Professor George Szekeres (1911-2005), mathematician

Professor George Szekeres. Interview sponsored by the University of New South Wales.

George Szekeres was born in Budapest, Hungary, in 1911. Although showing an early interest in and talent for mathematics, he studied chemical engineering at the Technological University of Budapest and then worked in a leather factory. In 1939 he fled Europe with his wife, Esther, and spent the war years in Shanghai.

Szekeres went to the University of Adelaide in 1948, where he was appointed initially as a lecturer, then senior lecturer and reader in mathematics. In 1963 he took up the first chair of pure mathematics at the University of New South Wales, where he stayed for the remainder of his career. He officially retired in 1975, but continued publishing original papers for several years. In 1976 he received an honorary doctorate from the University of NSW. Professor Szekeres passed away in 2005.

Szekeres mathematical work extended over relativity theory, combinatorial problems in geometry, group theory, number theory, abstract algebra and real and complex analysis. He is perhaps best known for his coordinate system for understanding black holes in cosmology.

Teachers' notes to accompany this transcript.
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Interviewed by Imogen Jubb in 2004.

Contents


Earliest memories

What are your earliest memories?

They are mostly family memories. I was brought up in Budapest. My father was really quite well-to-do. He was practically illiterate as far as I can gather, but he acquired a big leather factory in Budapest. We had a kind of river hut near the factory, where we spent the summer holidays.

When you were at school, did you know that you were cut out for mathematics?

In the last two school years it was obvious that I had a very good ability to solve mathematical problems. But there was a complication – a well-known old story. My father had no thought of mathematics; he just expected that his oldest son would continue with the leather factory and make it a flourishing enterprise. So I was brought up as a chemical engineer, a highly unmathematical profession at that time. I never went to a mathematics class. But as it worked out, I drifted to a new life which was not like my father imagined at all!

My mother was perfectly happy with whatever I was doing. She wanted to give me a chance to do mathematics. But of course I had to earn money, and chemistry was a much better paying proposition.

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Crucial influences

Did you have teachers who influenced your skills in chemistry or mathematics?

Not in chemistry, but I had an extraordinary physics teacher. He certainly had a positive influence. I really took to him very kindly. The physics he taught me came to be quite handy later, when my interests got mixed up occasionally with physics. The thing for which I am best known is my black hole coordinates system, which goes back to his teaching: what matters is the way you look at the problem.

He was a very good mathematician; he loved mathematics. So he was the one who suggested to me, when I was a high-school kid in my one-before-last year, that I should subscribe to a journal, which was the second great influence on me from my school years.

The journal has a complicated name: Középiskolai Matematikai és Fizikai Lapok, which means 'mathematical and physics high school journal'. This was published weekly from Budapest, of course – there was Budapest and then there was the rest of Hungary. Every week we got a stack of problems, usually quite out of the ordinary. They were excellent problems for our sort of high-school kids. Although I was not really sure, while I was at high school, what I wanted to do later at the uni, through the journal I discovered that I could do mathematical problems and I became certain that I would like to be a mathematician.

Did you ever meet any of the people who made the journal?

Well, I met lots of collaborators who solved these problems. We sent in the problems, and the names of the solvers were always published. The last issue of the year even had the photo of the best solver! I am there.

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A new level of mathematical culture

You said that you went on to study chemical engineering rather than mathematics. What happened to your mathematical inclinations?

Oh, we had regular, almost clublike, seminars at the university where we got together those who were mathematically interested – we all knew each other from the high school student journal. And one of them was a girl called Klein, Esther! She is still with me as my wife. She was a very bright student, and was a permanent member of this group. (This is one of my particularly nice recollections from my younger days.)

The size of the group varied; at the most, there would have been about 10, including a chemistry student, a complete outsider! Practically everybody has now become a significant mathematician. It was a totally private enterprise, known as the Anonymous group because we always met on two benches in the main park of Budapest, under the beautiful monument of a historical figure in Hungarian history whose name was not really known, hence 'Anonymous'. He had written books on the history of his own age, about the 15th century. When I went back to Budapest the statue was still there but the benches were gone. So it would be impossible today to have such a group again. Little things like this sometimes matter, I think. The fact that they put there two benches created a new level of mathematical culture in Budapest. (Mathematicians in Hungary are known as the Anonymous group ever since!)

We met perhaps once a week and tried to get through the problems in a well-known book. These were collections of problems from mathematical analysis, and we tried to solve the problems, one after the other. It was a marvellous experience, I must say.

I still think back to those times as the best cultural upbringing that I could get. It reflected the culture in which a very devoted mathematics teacher in Budapest had, at his own expense, published the mathematics journal for high school kids. I haven't found the like of that journal yet anywhere in the world, including France. That was a good program, beautiful, but not glamorous. (The journal is still going, after almost 100 years, but it is very different. In our time there were a dozen solvers of a problem; nowadays sometimes there are so many they just give you the number of kids who have solved the problem.)

Do you think such a culture can be re-created elsewhere?

I don't think so. It belongs to the culture of a city or a country. You get the bright students here as we had them in Hungary, no difference in that at all, but the culture is missing. Some of us did try to set up a high school journal in Australia, but you cannot copy these things, unfortunately. You have to transplant some of the whole culture. To me there is a message there, that culture belongs to all these activities at least as much as how clever a mathematician you are.

Just to tell you what is the great difference: when I was with the University of New South Wales we started a student journal, called Parabola. That became very well known all over Australia, and there were some mumblings that perhaps it would be good to have one high school journal for the whole country. Australia would have been an ideal country for this, and some of us did try to set up such a journal, but it never happened. Parabola was published quite differently to the Hungarian one.

Do you think those sorts of journals can be on line on the internet so that more people can solve problems there, rather than in a small group?

Oh, I don't think so. I have no connection at all with the internet and so I cannot really properly assess it, but there is no doubt that the personal touch, which belongs to that culture exactly, would go out. We knew each other before we even met, because we knew the names of the people. And there was a spirit, we wanted to solve the problem, we each wanted to show that we were better than the others.

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Meeting Esther

Tell me about meeting Esther in the Anonymous group.

Well, I knew Esther quite a long time before we actually met at the university. It was a matter-of-fact thing, as we slowly all met each other. It certainly wasn't love at first sight, and when we began to go out it was not the two of us together but a whole bunch of kids – very bright, and often the talk was around mathematics. And to me she was one of them.

Esther one day came out to the group with a geometry problem, which in some way is solved but even today is not perfectly solved. And my own reaction was that I had an added stimulus to solve it because of the way she asked the question! And I could solve the first aspect of the problem – after some struggle, I must say. Ah, it took me about two weeks to solve it.

I've heard that you call it the 'Happy Ending' problem, because it led to you and Esther getting married.

Oh, it was Paul Erdös who called it the 'Happy Ending'. You don't get married because of something like that. You know, we have been living now together for 70 years, a long time. We became friends in 1933, and in '37 we officially announced that we were together and got married. (Before that we were partners, as you might say nowadays.)

What sort of wedding did you have?

Just a simple civic one. But Esther's mother was very religious and for her sake I went to a wedding ceremony before a rabbi. I had to put on a hat but I had never had one, so an uncle of mine lent me a hat for this occasion. This so-called church wedding was 100 per cent for the sake of Esther's mother. We couldn't care less and I think we both treated it as a joke. Now the world has turned so that although some people still stick to weddings, nobody really regards them as very essential.

Anyway, to make a living I got work in a leather factory, not in Budapest but in a small town of about 5000 people. Those times, in the mid-'30s, were becoming more and more difficult. You see, we lived through the time when Hitler came to power, and we all looked out for opportunities elsewhere.

And were they difficult to find?

They were almost impossible to find. That I should get to Australia didn't even occur to me.

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Escape to Shanghai

You went to Shanghai, didn't you?

Yes. The time was determined because Hitler was already in Vienna and we knew it was urgent for us to decamp from Hungary. We decided to go to Shanghai, which was a so-called free port where no visas of any sort were required. The only things we were required to show from Budapest were a certificate of inoculation against cholera and typhoid and a smallpox vaccination certificate. And because of that there were about 20,000 refugees from Europe in Shanghai. It was quite a unique event in human history, this huge migration to a miserable place like Shanghai just to save our skins.

Did your whole family move to Shanghai?

No, only the two of us and my older brother. (I had two brothers, but now I have none.) My older brother had contracted tuberculosis, which was a fatal disease during those pre-penicillin times. But we found Shanghai was an absolutely impossible place for a TB sufferer. He died just a few weeks after Hiroshima, when it looked to us that now we had survived the war and he could enjoy the new world.

We fled to Shanghai in 1939, so we had got away. But we heard later of what happened to other people who didn't leave. My wife's mother was murdered, under circumstances that in a civilised society are really quite inconceivable. Poor thing, she didn't harm a fly in her life. But nobody could do anything.

Our escape was quite legal, mind you. We were able to get a perfectly good, valid Hungarian passport – yet only a few months later there was a war all over Europe. In '41 or '42, though, we had to send our passport to Tokyo to be extended, because about three months after we arrived in Shanghai it came under Japanese occupation.

What was your first impression when you arrived in Shanghai?

Misery! The Huanpu is the main river through Shanghai and Esther said, 'Oh, it's full of sediment. The water looks awful.' We approached the port from the sea, because Shanghai itself is quite a few kilometres up-river: 'Shanghai' means above the sea in Chinese. We looked out at the sea only once in our whole Shanghai time, Esther, my son and I.

We never experienced any hostility by the Chinese in Shanghai. Though they tried to help in all ways, we had no money at all, the two of us. So I worked as a chemical engineer. By that time I certainly knew that I was cut out for mathematics, but leather chemistry was a more useful profession.

How did you establish yourself in Shanghai and find a place to live?

That was not very difficult, I must say. All those thousands of refugees had to live somewhere, so this had to be organised, but there was no problem with it. And Esther thought, ah! now she would be pregnant with a child. In Budapest we couldn't think of this; the incredibly uncertain atmosphere there in the late '30s was not one where a child would want to have to be born. But we were optimists! In '39 I was 28 years old, a very optimistic age: 'Let's have a child,' and that was it, no matter whether we could afford to bring up a child! So at the first opportunity my son was born, in '40, a year after we got to Shanghai. And now Peter is in Adelaide.

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Migrating to Australia and to university mathematics

How did you come from Shanghai to Adelaide?

It happened because of two friends, both members, actually, of the little group who worked under the statue of 'Anonymous'. They moved to Australia almost at the same time that we left Hungary, in '39, but on a different ship. He has died by now but she, like Esther, lives in an old aged home. Our friendship has never slackened.

They first came to Sydney. Somehow they had got visas to Australia. In fact, that was a great farcical story which shows how absurdly Australia looked – and still does today – at the refugee problem. You had to put down, I think, £250 in money before you were let in to Australia. That was in Hungarian currency a very, very high amount, but our friends found out how to put down £250 and then they used the same money to help all the refugees whom they met to get in. They were really quite hilarious about circulating it. You see, once you had one amount of £250, nobody asked you for it again, so the same one could be produced again and again for people like us, who had no money at all.

I am absolutely convinced that the same thing happens today in Australia. It was an age-old game; it was very difficult, really, to get in. So when the latest refugee crisis came up I had a feeling of déjà vu, I must say!

Anyway, they were already in Adelaide after the war, and they got for me a lectureship at Adelaide Uni. Once I had a lectureship at a respectable university in Australia, then there was no doubt that I would get a visa to this country.

When did you learn to speak English?

Still back in Shanghai. But my son's so-called mother language was German, for a very simple reason – not because I preferred the German language to the English but because the refugees around us in Shanghai all spoke German. We thought it was much more important for Peter to learn German so that he could easily communicate with his future friends. But in no time, once we moved to Adelaide, he forgot all his German. I was quite amazed at that.

How old was Peter when you came to Adelaide?

We came to Adelaide in '48, when he was eight years. Oh, for him it was good fun to come here.

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Putting down new roots

Where did you live when you first came to Adelaide?

In Blair Athol. It was quite close to the abattoirs, and occasionally on a hot summer's day the smells were not at all pleasant! But it was a new Housing Commission establishment.

What was your first impression of Adelaide, or of Australia?

Oh, people think that I must have got a culture shock. Nothing of that sort. In fact, my first impression was one of relief from the bedlam of Shanghai, suddenly being plonked down in the most placid city you can imagine in the universe. The contrast was unbelievable to me. We settled down very well in Adelaide.

Esther was happily teaching here for years – she was a very, very good high school teacher – and then she did tutoring at the uni and so on. And I never had one moment of problem, once I had got into Australia. I started off as a lecturer; a few years afterward I became senior lecturer; and a few years later I became reader, which is nowadays called associate professor. Then, in '63, I got a chair at the University of New South Wales and we moved to Sydney.

We spent about 15 years in Adelaide, so I know Adelaide in and out. When we moved back here it was like returning to my original Australian hometown.

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Black hole coordinates

Perhaps you would explain some of your work. What about your black hole coordinates?

You know, it is probably through my little paper on the black holes that my name is best known to the widest readership, yet I never mentioned 'black holes'! That term didn't exist then. But I must say this was one of the papers which caused me the least effort. Somehow it was in my head, and I think I put the whole thing together in one afternoon. Sometimes you can put an incomparably bigger effort into a paper which affects people much less.

By the way, I tried to persuade the theoretical physicists that what I did there was not much different from the work of an earlier cosmologist, Georges Lemaitre. I could never dig up his footnote where he suggested something similar to what I worked out in this paper, but I did mention his name in my black hole paper.

Actually, I was interested in a much more general problem in geometry: what you should call a singularity of a place. This was at that time a very ill-defined concept, but I gave a method for deciding whether a point is a singularity or not. This was my purpose, and what they later called a 'black hole' was merely a little illustration of the method.

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An enduring graph theory problem

And graph theory? Can you explain that fairly simply?

Ye-e-s. In fact, Esther's great problem is a mixed graph theory. Her problem is very simple, as I will explain to you, but the answer is not so simple.

Firstly, this is the most usual way to express graph theory (but it is really much more complex). Say you take a number of points, then you pick out pairs of these points and connect each pair with a line. What you get is a graph.

In normal parlance, to draw a 'graph' means you plot your income or business data, but for the mathematician a graph simply means a visual picture of data. For example, suppose you take 10 points and to each you assign a number, an integer. Say to the first you assign 5 so you put it at a certain point, then to the second you assign another number and you put it at its appropriate point, and so on. Graph theory is the study of that sort of graph.

With that explanation in mind, let us turn to Esther's geometry problem. It is almost a schoolgirl's problem. She noticed that if you take any five points in a plane, then whichever way they are situated in the plane, you can always pick out four which form a convex quadrilateral.

I don't want to give you a high-brow mathematical definition of a convex quadrilateral but on paper I can show you how it differs from a concave one. [Draws] Here are four points; this is a convex quadrilateral. Now I will take another four points but this time they have a triangle inside them. This is concave – simply because if you take the 'envelope' of the whole configuration, this triangle then contains in its interior another point.

What Esther discovered was that if I give you any five points I can always pick out four of them which form a convex quadrilateral. She asked then, innocently, the following problem (which became my not quite solved problem): how many points in the plane do you need so that it should, with certainty, contain say five or six or any specific number of points – k points – which are in a convex configuration?

This turned out really to be a tricky problem. I could prove at that time that if the number of points is big enough, then you can always select a certain number – k – of points which are in a convex configuration. What is troublesome, what is unsolved, is that you don't know how many points in a plane you have to pick out, so that they should always form a basic convex configuration of k points. People have been able to show by experiment what the answer is likely to be, but so far nobody has managed to do it theoretically – minus 2, minus 1, what would it be?

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Combinatorics: a new branch of mathematics

What sorts of applications result from solving mathematical problems?

Well, the proof that I gave in my solution to Esther's problem was a bit intricate but it started off a whole branch of combinatorial mathematics. So my great contribution was not so much to solve the problem but to create a new branch of mathematics. It is nowadays called not by my name, unfortunately, but by that of a well-known British mathematician and logician, Ramsey – and even then for quite different reasons. He was interested in the main thing on which my proof rested but I didn't know about his work until later, because mathematicians don't really read logicians' works!

Could you tell me a little bit, then, about combinatorics?

One of the primitive, first problems in combinatorics is shown by this typical high school mathematical problem: if you have an object and you want to pick out k examples of this, what is the number of different ways you can do so? It is very easy to answer that. The magic formula that gives it is l times l-1 times l-2 times l-3 and so on, over k factorial. K factorial is k times k-1 times k-2 and so on. This gives you the number of ways how you can do various things in high school mathematics.

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From chemical engineer to celebrated mathematician

I believe you have become a Member of the Order of Australia for your achievements in mathematics.

It was certainly nice to get the Order of Australia, but I don't like to hang these things on the wall. Then I found that hanging it there was quite a shrewd move, because everyone seems to notice it when they enter the house. Even the cleaning lady! That's how your standing in the community goes.

When you talk about my achievements in mathematics, did you know that I became a mathematician without ever having a mathematics degree? It was very exceptional, I can tell you. I have a Doctor of Science degree from the University of New South Wales, but more an honorary degree. I was the head of the Pure Mathematics Department for years and years, and I think then they got the brilliant idea that they would give me an honorary degree – after I had got through quite a large number of PhD students! It is really very curious, my story. I think I was unique that without any mathematics degree I became a Fellow of the Australian Academy of Science and so on, and even an Honorary Fellow of the Hungarian Academy of Science, which people seem to know about but nobody ever mentions.

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A teacher, researcher, restless inquirer

Have you always enjoyed teaching mathematics?

I liked it very much, yes. And some classes took very well to me, I must say. This was a mixed affair. I didn't like to teach big classes, although in New South Wales I had occasionally to take big classes. I felt very comfortable with 20, at the most 30, students; then I could have very nice relations with the classes. I needed the personal contact with students. It didn't give me pleasure just to rattle off what I wanted to say to them – I wanted to use anecdotes and what not. I liked my contact with students.

Did you have a favourite area of research?

My interests flitted always from one subject or another – I am just that sort of person. I had an unusually large number of areas of research. I never settled down to a single subject, whereas in the present day people just settle down in a little narrow nook of mathematics and then they can live all their lives in the same area. When they turn 90 they publish in the same area as when they were 30 years old! That happens very often.

Do you think there is a problem that if you have only a narrow view of one area of mathematics, you miss out on the bigger picture?

That was really not my reason. It was simply that I am made like that. I cannot stick to one subject. But I do not change my interests: I have a couple of left-over problems from my old times. In fact, my last activity was to use the computer to try to solve a particular combinatorial problem.

I always thought, 'Ah, now I have settled down in retirement, in peace and quiet, nothing will interrupt my work.' So far it hasn't worked. First of all, your brain certainly goes downhill as you grow older. There is not a shadow of doubt. I am objective enough to watch what is happening to me, and I know that is a physical process that I cannot do anything about. It is very rare that mathematicians continue with their mathematics after 90, but I am now 94 and I am still doing some! I am just fortunate that I have no very serious health problems.

Esther, on the other hand, has to stay in a nursing home, poor thing. Every day I visit her still, and occasionally I take her out in her wheelchair for a little walk. But really she is now very helpless and it would be impossible for me to have her here. I cannot take care of her.

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A happy music-maker

I know you have a keen interest in music and played with an orchestra. Could you tell me a little bit about that?

I am a very keen musician. I play the violin and viola. I chose the violin because this belonged to a good education, but in point of fact I became absorbed in music. I was six when I started to learn the violin. I will tell you how I have my present instrument. When I first went back to Budapest after the war, I visited my old violin teacher – he was then well over 90 – and he sold his violin to me. (He was still alive the second time I went to Budapest, too.) Do you know, I was probably one of his favourite pupils. Anyway, that lovely old instrument was made in 1815 or something.

In Adelaide I never played in an orchestra but I did play a lot of chamber music. Then I went to Sydney and I joined the Ku-ring-gai Philharmonic Orchestra. This was very nice, and I got a liking for orchestral playing. In chamber music-making you have four people together, and only a pianist is needed. In orchestra playing you have a whole society around you, a crowd, and that's quite different. You have to be very careful how you play, because one player can do a disaster to the orchestra. It is really a bit of a responsibility, and I finally thought in the last year I was in Sydney that that was about enough, I could not carry on and produce the right quality of music.

Were your parents and your brothers interested in music?

In my mother's family, music never entered anybody's mind. My mother was practically tone deaf – I don't think she was able to reproduce singing on a particular pitch. My father never played any music; he was an illiterate person and his only cultural ambition was to make money. But I found out that his father was a church cantor in a small place in Hungary, so after the war I went with Esther to visit the place. Unfortunately, we couldn't even track down a tombstone from the old times. There were several gifted musicians in my father's family – one was almost a concert pianist – and that is evidently the branch from where I got my musical inclination. Really, music comes very easily to me. Do you know, I never ever practise, except if I sit down with friends to play some quartets or something.

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Generations: the stories and influences continue

Is there evidence of where you and Esther got your mathematical ability from?

That is a good question, but the answer is zero, an absolutely total blank. Esther, particularly, has no idea. She was a so-called illegitimate child (which now means nothing). Her mother was a housemaid in Carpatho-Rusyn, which at that time belonged to northern Hungary, and was seduced by a well-to-do young man. They tried to elope but when they got to the border they were stopped. And when it came to the point that he had to make a decision, he just shrugged his shoulder. So that was it – a very melancholy story. I never knew Esther's father and I don't think she ever met him, because her mother then, with this shame, moved to Budapest.

Are your children as interested in mathematics as you and Esther are?

Only one of them. My son became a mathematical physicist and was working with Paul Davies for a while. Peter says little about this. Like father, like son, he is not interested in publicity at all.

My daughter Judith has a maths degree from Wollongong, but by now she probably doesn't know any of what she learned. She is interested in university administration, so she is really in the enemy camp – but still we have good relations! There was a time when she changed jobs every one or two years; she just never settled down to a job. But now she is doing a PhD in university administration. She loves it, and she has produced several papers on the subject.

You mentioned that Peter lives in Adelaide.

Yes. That is why we moved here. I was happy living in Sydney, but on my last birthday I lost access to the drivers licence and that did it. We couldn't possibly continue to live at Turramurra, in the bush; it was not practical. So we happily moved to Adelaide. All our family is here. It was the only logical place to move to.

Do you have any grandchildren?

Ah, that's a trick question. We have, actually, but rather a step-grandchild, who comes from the first marriage of my son. He is Viv Szekeres, who is a big doer in the Migration Museum here in Adelaide.

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Enjoying life in a beloved city

You've mentioned going back to Hungary for the first time after the war. Have you got a favourite place in Budapest?

Budapest everywhere is my favourite place! There I was brought up, and I owe 90 per cent of what I did later, in turn, to the upbringing in Budapest. When we went back for a visit, I found the same intellectual atmosphere still there.

I went back to Budapest quite a few times. I had no quarrel with the regime in Hungary, even in Communist times. They did a few unpleasant things, mind you, so they were not quite innocent, but somehow basically I had respect for what they originally aimed for, to change Hungarian society to something less mediaeval. And they had! Once power got into their hands it was totally perverted, corrupted, but it didn't influence my wish to return.

I loved Budapest. It was very nice to be brought up there, because there was a sort of fermenting intellectual life which was very different from what I perceived later in Australia. But perhaps the times are gone for this sort of thing. When I go to Budapest I still have, a little bit, the feeling of something left over from those earlier times. But in some ways those times were very difficult and all the young ones who were around me were politically active in a way. I was never really active, because I would have made a rotten politician and, sure, I never quite liked political activity.

In a way, Esther was much more 'active' than I was. I was just going along with her. Nowadays her involvement doesn't look very serious. She was never a party member, a Communist or anything like that. But certainly she strongly felt that the ruling group was a rather reactionary regime – and it really was. Admiral Horty was the regent, the stand-in for the king. (Hungary was technically still a kingdom.) But to me, to all of us, it was not a pleasant regime.

Did your friend from Budapest, Paul Erdös, stay in Budapest, or did he leave as well?

He left Budapest in the mid-'30s. He was the nearest to what I would call a mathematical genius, and he became one of the leading mathematicians of the century, a very, very significant person. Finally, when he died, they counted 500 publications, which for a mathematician is quite a respectable number, quite unusual. I don't think I have collected more than 100.

We had a very good friendship, even after he left, and he came to Australia several times (which was largely my doing). We had several joint publications, the first being on the 'Happy Ending' problem when we were still practically university students.

You say in Hungary one of your favourite things is the intellectual environment. What is one of your favourite things in Australia?

Oh, I could tell you in one word: Australia is a very civilised country. And I love the civilised life that is in a civilised country. I found it here for the first time in my life, because Shanghai was certainly not one of those, and that to me meant very much. Once we settled down in Adelaide there was no looking away. Only if you have seen and you have lived in lots of other countries can you really appreciate the 'civilisedness' of Australia.

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A favourite number

Finally, here is a different sort of question for you. Have you got a favourite number?

A favourite number! Well, there was a time when I had. It was 137, the value of a defined structural constant which governs, in a way, the electromagnetic interaction sequence. But numerology doesn't work when you apply mathematics to the physical world.

At first Arthur Eddington, who was a very great man in English science, had some crazy theory in which the structural constant was exactly 137. Of course, as people experimented, measured it more exactly, it turned out to be 137.12 or something.

Eddington was a person about whom it was said that the philosopher thinks he is a marvellous physicist; the physicist thinks, oh! he is a very good mathematician; the mathematician thinks, oh! he is a good philosopher. But I liked his work and it had an effect on me.

Nowadays hardly anybody knows him, but he was very significant. After the World War he took part in a famous expedition in the history of science, to watch a solar eclipse somewhere in Brazil – the only place where total solar eclipses are visible. The intention was to measure the bending of light under the gravitational field which exists, and to demonstrate it experimentally. (It turned out that it is twice as big as was originally thought.) Unfortunately, just at the critical moment there were clouds all over the place and they couldn't really observe anything. These things happen, I am afraid! But Eddington's name was very well known.

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