty in one’s equations than to have them agree with experiment”. It’s there, written in Dirac’s own handwriting, so to speak, along with the statement – “God appears to be a mathematician of a very high order.” Dirac really believed this, and I want to say this very clearly – if he saw a theory and it was ugly, he would dismiss it out of hand, as his friend Heisenberg found when in the 1970s, a decade after this, he sent Dirac his latest theory, and Dirac wrote in one line – “Dear Heisenberg, Thank you for sending your new theory. I have looked at it. The equations are so ugly, it cannot possibly be right.” When Heisenberg got that letter, he wrote back and basically said, “Paul, Come on…” and Paul wrote back and said, “I’m very serious – it makes no sense to deal with a theory this ugly.” By 1969, his tenure as the Lucasian Chair in Cambridge was up, and he moved to the physics department ranked 83rd in America. This was at the Florida State University, where he became the apostle of mathematical beauty. He gave some 600 talks all over the world, actually – right down to Australia, right across America – if you look at those talks and the transcriptions of them, he hardly ever fails to mention the importance of beauty. He also lightened up as a human being. Contrary to the ascetic, etiolated person that we’ve been reading about in previous works of Dirac, this was someone who used to read John Le Carré, used to go to classical concerts very regularly – Mozart, Beethoven – read Tolstoy’s ‘War and Peace’, even met, on one occasion, Marlon Brando. It was not a successful meeting. He even acquired a television at one point, because his favourite artist on television was Cher, and in order to avoid a mental argument with his wife, he bought a television so that he could watch her and Elton John and Sting, his favourite artists at the time – so much for Dirac the ascetic. By the time he was 80, he felt deeply disillusioned, because he knew that other people regarded him as a silly old fuddy-duddy – I’m caricaturing, but that is an accurate caricature – someone basically whose rejection of the modern field theory, the theory that he created – they thought this was absolutely absurd. And when he got back into his home in Florida from his last visit to Britain in 1982 – he was 80 years old – there was a letter from John Wheeler, Feynman’s supervisor, on his doormat and it’s a very touching and generous letter. I just want to read two lines from it – “I write to tell you what I’m not sure you divine – how many of the younger generation as well as the older one look up to you as a hero, as a model of how to do things right, of a passion for rectitude, underlined, as well as beauty. May your influence keep on growing.” Well, Dirac was right – people did see him as a bit of a fuddy-duddy, but they knew that he was a class act. And one of the people who knew that was the greatest mathematical physicist of our time, Edward Witten, who met him that summer – and this is a picture which Edward has very kindly allowed me to use here, of him talking to Dirac. Edward doesn’t remember much of that conversation, except to hear the great old man execrating quantum field theory – the theory that he had – this is Dirac – co-invented, and I believe he advised Witten – “Do something different. Just move on from this awful, awful theory.” Two years after this picture, Dirac died – spared the prospect of losing his mind, something that terrified him – and his very last lecture, written effectively or dictated on his deathbed, was about the abomination of quantum field theory. You can go and visit his grave now in Roselawn, Tallahassee, buried with his wife, a dog – not her actual dog, but the stone dog up there at the top. We just ought to reflect that Dirac is one of the truly great thinkers this country has produced, and like all people of great and truly great achievement, he is posthumously productive. Still, not just his basic equations of quantum mechanics, but his thinking about the way you do theoretical physics; his thinking about the magnetic monopole, something I haven’t mentioned, which people are still, theoretical physicists are still looking for, a fundamental in their theories; in the technical work he did on quantum field theory, desperately trying to find what was wrong with it, still being used today – you go and Google ‘Dirac’ in the modern papers and you still see his name coming up every single week. I would say – I know I’m biased, but I would say that Dirac should be [INAUDIBLE] better than any of those people in quantum mechanics, although he was so modest he never claimed to have invented the subject himself. What he left more than anything is this legacy of appreciating beauty and not relying on ‘here today, gone tomorrow’ experimental data, but having faith in theories that might superficially look wrong, but had greater potential in the longer term, which is, as you’d know, the fundamental philosophy that gives string theory such encouragement, that although there’s not experimental support for it directly, it has so much mathematical beauty and richness that they’re minded to keep on the faith to persevere with it. They say that Dirac never changed from when he was a little boy to when he was an old man – you look at his signature – it seemingly never changed. But in aesthetic terms, I think that’s completely wrong. He began his life anti-religious and anti-philosophical, and he ended his life, with his thinking on beauty, as a religious philosopher. Thank you very much.

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  1. I believe the lecture mentioned at 35:18 is "The Relation between Mathematics and Physics".  I understand it was given in Edinburgh, February 6, 1939 in relation to the JAMES SCOTT prize. I hope this text helps with finding a copy.The video description, or linked website could benefit from a list of references and maybe even trustworthy sources for the lectures and papers mentioned in this talk.

  2. (Isotope, Element) ($charge, $ dipole ) (x,y,z)size (x,y,z)distance (t_half life & Fr_cycle)
    (2*#,#) ($:#,$:#)(x,y,z)_size (x,y,z)_distance T+half_life Fr=Cyclic

  3. 35:43 "Mathematics is a game where mathematicians invent the rules. Physics is a game where the rules are given to us by nature. What is interesting is that the rules of nature appear to be in the same mathematical rules as the mathematicians have concocted"

  4. Dirac is my favorite because his theory fits my theory! Like he doesn't like quantum mechanics because I can't fathom who would. Thankfully it isn't that way but I like it because it allows us to do anything we like (time travel; pan jumping; and, so much more)!

  5. Mathematics IS the true fabric of reality. Mathematicians can't invent any rules. Everything is already there or here.. what have you. Mathematicians just uncover.. not discover the rules of the game. The rules are embedded in everything in the known universe. What we see as chaotic is just a set of rules that we don't understand yet.
    Physics is just the manifestation or effect of mathematics interacting with matter in our "real world".
    There are no "laws of physics" that manifested after the Big Bang. Mathematics IS all there is but the abstraction can't be made with our minds at this level of consciousness.
    Read Leibniz and his monadology..
    The Fourier transform allows you to go the mind or frequency domain and come back without harm. Everything (atoms, molecules, human bodies, the universe) is a signal and as such can be described by Fourier analysis => All is mathematical.
    Calculus leads you through integration to upper dimensions from the point to the line to the plane and volume.
    The material world is only energy trapped in spacetime templates that gives you a solid appearance where you can interact with "the laws of physics".
    We are still far away to reach the point where reason and logic will take us anywhere/whenever without literally going there.
    The journey will be long but it's worthy.

    PS I will not respond to any comment, because controversy is not my strong point. Feel free to post whatever you want.. It's a "free world"… for now.
    All best

  6. The word 'religion', with its emphasis on belief in the absence of evidence, or even in spite of contrary evidence, has no place in any narrative that has to do with science

  7. How practical are Dirac's theories for technology anyway? "Magnetic monopoles, can we eat this"? Why do we make the mistake to call the over use of math "beautiful"? It simply isn't, math is only necessary to improve our efficiency in order to give us a change for survival. What I think is very ugly is to introduce all kind of unproven assumptions, expressed in "beautiful mathematical theories" that complicate physics theories beyond the comprehension of all. For instance, it is extremely easy to simplify Maxwell's electrodynamics by applying Occam's razor, such that the resulting theory is much easier to understand for any student, and such that we can throw overboard the "beautiful beautiful" mathematical "gauge theory" and "symmetry". Occam's philosophy is way more important than the "principle of beautiful math", and since Occam's razor has been buried by overactive mathematicians we all are staring in the abyss of mass extinction now. We are very unsuccessful at the moment as a species of scientific animals, thanks to "beautiful math".

  8. i would love to help you being myself…thank god there are people like you around…you can count on me if it is of your interest…btw, thanks..:)

  9. If physics has to be beautiful to be true, is it also the case that, for example, politics must be beautiful to be true – here we have the unfortunate source of Utopianism …

  10. Don't they even have the funds to attach a microphone to the speaker? The sound keeps going out and coming in – it's very irritating.

  11. I'm reading his book, The strangest man, its really good, love the stories on the development of quantum mechanics.

  12. This title attracts some real religious people? lmao. It's just an analogy. My religion is philosophy. Maybe because my parietal lobe isn't developed enough to embrace math as my belief and I often feel I lack the mathematical way of thinking in my study.

  13. Dirac once said he thinks Schrödinger is the person most similar to him. I don't understand bc Schrödinger is obsessed with philosophy and Indian religion and was arduously questioning the philosophical meaning behind the formulas. He even dismissed the particle model just because of his strong philosophical belief that the world is continuous, in spite of the controversy.
    I thought Dirac would be someone with a first-rate mathematical mind and created a lot of models to simulate the actual world that academia likes. But in fact, he is just indeed a philosopher. Now I fully understand why he says so. Both of them head in the cloud.

  14. Couldn't choose a sub so this'll work

  15. 35:40 "Mathematics is a game where mathematicians invent the rules. Physics is a game where the rules are given to us by nature. What is interesting, is that the rules of nature appear to be [written] in the same mathematical rules as the mathematicians have concocted." -Paul Dirac

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