The Universe Speaks in Numbers: Michael Atiyah interviewed by Graham Farmelo

[Music] Some Michael Atea was one of the finest mathematicians of the past century. He died last January, only a few weeks after he gave me the interview you're about to hear, recorded on the 1st of November. Then in his late 80s he was still working hard, looking to the future, barely able to contain his enthusiasm for his subject. My name is Graham Farmalo and I'm the author of the universe speaks in numbers about how the mysterious harmony between physics and mathematics enriches our understanding of the universe. Technically brilliant and amazingly imaginative, Michael Atea was also a generous spirit, as I've seen at first hand over the past three years. He's one of the leading figures in my story and he spent hours talking with me in his modest apartment in Edinburgh, with a splendid view over the surrounding hills. One of his favorite themes was that we should value mathematicians of every stripe, those who prize rigor above everything else, those who are more concerned with ideas, those who are practically minded, those who like their subject presented as abstractly as possible. There are great many types of mathematician he told me and we need all of them. Atea never much enjoyed manipulating X's and Y's. He was not algebraically minded. No, he was above all a geometry, fascinated by shape, size, properties of space and so on, and he loved to exercise his visual imagination. Relatively late in his career in the 1970s, he began his journey to becoming what he described as a quasi physicist, fascinated by the geometry of gauge fields which will be coming central to the work of particle physicists. He began to collaborate with dozens of others to elucidate the mathematics underlying the physicist theory. He had a favorite metaphor. Before the 1970s, the physicists working on gauge theories were digging one tunnel while mathematicians were working on a related subject in a completely different tunnel. The two groups were pretty much oblivious to each other. Michael was present when the tunnels intersected and he marveled that that intersection appeared to have been perfectly engineered. I remember greeting him at his front door when I arrived on that November morning. Beaming and leaning heavily on his walking stick, he said he was glad we weren't scheduled to talk the day before because he'd had a nasty turn, possibly a mini-stroke. He stopped to order him to rest so Michael spent the rest of the day listing to Bach. The first time in 20 years that Michael has spent an entire day without doing any mathematics at all. I began by asking him about his youth. It seems that he shone from the word go. So, Michael, you felt you were a mathematician or your parents saw you were a mathematician right from when you were a boy. Is that right? Yes, he saw you exchanging my pocket money, making money. He was a mathematician and I was always best mathematics. I only once ever failed to come first. Mathematics, I was very corrupt. I was obviously going to be mathematician, but I've been to other things. Small boys, I was being Indian drivers. I was into being chemist, pouring dangerous liquids into other things, but I was experiencing the place. So I played around with chemistry. But then I was ready to do the math. It was clear I was going to be mathematician. And you went to Trinity College too? I went to Trinity College, came to me, which is a home wall, great mathematician school. Yes. And did you feel you were really good there? Or did you feel that you were up with people at that time comparable to you? Well, you don't quite know. I went to a very good school, not not by accident, but became to this country. My father said, "What's the best school for mathematics in the country?" He said, "Magester at Gammeschool." I went to Mathematics in Gammeschool and I had my business and teachers, and worked in the hard, and we all got scholarship to Trinity. So I knew I was pretty good. Right. But I didn't know how good. Yeah, indeed. So when we went to Trinity, there were a lot of other guys who came from fancy schools and threw their weight around and I said, "These guys are smart." But then the I was top. So after the first year I knew I was top. And then after that, I was sitting, "I'm sorry." That was the sound of the Tias Dorbel, the double glazing people had come to measure up his windows. A few minutes later we resumed. As a student at Cambridge, he was, of course, outstanding. Chief among his mathematical heroes was Hermann Vile, who also made visionary contributions to physics, setting up the type of theory known as gauge theory, now used to describe all the subatomic forces. The first, let's go back to Cambridge. Some of the people with a prodigy didn't go very fast. I was not a prodigy. I think he just called it Egypt at 16. And I got a university there, and none of it did. But if I didn't, I came to my international school. And after that, I could have avoided national service, but I didn't. But the national service. Yeah, how long did it take two years? You did it. You know, I still hear the Marshall tone in your voice on that. Let me tell you this. In the army, I rode to the Great Heights of Acting Lands Corporal. I had to drill a squad round the square. I was really out. I was like, "Rail is definitely rude." And then the regimental sergeant made a voice with horse. And to me, "Hermann, I wish I had a voice like yours!" I had a military career. You could? Well, that would have been quite a lot of mathematics, I have to say. But on the hand, the voice, the character across the barracks square, helped me in the lecture. I'd like to heard your voice before that military service, because I do think it added something to your anyway. There's just a review. There's too much, obviously, too much going to detail. But you were quickly on the international stage. You even went to a boobarky conference I heard. And you also saw your hero, Hermann Vile, at one point, never actually met him. Yes, I heard him give a talk to the Amsterdam International Congress. He really gave up fields, battles, two people away, and he was well. And he was marvellous speech. Oh, but my old was a man of militial words. And even though he said he's spoken in a language not sung by the gods of his cradle, I would say that. He knows one of the characters, he's an English person. Oh, right. I can sense he's a real, someone you really admire. Absolutely, absolutely. What is it incidentally? Could you saw my walk particularly? Did you admire him at that stage in your life? I admire him at several stages. Oh, right. I remember my supervisor was Hodg. Who knew these people? There were not many around. And he said, Hermann Vile was called "Holy Good Hermann." He thought he was a bit pompous. Oh, really? Okay. All right. It may have been just an old start. You know, remember he's from a different different generation. He was called "Holy Good Hermann." I heard that from my supervisor, but he was marvellous speaking. He could be holy, holy speeches, like the conceities of some of them. He was independent. And then later on, I heard nobody done everything everywhere I went. Who was there first? Hermann. 50 years after he died. I was asked by the National Academy to write a bit of it. Nobody got around to do any. Oh, that was terribly up. I did it. I thought, great. I can tell you. Instead of saying, "We're in time to die." What would you think that will be in the next few years? I'd say, "What would you make of the last few years?" So I'd write and then I wrote that very nicely. And then recently, I just got more thing that he did. So I could write another version now saying, "I didn't talk about something he did. I didn't talk about his work in Norton Logic. I didn't know he was working in Erusvedic. Now I know about those. So I could write a third installment of appreciation. So I understand all that. My life has come to the end. Just by called up with Erusvedic. So he's my trailblazer all the way through. Well, what is amazing about a physicist's point of view, I may say, is of course that he was an authentically great mathematician who made seriously good contributions to physics. Absolutely. He made a real pioneer. You know the day is, think about it. It wasn't the one usual. Carp Maxwell was an undoubtedly great physicist. But he was also a mathematician. William Rowan Hamilton was a great physicist and a really mathematician. I didn't know him. So it's only in recent times that people thought he called me a great mathematician, an anagrate physicist. It's a mistake. Yes. And if you try to preserve that boundary, you see yourself. But Vile was, we're sorry, making contributions relatively early in his career. He was. To physics. But in your case, if I may say, I think it's fair to say that you mean you had already established yourself in the world of mathematics very firmly in the early 1970s when physics caught your eyes. Is that correct? Yes. It's partly because by this stage, mathematician physics are both particles. So it took you longer to get the front line. And so I wasn't allowed to, my middle 30s, that I began to see the end of mathematics going. And that's how I was interested in physics too. You've described to me a many times about how you were met in your keeps office. Yes. And that's where you first set eyes on it would whip. Exactly. And you'd You felt like what a memorable meeting I remember. - Yeah. - He stood out as a young man and one of the most better than him. - Yes. - And I was very surprised, but I had met him before. And more I thought about it. And what obviously it was. So I invited him over to Oxford. - Yes. - And he gave over and gave him more of a thing. And so he obviously, great star. But I just, I found him, he'd landing on my plate. I just flew over to meet him and suddenly, it was, so that was already quite a dramatic shift. - Yes. - The moment it was ripe, the mathematics and physics already collapsed. We didn't even realize it. - Yes. - Nobody realized it. - Yeah, yeah, yeah. - Well, there were glimmerings, gang, churn, you know, but, but, but, it was only being beginning to be felt. - Yes. - It wasn't the revolution yet. It was simply a, simply a sort of a trauma. - No, that's right. Well, of course, for physicists in the '70s, this was a time that their standard model of the basic forces of nature was shaping up. So if I may say you're the area that you, an Edward Whitman look at, which was relatively a backwater for physics, but this was an area that, you know, in the hands of you and your colleagues, it got bigger and bigger, basically. - As per this, we were coming here to top in, anomalies were as well, rather, refined pieces of the theory. - Yeah, yeah. - But, on the other hand, Arthur risked it on more foundations. When you're in down those foundations, you make the same foundations, you make the physics. - A tear later told me he regarded himself as both Edward Whitman's student and his teacher. It proved to be an immensely influential partnership. I asked a tear about the cultural shifty experience when he moved from the world of mathematics to the world of physics. He began a long riff on some of his favorite subjects. He attacked the Institute of Nobel Prizes, dismissed critics of the mathematicians new and close relationship with physicists and reflected on the Babaki group, which exerted huge influence on mathematics from the late 1930s. This group put an extremely high premium on rigor and a correspondingly low premium on applying mathematics to the real world. But the agenda was too dogmatic for a tear and he doesn't mind saying so. - Tell me about how it felt to move from a mathematics culture to a culture when you were much more closely with physicists because that must have been a change for you after all those years when you're doing just pure mathematics. - Well, in one such as a discontinuous change, it seems. I'd always been interested in these things and I gradually became more and more interested and it was learning process. When you learn, you don't sort of suddenly learn all at once, you learn by seeds. You gradually pick things up. The best way you learn is by being a princess to the master. So I would go around with people like that. - But he was learning from you too, I'm sure. - Yes, of course, it's a mutual range but we were learning from each other and I would learn in my physics from talking about my right physicists. And I realize that my media number of them, all physicists, especially who's got no surprises, tend to be little bits primordonance. - Do you think that's true of the mathematicians as well or is that just physicists, you think? - I think they're more primordonance in theory. They get no prize. - Oh, okay. - Okay, then after you prize them, basically, the real prize was a disaster. It's generally speaking, you mean? - Generally speaking. - Right. - It was, Freeman Dyson didn't get no prize, that's, he saved that, sorry, so you can write. But all the others have no surprises and it's immediately, it gets, it gets checked fast amounts of attention, publicity, press, money. And I was at, it's very hard for them to get do these serious work. What they do is they say, well, I've solved the problem of, University, I've solved the problem of University, now they go on and have a grand, sometimes this is the same too. It's not good to, it depends on the individual personality. Some say, I've done this, if we don't call code, it's not the case, he, I mean, done that. He's well, I've solved that. I've an analyst, I solve the problem in London. Now I can be solved on an important physics. So you change it to physics. And he's been 20 years, I don't think he's anywhere. So, you, you, you try, I feel completely. Yes. But what the physicist was so extraordinary at that time in the 70s was how the physicists and mathematicians were working so closely together. Yes. Right, after so long apart. Right. Well, there were different, there were different theories. Some people said, is, are the mathematicians just coming get for one night stand? Yeah. Well, there's going to be a long manage. Yes. Well, I'm the whole Muslim thought just passing that right. Yes, yeah. No, no, that would turn to be wrong. Right. They were coming together again, as they'd been in the past. But one of the things that I would have thought was been different was that mathematics, often people say, moves it more stately, a slower, more reflective pace, to speak. And the physicists tend to be very, very quick at coming up with things and quite happily discarding them in five minutes. You know, there's different speeds of which the cultures worked. Did you find that at all? Oh, well, yes. But more subtle way. Yeah. The physicists love fast-calculation formulas. They lost its creakest mental results. They were in the heart. Patients take their time. But nevertheless, they-- something they travel fast, and they say, "Fastily." If they've been working and waiting probably for 100 years, gradually, gradually, gradually, something they can be a revolution and something they can help us work. They can be a David Hilbert, yeah. He has put an end, a whole century of work on invariant theory by saying there are only financial ideals of hydrogen and bang. So there is a tremendous-- like when Einstein came along in the general theory. So mathematics that are big steps forward, like that, made by people of reading some stature. And who he believed, but eventually he worked. There are fast movements and there are slow movements. Slow movements are simply plotting along. The fast movements are strict genius, inspiration. And I mean, they know what all-- they probably happen in every field. I'll just mathematics the physics. They don't have any music. They have poetry, painting. Every way you go architecture, there's continual accumulation of the past, classic stuff. And then suddenly it comes along with the designs that totally new building. Or new music. But you don't have to spend all the time. So I think that's the nature of human mind. That does these things. I'm having a video as an upon that. Tommy, for many people, I'm sure including yourself, you regard this coming together of the mathematical of physics communities is a good thing. But some people thought it was a bad thing for mathematics. As you know, Jack Inquin said that it was the poisoning the worlds of pure mathematics or to paraphrase them. But what did you-- what was your view about that? I thought it was clear wrong, of course. Because they had two views. One was that mathematics could only be done if it was to be rigorous. You couldn't have really ideas mathematics. That was to give it into the closed-handers of the physics. And so what we were doing, what people were doing at that time, we explored human mind. We didn't know how to prove things. We know what the theory was going to prove. But we were grouping our way. And I felt that this was a world worth right exercise. Debbie, no, no. He doesn't do that. Your time's in mathematics. Never touch something with his bad form. He's not rigorous. Well, that's hopeless. Go back and read it. But I was a rigorous. I'm just going to run my desk and I said, it's always not rigorous. Yes. Well, hold on a minute. Just a challenge for a second on that. I mean, with your famous index theorem, you proved it in multiple ways. I mean, you were very keen to have established that as a rigorous thing. So it has a big part of your career. Yes, of course. I would have brought up that way. I went to book back here. So of course, I would well train in pretty mathematics. There would be no solutions. There would be-- well, not in pretty mathematics. In Canada, there would be great peer-to-peer Italian mathematics. But you think, woolly. And then long people like Andre Faye said, no, no, this is all rubbish. Read these foundations. Throw it all out. This is going to be done. This is the boot-parky-- Exactly. --the issue. Yeah. Well, it has its merits, clear the way the old stuff, or the pressure is the way the cobwebs. And it's hard with clean sweep. But you lose a lot of the places. They've got a lot of these eye through where there's a cobwebs. Actually, the cobwebs had a lot of in them. You go and bring them all out again. But inside the cobwebs, there are actually some jewels. Yeah. Yeah. And so this sweeping away the past and discovering that you make too much sweep away, what happens is all revolutions, too. You cut off your heads, and then you say, why do we cut off lowers here? Well, one thing I'd just like to ask you about is you took on quite soon after you moved into the physics area. You took on students working in this relatively new territory. One of them is Simon Donson. Yes, of course. What do you remember of him? Because that was a famous incident in this subject area. Yes, but it was quite soon when I was in the United States. I got to know a lot of brilliant students. The neemers' period was Simon Donson. And he was one of the best students in game, but he was a very quiet person. He had a sound, I really didn't know. His assistant and took a little while to realize how originally he was. But he was extremely original. And he took a few hints that Rand must, suddenly, and developed them into a magnificent flower. Looking for young mill theories in particular, which have their basis in physics. Exactly, you all came up very fast. He did this all his first and second year as a student. He was a genius with care and with not slow, but thunders. He did all within year or two, but it wasn't rushed. Yes. A week here and a week there. Yeah, I see. Or anywhere you are, the theory was completed. I was really, really. I was really trying to imagine watching it. I was privileged to watch it. Really? Yeah. Not only I was privileged to help along with the roots. So if you're a teacher and you have a great student, what's your duty? Yes. His energy helped him. So I helped him by getting the talk of the International Congress and also, many of the self-students. I got him. When I was a first out, he was very young. I used my influence as I had because I have no administration using my influence. In a good cause. And no better cause than to progress, but it's good. So he was shedding light very generally speaking on four dimensional spaces. Absolutely. And using the-- That was my way, the biggest discovery mathematics in the 20th century. Really? Yes. That light? Yes, really. Well, let's say the last half of this. All right. Last. Okay. Still it's momentous. I think it's the biggest thing. My father, the biggest thing that was, you know, when people look back from the past future, they will say, "Well, I think the final is one name that will sound out of that club, Maxwell." Yes. And the other name will sound out with his sound mother. My goodness, right? Praise it. Praise it. I mean, I mean, I would be glad if it was Einstein too. Yeah, yeah. Okay. And then, of course, as I understand it, you actually brought up the reggae wood Whitney into this area. Yes. I made, well, I made even my tea. We finished very well together. I realized that once, that he was a brilliant man and I'd write him over, he'd make music lectures. And before I knew where it was, I was running the heap up. So it's nothing more satisfying than having brilliant students who lead the head. And I've been very fortunate to have a large number of brilliant students in very many different fields. And they all created large spots for themselves. And some of my students have driven into the field. But they've been written and got a field medal. They have yet another prize. That's indication. You will get one. But what's your view, if it's just one last last question, that many people see what you and your colleagues have done as a great achievement. And it's how it's enhanced physics for some people think that this has taken physics in two mathematical directions. What do you say to them? What is physics meant? What is mathematics? I think, no, simple answers. But basically, a scientist, let's be a scientist, looks at the world through his eyes. He tries to understand it. His eyes gets his brain. He has to make a mental picture in his brain. What is he outside? That is mathematics. What is the outside world? We don't know what the outside world is. And the inside world is as far as possible made precise rigorous as best you can, making mathematics. And now, if you read James Clark Maxwell's books, he said that exactly. He must have distinguished carefully between mathematics and reality. We don't know what reality is. He was a very deep thinker. He died young. Well, first of all, thank you for getting Maxwell's statue put up in Edinburgh. I know you were a prime mover behind that. I was the prime mover. I was the evener. I entirely, in my every now and then, I was there. One of the greatest achievements of my life. Oh, to put that back up there. Absolutely. I mean, I'm very. It's almost a please that's succeeded. And now, obviously, the people think, God, you know, we've been there. Yes, he does. That statue looks like it's 150 years old. It's not like actually it does. Well, he's died of that purpose. But it's just today, they're just putting out plaque there. On the side, you know, for the general public. Who was Clark Maxwell? Yes, yes. No, Clark Maxwell is. Go there and press the buttons. It's just to be installed today. Well, as you say, that was a really worthwhile achievement making. He's a fountain center in Edinburgh. Okay, Michael, thank you very much indeed. Have a good day. Delighted. It was good to hear that Michael never regretted his move too, or rather towards physics. At the end of the interview, he began to talk, as he often did, about the Scottish natural philosopher James Clark Maxwell. Perhaps most famous for his pioneering theory of electricity and magnetism. Maxwell also thought deeply about the relationship between mathematics and physics. Our remember drawing Michael's attention to that lecture a couple of years before. And it was wonderful to see him beaming with pleasure as he read Maxwell's words on this subject for the first time. Before I left his apartment, Michael insisted on showing me the black and white photograph he'd recently acquired of James Clark Maxwell. It was Michael told me once the property of the son of the physicist JJ Thompson, over at the electron. I asked Michael if I could take a snap of him holding that photo, and of course he enthusiastically obliged. As I left, I couldn't help feeling a little sad. Michael handed me a copy of the booklet he'd prepared for the memorial service for his wife, Lily, who passed away a few months before. He was, he told me, soon to attend the memorial service in Oxford for his recently deceased brother Patrick, a distinguished legal scholar. The sad times he said, adding that he was determined to make most of the time he had left. I sensed that he knew his days were numbered. But as we heard in the interview, he had loved his life as a mathematician and been proud to help bring his subject closer to physics. He was one of the great unifiers of our time. And he's much missed. A quick post-cript. During the summer of 2018, Michael read and checked the chapter about him in my book, The Universe Beaks in Numbers. While I was writing that chapter, it often occurred to me that his biography was just crying out to be written. I hope that some ambitious bographer will take up that challenge and give us a fitting memorial to a truly great life.