Professor Bernhard Neumann earned a D Phil from Friedrich-Wilhelms Universität in Berlin in 1932. He completed a PhD in mathematics at Cambridge University in 1935. In 1937 he took up a three-year temporary position as assistant lecturer at University College, Cardiff. From 1940 to 1945 he served initially with the Pioneer Corps, then the Royal Artillery and finally the Intelligence Corps. In 1946 he became a lecturer at University College, Hull. Neumann moved to the University of Manchester in 1948 and spent the next 14 years there. In 1954 he received a DSc from Cambridge University. In 1962 Neumann arrived in Australia to take up the appointment of Foundation Chair of the Department of Mathematics within the Institute of Advanced Studies of the Australian National University (ANU). He served as Head of the Department until retiring in 1974. In addition he was a Senior Research Fellow at the CSIRO Division of Mathematics and Statistics from 1975 to 1977 and then Honorary Research Fellow from 1978 until his death in 2002.

Interviewed by Professor Bob Crompton in 1998.

- Introduction
- Antecedents
- School years in Germany
- A very young
*Doktor*in mathematics - A doctorate in England
- The genesis of a remarkable partnership
- Wartime – from interned alien to British Army stalwart
- A return to Germany, then together again at last
- Writing about group theory
- Manchester highlights
- Signing on for Australia
- Two Neumanns at ANU
- Family careers
- Fostering mathematical talent
- 'Napoleon, my Father and I'
- Prizes and honours
- A lifelong musician
- Babbage's engine and the papers of Ada Lovelace
- A working retirement

Professor Bernhard Neumann has played a dominant role in mathematics in Australia since his arrival in this country in 1962. He came to Australia to take up an appointment as the Foundation Chair of the Department of Mathematics within the Institute of Advanced Studies of the Australian National University. He and his late wife Hanna, also a Fellow of this Academy, who was Professor and Head of the Department of Mathematics in the then School of General Studies, now the Faculties, taught and influenced many young people with mathematical talent, at both the graduate and undergraduate levels, and their influence spread downwards into the schools.

Bernhard Neumann's distinguished contributions to mathematics are many and varied, mostly on the theory of groups. His original work is to be found in over 100 papers, but in addition he is the author of two books and numerous reviews, and he has written essays about a number of famous mathematicians. In his six-volume series, *The Selected Works of B H Neumann and Hanna Neumann*, are to be found fascinating commentaries of the life work of Hanna and himself, as well as about the many famous mathematicians and colleagues with whom they've been associated.

Professor Neumann's long and distinguished career began in pre-war England, following his early studies to the doctorate level in Germany. By the time he arrived in Australia, his eminence had already been recognised through his election to Fellowship of the Royal Society. In this interview we will follow his career from his early years to the present time, although there will be time to record only some highlights.

He continues his zest for life and his undiminished interest in mathematics and mathematicians. His work sees him attending his two offices daily – one in CSIRO and the other at the ANU. He commutes to them on his bicycle and there are few Canberrans who are not familiar with the sight of a blue-helmeted cyclist steadily pedalling here, there and everywhere, come rain or shine.

*Good afternoon, Bernhard. I have been very interested to read about your work and that of your late wife Hanna, and the remarkable partnership between the two of you. I know that you were born in Berlin-Charlottenburg, Germany. Would you like to tell me about your antecedents? *

My paternal grandfather, Bernhard Neumann, for whom I was named, was born in 1835, and he married into a steel firm in Karlsruhe, in the south of Germany. My paternal grandmother was born on 19th January, 1840. My maternal grandfather, Hermann Aronstein – from whom I have my middle name, Hermann – had a very large farm called a *Rittersgut*, in Westphalia. A *Ritter* is a knight, and knights had big farms whereas ordinary farmers had probably smaller farms. This *Rittersgut* must have been in the family since the early 19th century but it was later sold. Although I never knew my grandfathers, we went to my paternal grandmother's 80th birthday, in Karlsruhe, and I knew my maternal grandmother very well because she lived in Berlin not very far from us. She died in, I think, 1921.

Both families were Jewish, but my father was not a practising Jew. My mother would go to the synagogue for the high festivals. I'm not a practising Jew, but I'm aware of being Jewish and I've been to Jewish services and so on, wearing a hat or a cap.

My father's eldest brother was, in fact, the grandfather of Mike Newman, who is a very valued colleague, a professor and associate dean in the School of Mathematical Sciences at the Australian National University. My father's sister was killed in an accident in about 1926. The next brother was a medic who was interned during the war in the Camp de Gure in France with his first wife, who died there of natural causes. He married again, eventually migrated to England and lived out his life in Oxford.

My father was the youngest of the four, born on 15th January, 1876. My mother was born on 28th April, 1876, the third daughter of Hermann Aronstein and his wife. My parents married in 1905, in Berlin. My father studied engineering, spent two years in the United States as an engineer and then held a job until the 1930s in Berlin, in the AEG – Allgemeine Elektrizitätsgesellschaft.

My only sibling, my sister, was born in 1906. She studied physics at the University of Berlin, became a physicist and worked eventually in patent law and patent physics in one of the large firms, probably ICI, in the north of England, until she married a Swedish schoolteacher and eventually moved to Sweden. By the time she married she was 45 years old and so there were no offspring. She died of cancer.

I was born in 1909 and so I lived through the First World War, when Germany was blockaded and food was in very short supply and severely rationed. We each got 20 grams of butter and 50 grams of marg a week, and a bread loaf of 1,000 grams. Some things such as potatoes were not rationed, and all kinds of dry beans were available. Coffee was hardly available. I remember being tremendously hungry during the war and well undernourished afterwards.

When the fighting was over, the Quakers – the Society of Friends – immediately came to Germany to do some good work by nourishing the undernourished children. One was measured for height, weight, age and so on, and my sister and I were, by their standards, undernourished so we both got the *Quäkerspeisung* – Quaker nourishment – which consisted of rice, milk, cocoa and sugar. This was distributed during school time in one of the 15-minute intervals. We would go with our plate and our mug, and queue up to receive it. It was usually too hot to have very quickly, so we got late to the next lesson. Into the doors of the classrooms little peepholes had been drilled by some of the pupils so that they could judge a good moment for their re-entry, and these were known as *Quäkerlöcher* – Quaker holes – even when I left school in 1928, when the new generation wouldn't have any idea why they were called that.

*Did your schooldays influence you towards mathematics as a career? *

I'm sure they did. I remember that when I was seven or eight years old we had just learned adding single-figure numbers and carrying – perhaps several times – when the sum was above 10. I went home, wrote down a long column of single-figure numbers and started adding them. The whole sum was something like 122, so the carrying went beyond 10 and I wasn't sure at all whether this was correct. When I showed it to my mother she gave it one glance and said, 'Yes, that's right,' and I still remember being very disappointed that she had not really checked it. I remember also that a little later in primary school we were doing mental arithmetic and when the teacher said, 'Eight times 108,' I shot up my hand, stood up and said, '864.' It really came so automatically. I was good at arithmetic, at mathematics, all through school life.

My father had two German volumes about differential and integral calculus – the then well-known Stegemann-Kiepert – which he had used as a student. I was fascinated by the beautiful curves depicted in them, so when I was about 12 years old I got hold of the first volume and started reading it, did all the exercises and so learned differential calculus, which at that time wasn't taught at school at all but at university. And when I was about year 10 or so, I invented three-dimensional analytic geometry and showed my teacher what I had done with it, but it was way beyond his training.

*When you began your tertiary education your parents were in Berlin, weren't they? *

Yes, but my first two semesters were at Freiburg, in Breisgau. Many students moved every semester or so to a different university. This was entirely possible because all courses were acknowledged by all universities and all students were entered in one book, no matter what university they were in. My Professor at Freiburg was Lothar Heffter. When he approached his hundredth birthday I dedicated a paper to him, sent it to the periodical that is edited in Freiburg, and had a reply by return: the evening before my paper arrived, the editor had heard on the radio that *Geheimrat* Heffter had died – at 99½! So the paper was dedicated to his memory, and appeared rather later.

*You were at Freiburg in 1928-29 and then at the University of Berlin until 1932. *

Yes. It was called the Friedrich-Wilhelms-Universität, after the King of Prussia at its foundation in 1810 – now the Humboldt-Universität, and I have a degree from both!

I took my Dr.phil. at Berlin, very early. For a seminar there I had to read a paper by a Danish mathematician. Somebody else had to report on it but I was the second string to his bow. I found that I could do something slightly differently, because he had something with four generators and I could do it with two. I wrote that up and showed it to Heinz Hopf, who was then a *Privatdozent* in Berlin, and he immediately asked, 'Do you want to take your doctorate with that?' I said, 'No. For one thing, I'm much too young, and for another, it's much too slight,' so he said he would take it to Professor Issai Schur, who was founding editor of the *Mathematische Zeitschrift*. Professor Schur sent his assistant, Alfred Brauer, to ask if I wanted to take my doctorate with it but I gave the same answer, 'It's too slight and I'm too young.'

It was left at that. I then went on holidays with a cousin of mine to Greece, and on the way back we visited Heinz Hopf, who had got a call to be professor at the ETH – the Eidgenössische Technische Hochschule – in Zürich, going there in 1931. When I came back for the next semester Alfred Brauer came again, saying, 'But Herr Schur wants you to take your doctorate with it.' So I agreed to.

A little later Schur himself told me that perhaps it was a bit thin and suggested that I investigate, using the same methods, what was later called the wreath product of groups. This I did in two weeks and it more than doubled the bulk of the paper, which I submitted as my dissertation. But I did it very, very secretly and didn't let my parents know. My sister was in the know. She had just taken her doctorate, and she lent me money eventually to prepare for my oral examination, which was in November of 1931.

For my Dr.phil. – Doctor of Philosophy – I took mathematics as both my major subjects, with physics as one of my subsidiaries. At that time, the other had to be philosophy, which then included psychology. The Professor of Psychology was Köhler, very well known for his work on apes and on Gestalt psychology, on which he'd written a book in English. By that time I had good reading English, and I read his book. When the time for the examination came, he asked me some questions that I could have answered from the first pages of the book and I was very disappointed that he didn't dig more deeply into it.

My physics examiner was Peter Pringsheim, an experimental physicist. I forget what he examined me on, but that went well. In mathematics my two examiners were Issai Schur and Erhard Schmidt. All the examinations were officially on Thursday, 19th November, but in fact one went to the professors beforehand and agreed on some time before that, so I had my examinations for a Monday, Tuesday and Wednesday. The Wednesday was one of the big holidays – perhaps All Hallows, quite a big holiday in Protestant Germany – and so I'd invited a friend for lunch. But then Professor Schmidt wanted to examine me that morning.

For these examinations I had rented a room in the city and bought – with borrowed money from my sister – a dinner jacket so as to go in finery. I went there, still without my parents' knowledge, and during Erhard Schmidt's exam we both got terribly interested in what we were talking about so that it took about an hour and a half instead of the 40 minutes that were allocated, and by the time I came out my guest would have arrived for lunch. I phoned my mother, who was angry that I wasn't home yet, and surprised her by saying, 'No, but I've just finished my doctorate.' I was the youngest or the second youngest *Doktor* in Berlin in mathematics.

*Almost immediately there came a major disruption to your life, when you had to leave Germany for England. *

Yes. I left for England in August 1933. I had been waiting for some professor to spot me and appoint me assistant, but I was still quite unspotted and so I had no job. There were not many assistantships available at the time. But then I knew I couldn't get one, being Jewish. If I'd had a job at the time I might have thought, 'Oh, this is so mad it must blow over' and I might have stayed, perhaps for too long. As it was, I got out and at the advice of a friend went to Cambridge, where I became a research student again, under the supervision of Philip Hall. He was a Fellow of King's College, Cambridge, and very well informed about a wide variety of things. At that time I was a member of Fitzwilliam House (now Fitzwilliam College) and Hall's 'supervision' took the form that I would go in to dine once a week and then go to his rooms in King's College, where we would drink his sherry, smoke his cigarettes and talk about rhizomorphs of plants and political history in Germany and everything. And about 10 o'clock we would drift towards talking mathematics.

*Hardy, who was a very prominent mathematician, advised you against doing a second PhD, didn't he? *

He advised the émigré mathematicians, who all came with doctorates from Germany, against taking another doctorate, saying, 'If you do good work, that's all that's needed.' Of the many of us who were at Cambridge at that time, only Hans Heilbronn took his advice, producing a very good piece of number theory, on the strength of which he was elected a Fellow of Trinity College and later became Professor in Bristol and then in Toronto. During the war I got into the Intelligence Corps and we became friends and played bridge. I was an absolute rabbit at bridge and he was excellent. But he was exceptional, in that when we had played as partners he would say, 'It might have been better to have played the king of clubs at that time,' instead of shooting me, as other bridge players would have done!

*A normal PhD in Cambridge took three years, I believe, but because of your German doctorate you were allowed to enrol for two years. I understand that you yourself weren't too happy with the progress you'd made at the end of the first year. *

Not at all. I had tried something that really was much too difficult and was successfully tackled only 20 or 30 years later – and not by me. At Christmas 1934 I realised I wasn't getting anywhere so I went back to look again at something I'd done in Berlin. Within a few days I knew I'd struck oil, and it just went on and on. I got more and more results, and by May I had to stop myself because I had to write it up. So I typed it on my little portable typewriter, with as many carbon copies as might just be legible. If I made a mistake, which was quite frequent, I had to rub it out on all the carbon copies, and all the mathematical symbols I had to fill in by hand. So it took quite a time to write this thesis, which was about 180 quarto pages long.

I submitted it, and the oral examination was arranged over lunch in Philip Hall's rooms. The examiners were Philip Hall himself and M H A Newman, and I was their first PhD student. I was asked two questions. One was whether I preferred beer or wine for lunch, and I answered, 'Wine.' Afterwards I was asked would I take my coffee black or white. I said, 'Black.' These two questions clearly satisfied the examiners, and I passed.

*You have written that Hardy commented on the 'German' style of some of your first papers. What exception did he take? *

Hardy ran the Hardy-Littlewood Conversation Class in Littlewood's rooms in Trinity College. He usually had visiting speakers but once he himself talked on how not to write mathematical papers. He gave two examples, one a 'German' style and one a 'Japanese' style, and as a paradigm of the German style he used the first sentence of my first paper in English, which had just appeared in the *Journal of the London Mathematical Society*. I think he objected to the word order, saying that I put something in front which should have come later in the sentence.

*What happened after you completed your PhD in 1935? *

I stayed on in Cambridge and applied for every mathematical job that was going – at an agricultural college, at the University of Malta, even a tutorship for the children of a very rich and influential Indian steelmaking family.

*But you did some lecturing in Cambridge during those two years. *

The second year I was there, I was asked to give a preparatory course for one that Olga Taussky was giving in algebraic number theory. I was paid £10 and there was a student evaluation of lecturers at the end. When I got my secret envelope and opened it, it just said, 'No comment.' The year after, I was offered the same course for £50. If I'd continued like that I would be rich by now. But instead I had been short-listed for a temporary assistant lectureship at University College, Cardiff, where I then spent three years as temporary assistant lecturer in mathematics. I had a fairly heavy lecturing load but it taught me a lot. The professor advised me to teach a course in applied mathematics, because it would be good for me – and it was.

*It was in England that you married Hanna, with whom you formed your mathematical partnership also. Hanna became ultimately a Fellow of this Academy, and volume 1 of the two-volume *Selected Works of B H Neumann and Hanna Neumann* has a splendid picture of her, which is exactly as I remember her. *

Yes, it's a beautiful picture. It has been reproduced a number of times.

*You met Hanna not long before you left Germany, I believe. How did that happen? *

I met her in January 1933, at the cafeteria. A mutual friend introduced us. At the time I didn't take much notice, because her name, von Caemmerer, was junior gentry and suggested somebody very conservative. Later I met her in the Mapha, the Mathematisch-Physikalische Arbeitsgemeinschaft, which was a mathematical-physical working group within the university – a wonderful thing which had its own rooms and its own library. When we talked I found that although she was not Jewish at all, she was very much anti-Hitler – as I was, naturally. We talked quite a bit.

Then, at Easter, I invited her for a walk in a suburban forest near Berlin, and she came on a long walk. Later she explained that it was really that she wanted to escape from her mother! But then we played ping-pong at the university and suddenly, by a mistake that was not a mistake, she called me *Du* – the more familiar address – instead of *Sie*. So we became very fast friends. Well, I fell in love with her.

We went for a bicycle outing, but on a steep downhill her brakes failed and she fell. I think she tore her frock and was bleeding and so on, but she reminded me later that the first thing I did was look after her bicycle and get the front wheel into shape again – and then I asked her how she was. I had told my mother I would introduce this girlfriend to her, and when we arrived at our home my mother immediately took to her. That remained so. My parents very much liked her.

In England I remained in touch with Hanna but very, very secretly. We could not openly correspond as that would have been dangerous, but we had been engaged since 1934 and had once met in Denmark in 1936. Hanna came there ostensibly to visit some friends, I came back from the International Congress of Mathematicians in Oslo, and we spent some time there. But apart from that we had corresponded very secretly. In my weekly letter to my parents I included one sheet which started with an exclamation mark and ended without a signature, and my parents would send it on to Hanna. And Hanna corresponded the same way with me, through a former geography teacher of hers – a very good friend and very reliable.

Hanna had in 1936 been warned that the senior professor of mathematics in Berlin would examine her for the examination that teachers took, the *Staatsexamen*. He would examine her in political reliability, *Gesinnung*, and fail her because he suspected she was friendly with Jews. So during the holidays the main assistant there, Rohrbach, arranged that she was examined by somebody else. She passed the *Staatsexamen* very well but she knew she couldn't proceed to a doctorate in Berlin. So when Rohrbach went to Göttingen as assistant to Helmut Hasse, she got a small assistantship there to try to take her Dr.phil. in Göttingen with Hasse.

In 1938 Hanna decided that war was not unlikely, and if we wanted to get married it was time to get out. She came to England then and we got married, but because of my parents still being in Germany we did not move together yet. She lived in Bristol and I in Cardiff until my parents came out, in February 1939. The four of us moved together into a little house in a suburb of Cardiff – becoming the five of us when our eldest, Irene, was born in August of that year, just before the beginning of the war.

*When the war began, were you still in Cardiff? *

Yes. I served my third year there, until the examination period about early June 1940. The British had learned from their experience in the First World War that there were Germans and Germans. They instituted small tribunals that interviewed all 'enemy' aliens and classified them A, B or C. A were the friends of the German régime, or at least not enemies of it, such as sailors who happened to be in a British port at the time, and they were interned for the duration. C were those who were clearly enemies of Hitler and they were treated as essentially friendly aliens – had the same restrictions as other aliens but nothing worse. The rest were B. We were all very clearly C and so could continue. I had thought of joining the Army but as a lecturer I was in a reserved occupation, and also my age group had not been called up yet.

Then in May 1940 the German forces overran the Netherlands and Belgium, and suddenly there was talk of a Fifth Column and the yellow press in Britain screamed, 'Intern the lot!' Eventually the government interned all B class adults and then C class aliens between 16 and 60. So I was interned, only a few days after we'd moved to Oxford from Cardiff, which was an aliens-protected area, being so near the water. After a few days at the Oxford police station I was sent to Southampton, probably to be shipped overseas, but just then a ship with some internees and, especially, some wounded Canadian soldiers, was dispatched to Canada but was almost immediately sunk by a torpedo. Quite some Canadian lives were lost, but apparently none of the internees. There were questions and lies in parliament about this.

Well, they decided they wouldn't send another ship from Southampton and transferred us to Lancashire, to a disused cotton mill with barbed wire around us. There were very interesting people there, including many academics and the Jesuit Fathers from a college near Windsor – one of whom, in hot discussion, fell into Latin. It was wonderful. Eventually we were transferred to the racecourse at York, where I joined a *Privatdozent* in classical studies in reading Latin, probably Virgil.

In about September-October many of the internees were released to the firms and universities who had asked for them back. Although University College, Cardiff, had asked me to serve a fourth year, I had been temporary because their top student had been sent to Cambridge to get a PhD but she needed a fourth year for it. When they didn't ask for me back, I thought, 'Well, I can't be so important as a lecturer.' I volunteered for the Army, joined in October 1940, and was trained in Yorkshire and then transferred to the south of England. Most of the time I was within reach of Oxford and I got my usual privilege leave and weekend leave, and even a special leave when my son Peter in Oxford was born at the end of December 1940.

After a while I joined the Auxiliary Military Pioneer Corps, the AMPC. Very soon it became just the PC, the Pioneer Corps – I believe after the war it became the Royal Pioneer Corps, but by that time I was long out of it. I was in the Pioneer Corps until 1943, when they decided they could trust some of us and allowed those who were fit mentally and physically to volunteer for combatant service. I was one of many who volunteered. Ralph Elliott, who was in my company in the Pioneer Corps, volunteered and eventually became a lieutenant in the infantry. I was sent to the Royal Artillery. I had to hand in my two stripes I had as a corporal in the Pioneer Corps but was given a 'local bombardier' stripe to keep me out of potato-bashing!

But then my Officer Commanding wanted me to go in for a commission. He sent me to a War Office Selection Board; they didn't select me. (I was a bit sore at the time but a few weeks later I was very glad, because all the potential officers they had selected were returned to unit because artillery officers were not being lost as fast as had been reckoned.) And so my Officer Commanding said, 'Oh, you are wasted here in anti-tanks.' It was very interesting. I learned to fire an anti-tank gun at a pretend tank. But he said I should do something more mathematical, and transferred me to Artillery Survey, where we used theodolites and did a bit of numerical work, but it was again outdoors. All my Army service during those years was outdoors.

*It probably wasn't taxing your mathematical ability to its full, was it? *

No, indeed not, but I did write a couple of papers while I was in the Army. Anyway, I was stationed not very far from Oxford, so I could cycle there for my weekend leaves and my privilege leave – and some French leave too, over the weekend – of course with the bicycle lamp blacked out. One hardly saw where one was going.

*All this time, Hanna was beginning her DPhil, wasn't she? *

Yes. In 1940 she had decided that with only two children to look after in Oxford she wanted to proceed to a DPhil, so she enrolled in the Society of Home Students – now St Anne's College – as a research student. She had to go in from time to time to see her supervisor, and she acquired a sidecar for her bicycle and became known all over Oxford as the lady with the two babies in a sidecar. She was supervised by Olga Taussky, who by then had married John Todd and was Olga Taussky-Todd, and had been evacuated with Westfield College to Oxford. She always told Hanna, 'Write it down so that I can read it,' but she found Hanna a tremendously unsatisfactory research student because Hanna never wrote it down until she'd finished her thesis – very, very long, very complicated, very outstanding. Olga Taussky then could read it.

Hanna finished that in late 1942 or early '43, and some time in '43 she was allowed to return to Cardiff – people were then much more relaxed about such things – to a little house we'd rented there, and from there she went to Oxford for her oral examination. I was by then in the Intelligence Corps and stationed not very far away, so I hitchhiked to Oxford and attended the lunch after her oral examination. By that time she was pregnant with our number three, Barbara, whom again she had in hospital, in Cardiff. There had been some haemorrhage during the pregnancy, so it was safer.

*When the European war was over, didn't you go across with the Forces into Europe? *

Yes. We had to send a unit of the Intelligence Corps to Germany and I volunteered for it because I hoped to make contact with Hanna's family. Having missed out on the long weekend leave for VJ Day, I got a long weekend leave in Germany and hitchhiked to Lübeck, where I knew Hanna's elder sister was. I found her address through the *Einwohnermeldeamt*, the official registry of German residents. When I asked for her, 'Oh no, she's still at work. But go up to her room on the third floor and wait for her.' When she arrived she was told, 'There's a British *Spiess*' – sergeant-major – 'waiting for you in your room,' but she came up very courageously.

We had seen each other briefly in 1934, after Hanna and I had got engaged, but not since then so we naturally had a lot to talk about. First thing, she organised a bicycle for me so that next morning we could cycle the 10 or 15 kilometres to the village where my mother-in-law lived. I had taken the precaution of borrowing an American kitbag – bigger than a British kitbag – and filling it with all sorts of food tins from the NAAFI for my mother-in-law. Although she had not been very happy about my marrying her youngest child, Hanna, she was then consoled because I'd already produced three grandchildren for her and a fourth one was on the way. The NAAFI tins were an additional pleasure, and very useful when there was nothing like it available in Germany.

I was demobilised later that year and came back to England. Cardiff had wanted me back but I didn't want to go there because they hadn't helped me out of internment. But I had applied for a lectureship at Hull. I hadn't got it because I couldn't come for an interview (being still in Germany) but then they advertised a temporary lectureship which I applied for and got. It was temporary because Bronowski, who had been an assistant lecturer, had joined the Royal Air Force and was not expected back until the middle of the year. So for two terms I was a stand-in for Bronowski. Then they created another, more permanent lectureship and I got that.

Bronowski wrote to the professor, 'I'll come back if you give me a senior lectureship or a readership, not otherwise.' The professor said no, so Bronowski decided not to come back. Hanna applied for his lectureship and got it. I had been in Hull on my own, in digs, but in September Hanna moved to Hull too, with the nine-month-old baby and the other three children. That was a great moment. There we were at last together, in the same department, and we did things together. Hanna stayed for 12 years, but in 1948 I was enticed to Manchester by M H A Newman.

*So the domestic bliss didn't last long, did it? *

Well, the academic year was a little less than half a year and so I was home in all the vacations and for most of the weekends.

*What is the distance between Hull and Manchester? *

Just about 100 miles, 160 kilometres. And once a year I would cycle across the Pennines from Manchester to Hull, taking between 11 and 13 hours, depending on the prevailing wind. In Yorkshire it was very flat – and very windy. But I wouldn't cycle back, because spinning out the time to my arrival at home was all right but spinning out the time going back to Manchester was not. I put the bicycle on the train. At that time there were very good trains between Hull and Manchester and Liverpool.

*This may be an appropriate time to say something about your research interests – perhaps in lay terms. *

The theory of groups is the theory of some very fundamental algebraic structures. It had been started really at the beginning of the 19th century and had blossomed very much around the turn of the century and early in the 20th century, but mainly as the theory of finite groups and of continuous groups. Abstract, infinite groups only started up in the 1910s to '20s. When I started looking at them, Issai Schur asked me, 'Well, if you know the generators and relations of a group, what do you know about it?' It was a very shrewd question, because in fact one knows very little about it. That eventually became Hanna's field also and she wrote a book for the Springer-Verlag called *Varieties of Groups*. I had started on that subject in my Cambridge PhD thesis and eventually wrote my Adams Prize essay at Cambridge on it. That was our main field of endeavour.

I had also done some other things. During one boring talk in the Hardy-Littlewood Conversation Class I thought of a geometrical problem which I then pursued, and it gave rise to one of my geometrical papers. Also, early in the war I wrote a geometrical paper which drew a reply from H F Baker, the grand old man of geometry in Cambridge, showing how one of the things I had done could be done in two pages using his approach. Well, naturally I had to referee the paper for the *Journal of the London Mathematical Society*, so in a paper which followed his in the *Journal* I immediately showed how I could do it in less than a page.

*You have just mentioned the very prestigious Adams essay prize of the University of Cambridge. What were the boundary conditions for the award of the prize? *

The prize is awarded every two years. In the years when I worked for it the subject was group theory, in the hope – unfulfilled – of getting Philip Hall to write the book that was in him. My essay, which was a lengthy one, gave the then state of affairs in what later was called varieties of groups, on which Hanna wrote her text. Winning the prize was a great thing, and the £300 prize money was put to very good use. All the children got £20 each, Hanna got the price of a new formal frock, and I used the rest for my full-dress gown at Manchester, the *Encyclopaedia Britannica* and field-glasses. I sent the essay to the *Acta Mathematica* for publication but they sent it back by return, saying they were full up. They hadn't even sent it to a referee. So I sent it to the Royal Society, and it appeared in the *Proceedings*. And it's still being used.

*You were 14 years in all at the University of Manchester, rising to the prestigious rank of Reader. What were the highlights of those times? *

I will mention the fate of my Adams essay. I corresponded with Kurosch, a mathematician in Moscow. Hearing of my essay he wrote that he wanted a copy of it for his book on theory of groups, published in 1944. He sent me a copy of the first edition, possibly still the only copy in the Western world. When this became known, the Germans wanted a translation of both the book and my essay, which appeared as an appendix in the German edition of Kurosch.

Then a Hungarian colleague said he wanted the book and also my essay (for an appendix) translated into Hungarian. He couldn't get hold of a copy so he asked me to send him my copy, which he would photocopy and send back. So I sent it to him, insured for about £120! It did come back and I still have it. So my essay became the appendix also to the Hungarian translation, which I think eventually was made from the second edition of Kurosch's book. That already contained many of the results of the essay, which answered many of the questions that the first edition had asked.

*Towards the end of your time in Manchester, Hanna did secure a job, didn't she? *

She did, at the Manchester College of Science and Technology. It is now the University of Manchester Institute of Science and Technology, but at the time it was a half-independent part of the university, independently financed by the University Grants Committee. The College had its own department of mathematics and the professor wanted to start an honours course in mathematics, but he was in applied mathematics and needed somebody fairly senior in pure mathematics. So he advertised and Hanna applied. It took a long time because they had to get people together both from the College and from the main part of the University, but Hanna was appointed. This was quite late, after the International Congress of Mathematicians in Edinburgh – where all our family had gone on bicycles. So we had to hurry up to get a house in Manchester and sell our house in Hull.

This was a wonderful experience. I'd travelled up to Manchester, where Mike Newman had a car. He had driven me around several houses for sale there, and I'd chosen one. So I told my bank manager in Hull, 'We pay so-and-so much for the house. Can you lend us that?' He said, 'We'll send our valuer and see what he puts on it. We don't give you 100 per cent.' But next time I went he said, 'We'll give you so-and-so much' – £500 less than we had to pay – 'but we'll also give you another £1,000 because you'll need removal expenses and so on, and we'll take your house here in Hull as security.' I still have that account in Hull.

So I told Walter Ledermann, who wanted to borrow some money for a house he was buying on the outskirts of Manchester, 'Oh, bank managers are not the ogres they are said to be. They're wonderful.' He went to his bank manager, who was an ogre. Later I formed a theory why my Hull bank manager was so forthcoming. His son had taken a PhD in physics at Manchester, and father had come to the degree ceremony. There I had been in my scarlet gown, and he must have thought, 'Somebody with a scarlet gown like that is worth the credit'!

We moved to Manchester in '58. Hanna and, I think, Peter went by train after seeing off the furniture removal vans but Barbara, Walter and Daniel, the three youngest children, and I went by bike – across the Pennines. We took two days of it, and found a lot of lovely berries during our move to Manchester.

*By 1960, I understand, people were fishing for you to come to Australia. Who was doing the fishing and what was the background? *

I'd visited Australia in 1959 for three months, which was an eye-opener. I visited all the universities, including the Australian National University in Canberra for a weekend. At about that time, without my knowledge, Pat Moran had called together the senior professors of mathematics in Australia to discuss the possibility of creating a mathematics department in the Australian National University, in what was to be the Institute of Advanced Studies. They had all been for it except T G Room, from Sydney, who said it would drain off all the junior talent from the State universities. But the university went ahead.

In about May 1960, Joe Moyal – who recently got an honorary degree from the Australian National University and who knew me from Manchester – wrote to me from Pat Moran's department in the Australian National University to say that they were creating a department of mathematics there. Was I interested?

I discussed it with Hanna and the children, but my parents lived in London and said, 'We are too old to move,' and Irene, who was nearly 21, was a student at Manchester and was clearly not going to move. I'm not sure that she was engaged already, but anyway she was clearly wedded to Britain. Peter had just gone to Queen's College, Oxford, and also would probably not move. Barbara was still finishing school and would go to university somewhere, but it was not clear if it would be in Australia. Walter had already said he wanted to go to university in Australia, without knowing that we were moving there. Daniel was so young, still at primary school, that he would certainly come to Australia. So it would clearly have disrupted the family and we decided 'no'. I wrote back to Joe Moyal, 'No, thank you,' but being very much attracted I wrote in the politest possible terms.

Next thing I had a letter from Mark Oliphant, who was the Director of the Research School of Physical Sciences in the Australian National University. He was 'much encouraged' by my reply. When could we talk it over? He came to London for the Tercentenary of the Royal Society , to which I'd been elected in '59, and we talked about it there, over lunch – he and his wife and Hanna and I. Later he reminded me that I'd said, 'Well, we are a housekeeper-gardener couple. You can have both of us or neither of us. And I don't want to be in a position to appoint Hanna to my department. You have to take up her credentials independently and make her an independent offer. Then we'll consider it.' They offered her a Professorial Fellowship, so in about October we signed on the dotted line. I had meanwhile talked to Pat Moran, who was on leave in Oxford and came to London. Well, we took it.

*Just for the record: at that time the new Department of Mathematics was going to be within the Research School of Physical Sciences, which is where Mark's interest and part in the story comes in. And Pat Moran's Department was Statistics. *

Yes, in the Research School of Social Sciences.

*You took up the Foundation Chair at the Institute of Advanced Studies and held the position until your retirement at the end of 1974, a long stint. What were the highlights of that period? Certainly you built up a very successful department. *

Well,* Sputnik* had gone up in 1957, shocking the whole Western world into giving science a lot of support, including financial support. Menzies had asked Murray, the Chairman of the University Grants Community in Britain, to report on the Australian universities. The burden of the Murray report – which was very good and very influential – was, 'If you want good universities, you have to put money into them.' That is just what Menzies wanted to hear, and he did. There was plenty of money about, but only a few mathematicians. Mathematicians were not easy to come by. So I did my recruiting. I leant over backwards not to encourage people from State universities to come here because, being aware of T G Room's reservations, I did not want to draw away the State talent. If they applied, they had to be judged with the others, but I did most of my active recruiting overseas. I had lots of members of my department from overseas, as well as research students.

Two early ones were from India, Narain and Kanta Gupta. Narain has written an introduction to the six-volume *Selected Works* in which he recalls how I recruited him as a research student and Kanta, his wife, came with him. He took his PhD with me. She took first a Master's degree in Hanna's department and then her PhD in my department but with Hanna and, I think, Mike Newman as her supervisors. Narain and Kanta went on to become Fellows of the Royal Society of Canada – very senior and successful mathematicians.

*Group theorists? *

Both. Very much so, yes.

*I wonder why! Having come out as a Professorial Fellow to your department, Hanna was soon appointed head of the Department of Pure Mathematics in the School of General Studies. * ways had a very good relationship, naturally, with the Department of Pure Mathematics, where Hanna was, but also with the Department of Applied Mathematics, where Archie Brown had been professor since before the Canberra University College was amalgamated with the Australian National University and became the School of General Studies. Whenever we had an application I would send it round to everybody who was senior to what the applicant was applying for, and that always included Archie Brown, who gave me wonderfully shrewd, good advice. So those parallel departments in the two branches of the ANU worked very well together.

*Eventually the amalgamation became so close that after you had retired the School of Mathematical Sciences was formed, wasn't it? *

That's right, yes. It was none of my doing but I very much approve of it because it brought us together – in the one building, in fact – and also the statisticians in the Institute. The statisticians in the Faculties are next door to us but not really part of us, officially having very close links with Economics. But we have an economic mathematician in the School of Mathematical Sciences. The people in Pat Moran's department came over to the School of Mathematical Sciences but not Barrie Ninham's applied mathematicians, because they are essentially applied chemists. The amalgamation did make quite some difference. Although we'd always worked very well together, it was very good to be together. We were first in the Hanna Neumann Building but that became too small for us so we moved over to the John Dedman Building, which is now the John Dedman Mathematical Sciences Building.

*All five of your children had very distinguished careers, taking higher degrees in tertiary education of one kind and another. Would you like to tell us about them? Perhaps you could start with your eldest child, Irene. You have told me about an incident when she was about 12 which told you in no uncertain terms that she, at any rate, wasn't going to follow her parents and become a mathematician. *

In 1951 we travelled to Oberwolfach [a famous mathematical research institute], stopping off in Mainz where Erhard Schmidt and I each gave a talk. Afterwards there was a party for the mathematicians, and Irene and Peter sat next to Hans Rohrbach, who had fluent English and asked Irene did she like mathematics. She said, 'I hate mathematics!' Very definite, and in the hearing of all the mathematicians.

We tried to persuade her secondary school headmaster to let her drop mathematics. If he hadn't known that we were both lecturers in mathematics he would have exploded, because he was himself a mathematics teacher, but he had to be polite and so he said, 'Oh no, there are timetable difficulties.' She failed her O level mathematics but she had been coached a bit by Hanna and said, 'Well, if that is mathematics, it might be interesting.' And on her second attempt, coached by Hanna, she passed it at O level.

Irene took a Master of Arts in English literature and lived for many years in Aberdeen with her first husband, an Indian who had been brought up in Nairobi and then studied at Manchester, in England. He became a Fellow of the Royal College of Surgeons and, I think, of the Royal Edinburgh College of Surgeons. When the marriage broke up he took the three youngest children with him to Nairobi, but that was no longer a comfortable place for Asians so he accepted an appointment in Canberra as resident surgeon, and moved here with those three children. The two eldest remained with Irene in Aberdeen, where she taught high school.

Irene later married an American Jew, an Associate Professor of History at New Mexico State University, in Las Cruces, New Mexico, and eventually became a lecturer at that university. Not having a doctorate, for some time she couldn't get a tenured job there.

*And Peter is a mathematician. He went with you to New York, didn't he, when you had a study leave there between leaving Manchester and coming to Australia. *

In 1961-62 Hanna and I took up visiting positions at the Courant Institute of Mathematical Sciences, New York University. Peter had already got engaged to Sylvia Bull, a fellow student in Oxford, and wanted to invite her to New York for the Christmas holidays, so he applied for and got an immigrant visa, took a junior academic job at a different institution, and brought her out. They then decided to get married in 1962, in Oxford, by which time we were back in England. I warned Peter, 'To marry as an undergraduate is doing the Bachelor's degree with one hand tied behind your back. All your fellow students will come for a cup of coffee and to cry on your shoulder. Getting married as a research student is fine, even a help, but not as an undergraduate.' Sylvia took a first class honours degree at Oxford, so if he hadn't taken a first class honours degree he would have felt terribly bad. But he neglected my advice. They got married in 1962 and next year he took a first class honours degree. Honour was saved, and he's now a very senior Fellow at Queen's College.

*What about Barbara? *

Barbara came out to Australia about a month after I had come out in '62, when she'd finished school, and taught for a while at the girls grammar school in Canberra until she went back for the academic year to the University of Sussex. There she took her Bachelor's degree – I went to the degree ceremony, actually – and met her future husband, who took a Master's degree in chemistry. They are both quite senior teachers, in Slough, he in science at the local grammar school and she in mainly mathematics but some statistics also, at a private Catholic school. They have two sons, now both married, and a daughter who is a student in Cheltenham, I think.

*And your fourth child? *

Walter had taken the College Entrance Examination Board examination in Liverpool before we went to New York. He did exceptionally well and New York University accepted him, so he became a university student in mathematics before he was 16. He was on the Dean's list for both semesters. (My theory was he wasn't interested in girls yet.) He wanted then to become a student in Australia but first he went for a semester to the University of Freiburg – where Hanna's brother was – and he learned some more mathematics and skiing and drinking beer and quite some German.

Then he came to the University of Adelaide, which gave him credit in mathematics and I think also in physics but not German, as he hadn't got enough of the reading knowledge or the literature, so he did one year in German. He did all this in the Faculty of Arts so he got a BA rather than a BSc. He did extremely well and got a very valuable scholarship, but only for study outside Australia.

In '65, when Walter had just taken his Bachelor's degree and was still doing his Master's thesis by dissertation, in Adelaide, we ran an international conference on group theory here in Canberra and he and Peter came to it. Peter, who is in group theory, told his young brother – who had by then done his Master's work in group theory – 'There are too many Neumanns in group theory. You are still young enough to learn something else.' So Walter went to Bonn, in Germany, and did algebraic topology there with Hirzebruch, the senior professor. By the time he took his doctorate, Hirzebruch wanted to keep him there. But Walter wanted to go to America, first to California and then to Princeton, where he met his future wife.

With the help of my travel agent I was able to attend Walter's and Ann's wedding in Princeton and then go with them from John F Kennedy to London, travel in England, make a side trip to Eastern Europe for a conference, and even return via Nairobi, where I had friends, as well as visiting members of the family in Johannesburg and giving a talk at the Witwatersrand University. And all this was done on one round-the-world ticket with only one stay other than the nominal destination, London!

Walter became a full professor at the University of Maryland at an incredibly young age. His wife, Anne, had degrees in mathematics and mathematical education, and later took a PhD in English literature but couldn't get a suitable academic job in that. In 1984 Walter for the first time revisited Australia, with Anne, and oh, it was a homecoming for him. He loved it. He and Anne wanted their daughter to grow up in Australia, so he accepted a job in Melbourne at the university, where he is now a professor (in mathematics, of course) and he has, with his topology, drifted back to group theory. It's somewhere on the interface. He is very highly regarded and I hope that before many years have passed he will be a Fellow of this Academy.

*Now there's Daniel. *

The youngest, Daniel, came with us to New York, went to primary school there, and then came back to school in Sale near Manchester, where we lived. When I left in '62 to take up my appointment here, Hanna stayed for another academic year because Barbara was still at school and Hanna had two research students she wanted to look after. So she came with Daniel only in '63, arriving in Perth, where the mathematicians threw a party for her. Daniel was then 12 years old.

He went straight to Telopea Park High School and then to Monash University, where he took his Bachelor's degree in pure mathematics and classical Greek. He wanted to become a schoolteacher but eventually decided to concentrate on his music. He had been taught violin and viola by a very fine teacher who was for many years the leader of the Canberra Symphony Orchestra, and she then employed him as an understudy. He prepared young pupils for her, in violin, for quite a while.

Daniel's wife, Liz, is very much a daughter in the family. She is the youngest sister of Jim Wiegold, who took his PhD with me in Manchester, as did Jim's wife. Liz came out with the Wiegolds when they visited Hanna's department for two years, and stayed on as an ANU history student. Daniel is a viola player in the State Orchestra of Victoria, formerly the Elizabethan Melbourne Orchestra. Liz took library qualifications in Canberra and has become a senior librarian at the University of Melbourne. Their elder daughter is just entering her third year in psychology at the University of Melbourne and the younger is entering her first year in music at that university. Meanwhile Daniel has taken qualifications in psychology, up to the Master of Letters, MLitt, externally at the University of New England – essentially to become a psychoanalyst, I think. I'm not sure that that plan is still alive, but at least his elder daughter has inherited the interest in psychology.

*You and Hanna had a wonderful reputation not only for fostering mathematical talent at all levels but for your personal hospitality to your students and staff and also a concern for their families. Your policy of open house went right back to the earliest days of your marriage, didn't it? *

Yes. In Hull we had an At Home on Saturday afternoon, where every student was welcome to come for refreshments. Hull was very small when I got there, with about 260 students – now it's a big university – and we knew all the students who took some mathematics, not just the honours students. They would come and we would talk about all sorts of things – football, and sometimes even mathematics. Hanna carried on this open house when I was already in Manchester, and eventually she found more and more that she was the only one who smoked. So in 1954 she gave up smoking, the first female I ever knew who successfully did so.

*I believe you were in Hull when you had your Egyptian student Kamal Yacoub. I gather that he needed to be brought up to speed and you spent a lot of time with him over several weeks, during which he and Daniel – then quite a young child – became quite close. *

Yes, that's right. Shall I tell you the whole story of Yacoub? A friend of mine in London wrote to me saying this Egyptian student had come to study with him for a doctorate, so he had said, 'Well, start reading the van der Waerden,' the wonderful book on modern algebra. The student had gone away and started reading the book, but never come back to him to ask questions and eventually had a nervous breakdown. The Egyptian government immediately hauled him back to Cairo, but then he wrote to this friend of mine asking for a research problem, probably specifying the theory of groups. My friend wrote to Philip Hall asking for a problem but Philip Hall answered, 'If he's read my papers and not come up with a problem, I can't help him.'

So he wrote to me. Did I have a problem for this Egyptian student? 'Well, here's a little problem that I had worked on before the war. I have a few answers but still it might be suitable for the student.' So he sent it to his student but I'm afraid he gave away from whom it came, so the student wrote to me, and from then on we had an enormous correspondence. He sent me sheaves of paper with calculations that were largely not very good, but eventually he went in for the Master's degree in London. For this he had to do some papers which were sent to the examiners with only a number to identify them. I got two of them and I knew both the handwritings. One was John Britton, who was one of our star pupils in Hull and then in Manchester; the other one was Yacoub. They both passed their Master's degree.

Then Yacoub wanted to go on to a PhD, and wrote pages and pages. Eventually he said, 'I can't go on like this. I must now submit,' even though I warned him that wouldn't be any good. He was called to London for an oral examination by my friend and me, and we decided the oral was all right but he would have to do a lot of work on the dissertation. He said, 'I can't go back to Egypt without my doctorate,' so I said, 'Well, come to Hull. We'll work together' – this was in the long vacation. He took a room in Hull and came seven days a week for something like seven weeks.

Every morning at about 9 o'clock we went up to the study and worked together, and about 10 o'clock Hanna would prepare coffee and would send Daniel up. He was about three at the time. He would come up and say, 'Father, 'Coub, coffee,' and we would go down and have a coffee, and then go on working. Well, because Yacoub took a fancy to his 'Danny', he always brought him some chocolate. Daniel was a quick learner, so after a while he would come up 10 minutes after we'd started: 'Father, 'Coub, coffee.' Unfortunately for him, we had watches.

*In Australia you have continued to play a very influential part in promoting mathematics. You were involved in the Mathematics Competitions and you were very much concerned with establishing the Mathematical Olympiads in Australia, initially under the wing of the Academy. What part did you play in both of those? *

The Australian Mathematics Competition is by far the largest in relation to population, with close to half a million Australian participants and about 540,000 in all. It's at school level, from year 7 to year 12, and is excellently done. I still admire Peter O'Halloran greatly for getting it going. All I did was encourage him.

*What about the Olympiads? *

I came to that through the ICMI , the International Commission on Mathematical Instruction, which is a subcommission of the International Mathematical Union. I was for a while on the governing committee, and at one time the Finnish delegation proposed that the International Mathematical Olympiads should have a site committee to determine where the next one was going to be, instead of a decision from year to year by just the people who ran any one of the Olympiads. I drew up some rules for it and so on, and I was made chairman of that committee.

At the next Mathematical Olympiad, in Budapest, I managed to sell the idea. That committee does some very good work, because the run-up time to these Olympiads is more than one year and they have to know several years in advance where it's going to be. I also wanted Australia to participate, and so the Australian Mathematics Olympiad and the Australian participation in the International Mathematical Olympiad were started. At the same time – this was about 1980 – I pleaded for the 1988 International Olympiad to be held in Australia, because it was then the Bicentenary.

Australians have done tremendously well in the Competition, especially in the last one, where we had only six participants and we got six medals – two Gold, two Silver and two Bronze, I think. That was outstanding, the best performance. China came tops and then probably Bulgaria or Romania or Hungary or the USA, but we beat all European countries. And the youngest Gold Medallist was an Australian.

*When you arrived in Australia, weren't you already a Fellow of the Royal Society? *

Yes. I had been elected in 1959, on a Thursday, and left on the Sunday afterwards for my first visit to Australia.

*It wasn't long before you were elected to this Academy, in 1964, and Hanna was elected in 1970. You served on Council and were Vice-President between 1969 and 1971, and in 1984 you were invited to give the Matthew Flinders Lecture. I have often wondered how you selected a subject and a title in such a theoretical subject as yours for presentation to a general audience of scientists, many of whom would scarcely know what a group was. *

I had for years had a number of talks for general audiences. Two of them were geometrical – very elementary, all two-dimensional geometry – and those I developed and gave again and again. And one on women in mathematics I have also given quite a number of times. I chose one of the geometrical ones but I had an audience response of nil. The Academy never published it; it was published later elsewhere. But the other one I gave often, under the title 'Napoleon, My Father and I'.

*What was the theme there? *

It comes from triangle geometry. If you take an arbitrary triangle – all in the plane – and erect equilateral triangles on the three sides, then take their centres and join them, you get another equilateral triangle, whatever you started with. This theorem my father had discovered when he was working on some transformer for three-phase electrical current, which had been invented in the '70s by Tesla and had developed into the natural way of transmitting electrical power. If you look at the high-tension power lines anywhere, you find they come in multiples of three except for the thin earth-wires on top, which shouldn't carry anything.

My father had published this theorem in two mathematical articles in an engineering journal before the war. At that time one still got an honorarium for publishing an article. In fact, he got an honorarium for each, and from that he had built for him a music cupboard and a music stand, both of which I still have. I knew about this theorem of his but didn't do anything about it until he wrote a book on polyphase electric currents. He had found a book by a Scottish author – in English – and asked the Springer-Verlag whether they wanted a translation of it, because it seemed interesting to engineers. They said, 'No, we want an original book. Will you write it?' So he wrote it. But this was already in the 1930s so they said, 'Sorry, we can't publish a book from a Jew. But you can have it. Do with the manuscript as you like.'

So he brought the manuscript with him to Wales when he and my mother came, translated it into English and offered it to a publisher. It was published late in '39, in English. I read the proofs of it, just to help him, and that reminded me of this theorem, which I thought surely must be capable of generalisation to other polygons in the plane. I found that generalisation, wrote it up as a paper and then, much later, after I'd already given some talks on it – it's very suitable for a popular talk – I found that somebody had called it Napoleon's Theorem. Since then, many historians of mathematics have been trying to trace it back to Napoleon, without success. It is known that Napoleon was very mathematically inclined and had many mathematicians round him, and it is entirely possible that he knew about the theorem and may even have found it, but there's no proof of that. The first reference that I now know of dates from 1826 but the first ascription to Napoleon dates from about the turn of the century. So that is why I call the lecture 'Napoleon, My Father and I'.

*Your CV shows a very long list of honours and awards, the highest of which was Companion in the Order of Australia, which you received in 1994. We've heard from you about the Adams Prize, but of your many other prizes – and your six honorary doctorates – which would have special significance for you? I think some may stand out in your mind, if for no other reason than the dress that you were awarded! *

The first honour was the prize of the Wiskundig Genootschap te Amsterdam, the Mathematical Society of Amsterdam, in about 1948. That was based on one of their *Prijsvraagen*, prize questions. It was a group theoretical question which was fairly easy to answer so I went on and answered more questions that they hadn't asked. That first prize had no money attached, just my name in their books.

*Not like the Adams Prize? *

No. The Adams Prize was certainly something very good. I much enjoyed every one of the honorary degrees. With quite a few I had to give the address, and here at the ANU I had once to give the address when Huxley got his honorary degree – but they've never given me a degree.

In Waterloo I got a Doctor of Mathematics *honoris causa*, and they gave me the hood for it. But even better, in 1955 the University of Western Australia gave me the gown and hood, which I now occasionally wear at formal occasions. The other formal gown I wear is the Manchester one. I have the Cambridge one but that is not very spectacular. Both Manchester and Western Australia are full scarlet.

*Very impressive. Which has the nicer hat? *

Ah, I think the Western Australian would go with a square, but I always wear it with a cartwheel.

May I tell you about something that I specially feel honoured about. The Australian Mathematics Trust commissioned Judy Cassab, a very famous portrait painter in Sydney, to paint my portrait. She did that last year, for which I had to travel a few times to Sydney. We had a preliminary session, then five sessions of two hours each, with a break for her lovely coffee, and she talked all the time and asked me questions, and I talked all the time. And so the portrait is not a photograph – it's myself.

*You have had a lifelong interest in music. What instrument do you play? *

Well, when I was very young I was stupid, so that at one time an aunt of mine consoled my mother, 'He might still make a reasonable craftsman.' This went on until my tonsils were cut, and I suddenly woke up and thought I had been really stupid. At school I had been 30th out of 36, and then suddenly I shot up to 9th, and my father noticed. He took me to an opera, Mozart's *Seraglio*, and I could then whistle the first bars of the overture. That remains with me to this day. And then he took me to a symphony concert, pointed to the cellos and said, 'That's what you want to play, isn't it?' So I said yes.

My sister had started violin, and I started cello from the age of nine. My father was self-taught on the piano but very keen, so we played piano trios, starting with Haydn. We took our instruments and one of Haydn's trios to play for the 80th birthday of my paternal grandmother.

I didn't do much with my cello while I was in Freiburg but I took it up again, with a teacher, when I came back to Berlin. When I went to Cambridge I did only a bit, and of course during Army service I couldn't do anything. In Cardiff I played in the college orchestra, and then when I went to Hull I played in the college orchestra.

When I went to Manchester I didn't want to take my cello back and forth all the time, but by that time the eldest children had been encouraged to ask their parents for recorders for Christmas so the children got descant recorders and Hanna and I bought ourselves treble recorders and I then played quite a bit of recorder in Manchester. I later bought myself a second cello but I never took to it. It was a French one that was a bit small for me, and eventually I gave it to my daughter Barbara.

Later I joined the Canberra Symphony Orchestra. Barbara, when she came out between school and university, also borrowed a cello, and we were at the same desk in the Canberra Symphony for the few months she was here. I was in that orchestra until I was 80 years old, when they eased Dorothea, my second wife, and me out because they had enough younger players. I was quite glad, because my eyesight was not too good. My left eye had always been pretty bad – astigmatic – and my right eye was also not too good. It was the beginning of cataracts in both. If I had a desk to myself I was all right, but if I had to share desks I couldn't really see the dots very well, so I was not sorry. But since then I've had both cataracts removed and my eyesight is enormously better than it's ever been in my life. Especially my left eye, which had been so useless, is now essentially my better eye, especially for distance vision.

*In recent years you've devoted considerable time to writing about famous mathematicians. From what I've read, your interest may have been stimulated in the first instance by your research into the papers of Ada Lovelace, during your time in Manchester. What was the trigger to all that? *

Ada Lovelace was the only legitimate daughter of Lord Byron, the poet. Her mother had learnt mathematics and astronomy from William Frend, who was a bit of an academic maverick. One of the people in industry in Manchester, in writing an early history of computers, found that Ada Lovelace had been involved in popularising Babbage's engines, which were the forerunners of modern computers. One of her descendants still had papers in her attic that belonged to Ada Lovelace, so he asked for the loan of them, deposited them in the Manchester University library, and then came to the Mathematics Department, where he often came, and asked was anybody interested in looking at them.

I found that the papers were largely letters to her tutor, Augustus De Morgan, who was one of the great mathematicians of the 19th century in England. These letters were in some disarray and were not properly dated but I got their pages together and put practically all of them into chronological order. I was helped often by the watermark in the paper, which gave a lower bound for the date, and then by internal evidence such as the birth of the children of Ada Lovelace or of Augustus De Morgan, or replies to previous letters. There were also some papers that belonged to her daughter, who had been tutored by the first mathematics professor of Owens College [later the University of Manchester], and who later became an explorer.

I wrote a report on Augustus De Morgan's evaluation of Ada Lovelace's mathematics, which I got from the papers about him. Augustus De Morgan's widow had written a memoir of her husband which was a very good source, but there were other sources too. And so eventually I studied the whole history of that time. So I read about all these people and collected their biographies and everything I could about them, up to the generation of at least Augustus De Morgan's children, one of whom was William De Morgan.

William De Morgan was mainly in ceramics and found a kind of blue that is known as De Morgan blue. His blue tiles were used a lot in decoration of the dining halls of the steamships of the time and they are now collectors' pieces. When he retired he wrote, for his own amusement, a lovely novel set in 19th century England, and published it at his family's suggestion. And when I travelled to England my father gave me that novel by William De Morgan, which I read with great pleasure.

*Ada described Babbage's 'wonderful analytical engine'. You've seen one of these. There are two, aren't there? *

There are two. The earlier one is a difference engine, which eventually was built precisely to his specifications and is now in the Science Museum, in London. It works and it's very well worth seeing. Parts of the analytical engine were built and some parts made their way to Australia and New Zealand, where Garry Tee, at the University of Auckland, has written very interesting articles about them. He is in computer science but he's a very fine historian of mathematics.

*If you're going to do computations you have to have some way of inputting information. How was it done? *

With punched cards, like the Jacquard loom. In fact, Ada Lovelace wrote at one time, 'As the Jacquard loom weaves flowers and birds, so the analytical engine weaves mathematical formulae.' An Italian engineer wrote a description of the engine in French. That was translated into English, and Ada Lovelace wrote annotations which are very, very good, showing clearly that she understood what it was about.

*In retirement you work very hard every day, still publishing and still encouraging mathematicians. You have two offices, don't you, one in CSIRO and another in the ANU School of Mathematical Sciences, for your different activities. *

Yes. When I retired, Joe Gani had just become Chief of the CSIRO Division of Mathematical Statistics and he invited me to join the Division. So for three years I was a Senior Research Fellow, with an honorarium that was useful to have but not so big that I felt I had to spend my whole time there, so I spent my mornings there. After the three years were up, I became an Honorary Research Fellow, which I still am. That is to say, 'honorary' means no honorarium. The Division is now Mathematical and Information Sciences, and I have an office there where I do most of my editorial work. I have a typewriter there and a telephone, and a wastepaper basket.

I'm editor or on the editorial board or honorary editor of quite a number of journals, but my main editorial work is the Canberra circular of the IMU, the International Mathematical Union. After one of the general assemblies of the International Mathematical Union, the then committee decided to set up a subcommittee about communications between mathematicians. It appointed me chairman, but appointed nobody else and didn't even let me know. When I read about it in the proceedings a few months later, I said, 'Well, the best committee to run is a committee of one, because there's never any dissension. It's always unanimous.' It runs beautifully!

I wrote around to all the professors I could think of and the various organisations, the American Mathematical Society and so on, asking what was required. And on the strength of the answers I started a local newsletter, to be distributed widely four times a year, just as an encouragement to others to do the same and to exchange news. I sent it to all professors in Australia and New Zealand, all the members of the various international committees I could think of, and then everybody who asked for it – for free. The first one appeared early in 1972 and I'm now preparing No. 105.

The newsletter used to list future mathematical meetings all over the world, deaths of mathematicians as I became aware of them, and visitors to Australia and New Zealand. The visitors don't appear any more but later I added, at the suggestion of one of the recipients, honours awarded to mathematicians, such as honorary degrees, election to learned academies, and so on.

*How many are on your distribution list? *

Until No. 100 it grew from a bit more than 100 to over 1,100 but then the School of Mathematical Sciences found they couldn't really afford it any more. So now it is only electronically available, although hard copies go to countries where the World Wide Web is not readily accessible, and I've narrowed the numbers down to about 310 to 330. That is now financed by the International Mathematical Union.

*What about your work in the School of Mathematical Sciences? *

Well, I have a terminal there, where I receive and answer my email, and apart from that I mainly deal with my mail. What research I do, I do mainly at home.

*There are still many facets in your long life that we haven't touched on but we must draw to a close. Thank you very much for giving us this interview. *

Thank you for giving me the opportunity to talk so much!

**© 2021 Australian Academy of Science**