Michael Atiyah was a distinguished mathematician with a stellar scientific career spanning over 60 years. He passed away on January 11 aged 89. He received the Fields Medal in 1966 and the Abel Prize in 2004, and is best known for his work with Isadore M. Singer on the Atiyah-Singer index theorem.
In October 2016, Atiyah spoke to C.S. Aravinda, the chief editor of Bhāvanā, a journal of mathematics, at the former’s home in Edinburgh.
The interview is presented in full, and has been lightly edited for clarity. Aravinda’s words are in bold and Atiyah’s are plain.
I am delighted to meet you. Which part of India are you from?
I am from Bangalore, which is in the southern part of India.
I have visited Bangalore several times. In fact, I have even planted a tree in Bangalore. There was a chap there at the Raman Research Institute who was a friend of mine, called S. [Sivaramakrishna] Chandrasekhar – not the astronomer. He worked on liquid crystals. He said he was also a nephew of C.V. Raman. They are all related.
Many years ago I was reading a paper of C.V. Raman. I think I was most impressed by a statement saying something like, “It is from my collection of diamonds, I have discovered the following facts.” [Laughs] Do you know other scientists who say “I have diamonds”? He was a rich man and had a big diamond collection.
You also have other Indian connections. I noticed that, in 1966, the year you were awarded the Fields Medal, the Indian mathematician Harish-Chandra gave a plenary talk at that conference.
Yes, he gave a plenary talk there. When I was a graduate student in Cambridge, I went to Amsterdam in 1954 and he gave a plenary address there too. I remember a very clear impression that I had, which was that he spoke English much faster than any Englishman. In English, you have ups and downs. But he was like a machine gun, he spoke much faster. He spoke beautiful English. Of course I couldn’t understand anything. It was not the English I could not understand. I was a graduate student and he was professor or something and he was talking about advanced work. I was just finishing my PhD.
You were finishing your PhD at that time?
I finished my Ph.D. in 1955. But I was just beginning my career, and he was several years older than me. He was smartly dressed. Yes, I remember very clearly that first meeting. Of course, later on we met as colleagues. I visited Princeton, but then he was in Columbia at the time.
I think you visited Princeton in 1955-1956. But he visited Princeton again in 1956-1957, a year after you left.
Actually, I was still there for the fall term in 1956. Of course he became professor later on. I went to Princeton for seminars. I was certainly there in… oh dear… [laughs]
I think you went there sometime in 1969. Because Nigel Hitchin mentions in some place that soon after he finished his PhD, he went with you to Princeton.
He came as my assistant. That was a good time. Anyway, later on there was another Indian who came to work with me – Patodi.
Vijay Kumar Patodi, yes. I was going to ask you about him too.
Very brilliant man. And a very sad case. He died almost at the same age as Ramanujan.
Around the same age, in his early 30s, yes. He died of renal failure.
His case was more complicated. Anyway, at that time my interests were not very close to Harish-Chandra’s. My interests became closer much later, possibly after he died. When did he die?
He died in 1983, at the stroke of his 60th birthday.
I know that. He was going to have an operation but he couldn’t have it. So we didn’t really interact much. But I got interested in that kind of mathematics probably after he died, 30 years ago.
I have read somewhere that he was going to give a talk somewhere in England, I don’t remember where. And then he had a heart attack and cancelled his visit.
Yes, in 1982. At that time, I was back in Oxford. There, I had a succession of Indian visitors who came to work with me, mainly from Bombay who were students of M.S. Narasimhan. A whole succession of them. I got to know S. Ramanan very well, a very nice man. T.R. Ramadas came a little later. They all came to work with me in Oxford in that period. Yeah, it was quite a strong Indian connection. Long time ago.
So you first heard Harish-Chandra at that Amsterdam conference in 1954. When you were at the Institute for Advanced Study (IAS) in Princeton later, was there any interaction?
I was at IAS as faculty from 1969 to 1972, and Harish-Chandra was already there. We were only about eight or nine colleagues and we had to meet to discuss things. I got to know him from close. We got to know each other’s families, as we all lived quite close together. For instance, their daughter Premi married Pierce, who was a fellow at Trinity College, Cambridge.
But we didn’t really overlap much mathematically. Our mathematical interests were a bit different. But I got to know him well. Both he and his wife were very tall and upright. They were imposing Indians you know, and I was short, but they were nice to us. They lived on Battle Road. I also knew Armand Borel very well, and he was very friendly with them. I think Harish-Chandra came from Allahabad and not from Bombay. Originally, he was a physicist.
Correct, he did his PhD with Paul Dirac.
You know this story about Harish-Chandra and Freeman Dyson?
I do, but please tell us about it.
I think it’s a more or less true story. Harish-Chandra and Dyson were both graduate students in Cambridge after the war. Harish-Chandra was doing physics with Dirac and Dyson was doing number theory. While they were walking down the streets, the story is that Harish-Chandra tells Dyson, “Physics is in a mess and I am going into mathematics”. Dyson said to him, “Physics is in a mess, and that’s why I am going to go into physics.” And they switched over.
Of course, Dyson still kept an interest in mathematics. Harish-Chandra used his knowledge of physics to direct his mathematics. He worked on infinite-dimensional representations because of the work of the Russian school led by Israel Gelfand. Harish-Chandra wanted to do it more rigorously.
So Harish-Chandra and Dyson had this very odd connection. I got to know both of them. I knew Dyson very well too; he is still very much around and must be about 90 now.
Both Harish-Chandra and Dyson were born in the same year, 1923, and so Dyson must be about 93 now.
Exactly. More recently, at the Royal Society in London, as a tradition, if you have been a fellow for 50 years, they give you a nice little dinner for which you could invite your friends. To succeed in this, you have to be a mathematician or physicist, you have to be elected very young and you have to get very old. So not many people have qualified [laughs].
When I was President of the Royal Society, one person did qualify, and that was Rudolf Peierls. He was involved with the atomic bomb. I had to preside at his dinner, and we had Hans Bethe as his guest. After I left the Royal Society, when I was getting to my fifty years [as a fellow], I wrote to the Royal Society, more or less saying “I hope you haven’t forgotten that there is a tradition.” And they wrote to me saying “Oh, we’ve forgotten all about it. For the last ten years, we haven’t had any. Oh dear, what are we going to do?” [laughs]. So they said, “Ah, we’ll invite everybody who were elected in that ten year period.” Only two people came – Dyson and me. I was elected for fifty years, and he was elected for sixty years. None of the guys in between were able to come, so it was rather funny. I have slight disagreements with Freeman Dyson, but he is a strong minded person with strong views.
Harish-Chandra and Dyson were both six years older than me. So when I went as a graduate student to Amsterdam, I was 25 and Harish-Chandra was 31. In terms of age, the difference was only six years, but in mathematical terms it is the difference between a post-graduate and a senior professor.
You came back to the UK from IAS in 1972. Why did you come back?
Well, when you make a decision, first of all, you don’t know why you’re making it! [Laughs]
There can be many different causes. Even if you can easily list the causes rationally, the decision is usually an emotional one. And you don’t admit it. I can talk for hours but there are a few factors. One is we had been in America for years and my wife was not very happy. She had a better job in the UK than she had there. Also, we used to spend half the time there and half the time back here, which was not very good for her because she could not get a job properly. Plus my children were growing up – the eldest one was 16 and if we had stayed for a few more years, he would have gone to college in America and then we would never be able to leave. So it was now or never.
And thirdly, I was at the institute when it was an unhappy time between the director – at that time it was Carl Kaysen – and the faculty, particularly the mathematicians, including André Weil. I was caught in between and I felt very unhappy. It was a difficult decision, as I liked the institute and it suited me very well mathematically. But I felt that I was being selfish in putting myself first. My family comes first. A job turned out for me here and I came back. It worked out very well and I got lots of brilliant students. It was really a toss of a coin, and my heart made the decision. It was not rational. Sometimes your heart makes a better decision. [Laughs]
Yes, I think so too. As you said, when your heart makes the decision, there is no reason why.
Precisely. It is very complicated. It’s an emotional response which has many factors.
I have been to the IAS as a visitor, a young man, an older man and I’ve known all the people and all the directors very well. It is a funny place. It can be marvellous and vibrant for the right person at the right time. Its most useful function is that it is a place where young people go for postdoctoral work. The school of mathematics was a big one, and a large number of post-graduate people came there either for postdoctoral work or on their first sabbaticals. They were all very young and active and some of them, having been in the army, were delayed by five years.
[This stage in one’s research career] is a very formative period. Everybody is full of ideas. They go to seminars at the university, at the Institute, and the faculty on the whole have very little contact, with a few exceptions.
The Princeton University is also close by…
Of course; the university is fine but the institute was meant to be separate, you see. And some people were very separate – they didn’t come in at all, they didn’t mix with students. Sometimes, each person would select assistants who were more or less right-hand men. Otherwise, all of them were selected by competition and some faculty would attract more students and used to work with them – and some did not. But it depended mainly on personalities, and in some cases the areas of interests.
As a young visitor, I hardly knew the professors. Although, through one or two lectures, I got to know some of them, like Dean Montgomery, quite well.
Was Atle Selberg also there at that time?
Yes, he was there but he didn’t interact very much. I wasn’t doing number theory very much. We didn’t interact with all the famous people at all. On the other hand, they were the people – the flagships – that brought the money in that would enable the young people to come. So they were kind of the umbrella. But the interaction between the postdocs and the faculty was very small. Some people interacted quite a lot. For instance, Borel interacted quite a lot because of his wide interests.
He used come to India quite often because he loved Indian music.
When I first went to IAS, he wasn’t there. He came later.
All the faculty at IAS were very clever people obviously, but sometimes there were odd and unusual personalities who didn’t get on with the other faculty or the students, or had some kind of problems. There was Selberg and Arne Beurling and they worked on their own to a great extent. They were Scandinavians – they didn’t have much contact with others. There was Marston Morse. He was retired but he was still active when I was there. He had a few acolytes, I would say. And Hermann Weyl was there before I arrived. He was a marvellous guy. He was a really great man, especially with young people.
The physicists were even younger and more active. All the mathematicians were slightly odd – not meaning they were bad but they were unusual. Some of them had one or two people, assistants, in little groups who were in their area. It was a very odd situation. Everyone wanted to go to IAS because there were famous people.
Another person who was there was Kurt Gödel. I had heard the name a little bit. He was a very odd person, extremely odd. He eventually died of malnutrition.
Gödel was the greatest logician of the 20th century. For a long time at the institute he wasn’t even a full professor. He was only a sort of a half professor. And then he had paranoid ideas. He thought that people were out to poison him. After his wife died, he starved to death. He just didn’t feed himself; he was really an extreme case. I knew him before that. So if somebody had serious psychological problems, the institute was not a good place to be. There was too much pressure.
John von Neumann was an enormous personality. Both Hermann Weyl and Einstein had died before I came. Their reputation still lives on. Princeton was the place which had all these names – Einstein, Weyl, von Neumann – who were great figures at the time. So you could chat with great mathematicians and physicists.
I looked through the institute records for a while when I was there. There was this talk by George Dyson, Freeman Dyson’s son. He had an odd history – he ran away from school, lived in a treehouse. Then he came back and became an author. He spent a year at the institute officially at the invitation of the director, accessed all the archives, gave talks. He was supposed to be writing a book. The title of the book was ‘Turing’s Cathedral’. It is about the history of computing.
A fairly recent book, yes.
It is really about von Neumann but he thought Alan Turing’s name would attract more people. So it’s called ‘Turing’s Cathedral’. Interesting book. I spoke to him when he was there, and he told me stories such as, for example, that the institute tried very hard to get Paul Dirac. They tried very hard to get Turing to stay; he had been working with von Neumann. But he didn’t want to stay. So there were a lot of successes and failures.
There were some people, like Carl Ludwig Siegel, who went back to Germany after the war (1951). So they attracted people but sometimes they lost them. But they tried very hard to get all the top people. They paid big salaries but still some people had good reasons not to go, all sorts of personal reasons.
As you said, sometimes it is a decision of the heart. Secondly, certain places suit certain personalities, I guess.
Of course. If you wanted peace and quiet at the institute, and you wanted to get on with your work with one or two people to talk to, had a good and stable enough family life, you liked the country, then it was a marvellous place. So many of these things were good. But I had my family worries about other problems, and eventually I left. The one thing that I missed when I was there: I didn’t have graduate students. I had one or two graduate students who were unofficial, a few of them who were my assistants, and did their PhDs at the university. When I came back to Oxford, I got a flood of good graduate students. All very brilliant. I was very fortunate.
Yes, you have a large number of them.
Yes! Simon Donaldson was my student. Graeme Segal was my student. And Patodi being a sort of a student. I liked having young people with me. It worked out very well. I came back just at the time when I was well known enough that people would come to work with me.
Since you mentioned Patodi: Perhaps you came to know about Patodi through his paper? Or was it when he was in Princeton visiting IAS?
I think I got to know him as a student of Narasimhan. What Patodi did was that he gave some very clever proofs of some difficult theorems in differential geometry. He developed his own formalism, which I couldn’t understand. Raoul Bott couldn’t understand it. We knew the results were interesting. So then, through Narasimhan, we invited him to come, and he spent two years at the institute in Princeton. Bott, he and I worked very closely together and we understood what he was doing.
Interestingly enough, subsequently, when the work we were doing got to physicists, the physicists rediscovered what Patodi had been doing in the language of supersymmetries. But we were there first. They gave, subsequently, a physicists’ proofs of what Singer and I were doing, but Patodi did it first. I don’t think they really gave him proper credit. He did it, he found it all by his hand. He was a bit like Ramanujan.
Yes, you mention that in your preface to the collected works of Patodi.1
He had a kind of intuitive feel for formulas and he couldn’t explain how he got them. And he was very clever. We struggled very hard to understand them. And through that we learnt from him and we published papers. He had very good insight.
But you see, like Ramanujan, he had extremely rigid habits of eating. He was a Jain. He had to go wash his hands before doing anything. He had to cook his own food. When Ramanujan came to England, he was somewhat similar. He was very fussy about the food. He was cooking on his own and he actually had malnutrition. He couldn’t get the vegetables that he needed.
Of course, that didn’t help him any.
In Patodi’s case, it may have been even more rigid, because observant Jains eat before dark.
Exactly. Very rigid. He also had a lot of serious illnesses, which he didn’t take seriously enough. He discovered he had kidney failure and also tuberculosis.
I see. I didn’t know he had tuberculosis.
I think so. But he certainly had more than kidney failure. When I got back to Oxford, we heard from people in India that he had kidney failure, which is a serious illness, and he needed a kidney transplant, which costs a lot of money. I contacted a friend of mine who was a surgeon and an expert at [treating] kidneys and asked him if he would consider helping. And I said, well, it costs a lot of money and I and my friends will try to get some money together to pay for it. He said he wanted to see his medical papers, so we arranged for it to be sent to him.
And when he got them, he told me that it was much more serious than I thought. He had kidney failure but also lots of other problems as well. This meant it would be a very delicate operation. I then found out that it wasn’t just kidney failure but that there was something more, so his case was very difficult. Still, we were discussing whether we should bring him to Oxford and have the operation done. But then we heard that there was an American expert who was visiting India who would consider doing the case. Then the expert went there but I think Patodi died while under anaesthetic before the operation.
He died tragically before the operation could be made because his system was so weak. He died at the age of 31. He wasn’t quite in the same league as Ramanujan but he was very good. So there are lot of similarities. Ramanujan went to Cambridge to work with Hardy. Patodi came to Princeton to work with Bott and me. We wrote a lot of papers together. I learnt a lot from him, his intuition. He learnt something from us. So here was a very parallel story. Ramanujan was probably ahead. But nevertheless, it was a lot of similarity.
I’m very happy to see that Patodi’s name is accorded and recognised now. Unlike with Hardy and Ramanujan, he was a very emotional part of my own life. I had got myself tied up because he was such a nice man. I think he was an easier person. Ramanujan I think, was a difficult person. Patodi was a very easy person, very nice person – a really modest person; and you don’t find really modest people in the world – and we didn’t have any problems. But his medical problems were more serious and he had this very strict food regime