Interviews with Australian scientists

Professor Cheryl Praeger
Mathematician

Cheryl Praeger was born in Toowoomba, Queensland in 1948. In 1970 she received a BSc Hons from the University of Queensland, having concentrated on mathematics. Praeger was awarded a Commonwealth Scholarship to Oxford University where she studied group theory under Dr Peter Neumann, receiving a MSc in 1972 and a DPhil in 1974. She returned to Australia in 1973 to take up a position as a research fellow in mathematics at the Australian National University.

After 3 years, Praeger moved to the University of Western Australia as a lecturer in mathematics, where she continued her work on group theory, concentrating on group actions and combinatorics. In 1983 Praeger was appointed to her current position, Professor of Mathematics at the University of Western Australia. She has been the head of the mathematics department at the University of Western Australia (1992-94) and the inaugural dean of postgraduate research studies (1996-98).

Interviewed by Professor Bernhard Neumann in 1999.

Contents

Quite mixed forebears
Country mouse to would-be city mathematician
Honours studies and an undergraduate achievement
To Oxford, the long way round
A doctorate, a Stewardship and a marriage
A valiant rescue attempt
Professional and family growth in Perth
Applying group theory and combinatorics
Getting into the mathematics of computing
'Surely somebody can suggest an algorithm'
A mathematics professor of a new flavour
Participation and advice
A special relationship marked by an honorary doctorate
One of many side interests
Collaborations with a Who's Who of colleagues
An Australian representative and 'assertive' lecturer
Research students and barricades
More visits to and by algebraists
A wonderful tutorial after 16 years

Teachers notes to accompany this transcript.

You can order the DVD from us for $15 (including GST and postage).

Funded by 100 Years of Australian Science (National Council for the Centenary of Federation).

Quite mixed forebears

Cheryl, I would like to start with your ancestry. Your forebears were from Chemnitz, in East Germany, and from Ireland. Do you know anything about them?

I do know a little bit about my forebears. The last three generations have all been born in Australia, including all of my grandparents. It took me a long time to find out just where the Praeger side came from, because although I had a letter between my Dad’s brother, Uncle Doug, and his cousin in Germany, the town had been renamed Karl-Marx-Stadt after World War II and so I couldn’t find it by looking in current atlases.

My forebears from Chemnitz had moved temporarily to Dublin, where I think the husband was in the diplomatic corps. After he died, his wife and family stayed in Dublin for a bit and then moved back. But, according to family legend, the Praegers came out to Queensland from Ireland rather than from Germany.

Taken in 1952, this is my
mother's favourite
photograph of me.

The rest of my family seem to come from various parts of Great Britain. On my mother’s side they came from Wales and England, and my father’s father married a Julia Ross, whose family had come from Scotland. So that’s quite a mixture.

I am intrigued by your German connection. Your middle name, Elisabeth, is spelt with an ‘s’, the German way, not with a ‘z’, and the name Praeger seems to be German.

I have been told that the name Praeger – a coinmaker – came from Czechoslovakia.

Of your grandparents, you only remember your mother’s mother?

That’s right. All of the others died before I was born, but Grandma lived until I was seven. I was the first grandchild and so my parents, especially my mother, took me ‘home’ to Brisbane by bus about every six weeks. I saw a lot of my Grandma and of my aunts and uncles: my mother was one of six children, most of whom lived in Brisbane. One lived in Rockhampton and another in Perth.

So when you got to Perth you had family there.

Yes, a ready-made family: an aunt and a cousin. (My uncle had died before I went to Perth.)

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Country mouse to would-be city mathematician

I believe that as a child you lived in Toowoomba and other country towns until your father moved eventually to Brisbane.

My Dad worked in the Commercial Bank of Australia, being transferred every few years from one country town to another. We lived on the Darling Downs – in Toowoomba, where I was born, and then Warwick. I was about to start school in Warwick when he was transferred to Margate, on Moreton Bay just north of Brisbane, so I began school there at Humpybong State School – a wonderful name.

After four years we moved again, to Nambour, about 60 miles north of Brisbane. By that stage Dad was an accountant in the bank. He underwent manager training and expected to be moved as manager of a branch somewhere, but I think the new manager in Nambour wanted him to stay longer to help him settle in. The delay gave Dad the opportunity to undergo some extra study to become a naturopath, and by age 40 he was sufficiently far advanced with that to decide to change his career from working in the bank to being a natural healer. The official title now for the sorts of work he did is chiropractor.

Did you go to secondary school in Brisbane?

Yes. I was in the old Queensland system: eight years of primary school followed by four years of high school. When the family moved to Brisbane I had already done one of my high school years in the country, so I had just three years at the Brisbane Girls Grammar School, as a day girl. I had been booked in there for many years, because Mum and Dad hadn’t been certain whether the town they would be in when it was my turn to go to high school would have a good high school, but Nambour did. Being at the girls school was very good. I was a very shy student but there I felt a freedom to enjoy academic work and enjoy school to the full.

What was the teaching like at that school?

I had wonderful teachers. Many of them were at the end of their careers, having devoted their whole lives to teaching, and I benefited from their experience. After leaving school I kept in touch with my English teacher and my two mathematics teachers, in particular. The mathematics course was good but probably a little old-fashioned, and I didn’t get a chance to learn a lot of new mathematics. When I had finished my work I used to spend time helping the other students, so I suppose I developed teaching skills while I was at school. Sometimes I wish I had been given the opportunity to learn a little more mathematics at school, but it’s good to learn other things as well.

When it was time to leave school, did you get career advice at the school?

No, they didn’t have that there, but I went to the government vocational guidance section. My agenda was to find out about how to study mathematics further.

And the adviser said, ‘Oh no, a woman doing mathematics!’ or something like that?

Yes. I’d been well brought up and was a ‘good’ girl, very concerned about people, and my answers in their aptitude test indicated that I should go into some career working with people. But the imagination of the vocational guidance officer was such that he told me I should be a nurse – he didn’t ask whether I was scared of needles or blood! I decided that wasn’t something that I wished to do, so he thought perhaps I should be a teacher. I said, ‘Fine. How much mathematics can I learn in a course to become a teacher?’ The various options for that didn’t include many mathematics courses so I asked for some other possibilities. That was when he said – really – ‘Well, you don’t want to do mathematics. Girls don’t pass. Two girls came to me saying they wanted to do mathematics. I advised them against it but they didn’t heed my advice, they took mathematics. They came back a year later and said they should have listened to me, because they failed.’

Reluctantly he did show me an engineering course description, which I looked at very closely. It had mathematics in the first and second years, but not very much that I could identify as mathematics courses in the third and fourth years, and I decided that wasn’t quite good enough either. So I didn’t get enough information there at all and I felt very dissatisfied.

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Honours studies and an undergraduate achievement

You enrolled then in the University of Queensland, where there were already some women on the mathematics staff.

Perhaps Anne Street and Sheila Macdonald arrived in my second year. I don’t think I met any women on the staff in the first year.

Sheila started as Sheila Oates, became Sheila Macdonald and now is Sheila Williams, which is a very good case against a woman changing her professional name on marriage. Whatever is on the passport, the professional name should really stay put from the first publication on.

I learnt that from you!

Hanna, my first wife, was already married when she first published, so she used the name Neumann. But if she had already published seriously under the name Von Kämmerer I would have advised her to keep to that name. Well then, in the second year you had at least some women on the staff?

Anne Street took my class for a full year course of linear algebra and the beginnings of abstract algebra. She was a very popular and very good teacher. It was the first course that she had taught at the University of Queensland, and we enjoyed it very much. I was lucky that there were women mathematicians in the department so it didn’t seem such a strange prospect to be a mathematician.

At the time of my BSc
graduation in 1969.

There were two pure mathematics professors: the Professor of Number Theory, Clive Davis, taught me for the full year of pure mathematics in first year, and Fenton Pillow was our lecturer for the full first year applied mathematics course. I thoroughly enjoyed the pure mathematics because it was so exciting to learn about so many different types of mathematics – the number system and analysis.

Well, they are both retired now, as are Anne Street and Sheila Williams. They are all retired, these young people! Did you continue with mathematics for all four years?

Yes. I also did Honours in physics in my first and second years, but after the second year, when I had to choose, it was quite easy to choose to concentrate on mathematics.

After your third year you applied for a vacation scholarship at the Australian National University and spent eight weeks in my department in Canberra, interrupted when you went to New Zealand.

I had planned a four-week camping holiday travelling by bus with a school friend. ANU – you – were very accommodating and allowed me to go, as long as I could spend eight weeks here. So it seemed like I was here the whole summer, with just the holiday in the middle – a very wonderful experience for me.

And in the eight weeks you solved the problem that I had suggested, just to show you what research in mathematics was like, and despite being an undergraduate you got it published in one of the international journals – quite an achievement.

It was a great thrill.

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To Oxford, the long way round

When you finished your Honours year, we offered you a research scholarship at the Australian National University. But you won a bigger prize, a scholarship overseas.

That’s right. I took a Commonwealth Scholarship to Oxford. If I had been staying in Australia I would have liked to work here but I did want to see England, and Sheila Macdonald had strongly suggested to me that I choose Oxford over some of the other universities in the UK. The possibility of going to Oxford was too good to miss.

I travelled with Kay Vale [now Kaye Stacey, Professor of Mathematics Education at the University of Melbourne], who had also been the only girl in her Honours year at university, the University of Sydney. She too had won a Commonwealth Scholarship to Oxford, and I found out about her via one of my colleagues in the Maths Department in Queensland. Although we’d never met, we corresponded and decided to travel together. It was lucky for both of us to have a travelling companion. Only a few months before we were due to leave, we found out from Neil Trudinger, who was working at the University of Queensland that year, about the 1970 International Congress of Mathematicians, in Nice. Discovering that it was possible still to obtain some reasonable accommodation there, we decided to go to it.

It is lovely in the south of France. You must have come across some quite famous mathematicians at the congress.

Oh, that was wonderful. I heard lectures by Poincaré and Walter Feit.

What else did you take in on that trip?

We negotiated quite fiercely about where we would visit, each of us making compromises. We visited Bangkok for a few days. We wanted to travel from there to Athens, and we had to spend an afternoon in Hong Kong. We saw Athens for a few days and then we wanted to go to Nice, but because we were obliged to fly somewhere with a British air carrier we ended up going to Rome and travelling by train from there to Nice. So it was a huge adventure.

When you got to Oxford, which college were you in?

St Anne’s College.

That was Hanna’s college also – still called the Society of Home Students when she was there, but St Anne’s College by the time she took her DSc in Oxford. How did you choose your supervisor, or how did your supervisor choose you?

Oh, I think in Oxford the students didn’t get very much say. I knew that I wanted to study algebra. When I arrived I was interviewed by Graham Higman, the chairman of the Mathematical Institute. He said it was time I learnt some more group theory, and I said, ‘Yes, sir.’ I’d been telling everyone in Queensland I was not going to be a group theorist, I was going to study universal algebra and category theory – both things I’d heard at the summer research institute in Canberra when I was a vacation scholar. For a while I had no supervisor but then I heard it was going to be your son, Peter Neumann.

Did you have to go to Queen’s College to meet him, or the Mathematical Institute?

Most of the supervisions were in Queen’s College, but occasionally we would get some extra attention in the tea-room at the Institute – writing on the white tables. That was fun. There would be a supervision and lots of things written on the table and we would have to protect the writing from the caretaker, who really wanted to clean the table, until we had copied it down.

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A doctorate, a Stewardship and a marriage

You finished your DPhil in 1973. Did you attend the graduation in ’74?

No. I had a research fellowship at ANU and my doctorate hadn’t quite come through when I left Oxford. I wasn’t allowed to be paid at the rate of a postdoctoral person until I had taken my doctorate, so I had to take it in absentia. A pity, but I was pleased to come back to Australia.

And we were very glad to have you back. You were officially in my department for three years, I think, but you had some time off in the States. Where did you go?

I went to the University of Virginia, where Leonard Scott was organising a group theory semester. They had some money for some important mathematicians and each time one of them said that they would visit, some extra money was found from elsewhere. So they did have a small amount of money which they used to appoint two young postdoctoral mathematicians for the semester, and one of them was me. That gave me my first opportunity at teaching regular courses, while a long sequence of group theorists visited the university and worked there. It was a wonderful experience.

Then you came back to ANU. Did you stay at University House?

Yes. I had stayed at University House before going to Virginia. When I came back I had planned to become a tutor at Ursula College, and I had even been offered the position when Ralph Elliott, the Master at University House, asked me to become Steward. (He had arrived while I was in America and I met him on my return.) So I decided to stay at University House and I was Steward until I got married.

John took this photograph
of me on our honeymoon in
August 1975 at O'Reilly's
Guest House in the
Lamington National Park
in southern Queensland.

Your husband, John Henstridge, was also in University House, wasn’t he? I think he was a research student of Ted Hannan, in Statistics.

He was living in University House, and had been elected as a Fellow of the House – a result of involvement in some resident unrest before I arrived, I think. As Steward I was an ex officio member of the governing body in the House so I got to know him as a fellow-member.

When you got married, in Brisbane, Dorothea and I came to the wedding.

Yes. That was in August ’75 and you proposed the toast to the bride and groom.

Ah yes. I still remember making a computation that you were one in a million, or one in 10 million or something – anyway, that it was really a unique thing.

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A valiant rescue attempt

While you were in Canberra as a research fellow, you won a medal for lifesaving. Tell us about it.

This was a Certificate of the Royal Humane Society of New South Wales. As Steward of University House, I had been asked by the Master to organise an excursion to the coast, because there were a lot of residents in the House from overseas who had not been outside of Canberra. So that Saturday about 20 of us went down the coast to Batemans Bay and then north to Pebbly Beach – a very beautiful place, with lots of kangaroos underneath the trees just at the back of the beach.

It was a big day. I had to get a special licence so that I could drive one of the university vehicles, a Volkswagen Kombi van. It was full of people, as various friends and colleagues came as well, including a PhD student in nuclear physics, Kyou Il Hong, from South Korea. Kyou Il had lived in Pusan and he told me that he was a very good swimmer, having swum in the sea south of Pusan very often. I think he missed this, and so he went in swimming before many of us had decided to venture in. While we were all sitting on the beach enjoying the sunshine, Jenny Seberry, a colleague from the Maths Department, noticed that Kyou Il was waving. We waved back but then realised that this was a cry for help. He was quite a long way out. A number of us jumped up and ran down the beach towards the sea. I was probably ahead of everybody else and I started to swim out. After a short time I turned around and noticed that the others had gone back to shore because there was a rip. I was just horrified to see how far out I was, in the short time I had been swimming. So I had been caught in the rip also.

I had to make a decision then whether to go out to Kyou Il or go back, and I decided to go out, because he needed me. When I got out to him he was fine but tired, and I was starting to panic because I didn’t really know how we were going to get back. I started swimming with him, pulling him with me and trying as hard as I could to go across the rip towards the shore. Together we managed to come to a sandbar about 50 metres off the shore, but the waves were terribly big and were dumping. We got caught in one of them and were turned over and over, and I lost my hold on him. Within what seemed to be seconds, two men on surf skis were there and I asked them to go and find Kyou Il. One of them continued out while the other one took me into shore, but they didn’t find him and after a whole week his body was washed up on one of the nearby headlands. It was a terrible thing. I’d only known him for a couple of months, and I had encouraged him to go on the trip, thinking it would be such a lovely opportunity.

The sea out there can be quite treacherous.

I had no experience of that before.

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Professional and family growth in Perth

Tell us about you and your husband going to Perth.

While John was still doing his PhD, I was offered a short-term position at the University of Western Australia. After John also was offered a tutorship for a year, we decided to go, as it was very difficult to get teaching jobs just at that time. John had to finish writing his thesis during that first year, so he completed it over the summer at the end of the 12 months in Perth.

When we arrived we were offered either a private flat, which the university owned, or accommodation in St George’s College, the oldest college at the University of Western Australia. We decided to stay in the college, because we liked the vision of the Master of the college at that time, Peter Simpson.

And you had always been involved with younger students, so this was very natural. I seem to remember we visited you at the college once.

That’s right. It was probably during an Australian Mathematical Society conference in Perth in May ’76, just a few months after we’d moved there.

When you started in Perth, Larry Blakers would have been head of department. I think I knew all of them there. It is a very nice university, with some beautiful buildings and grounds, and a very nice Mathematics Department.

Yes, thanks to Larry’s planning. He was very proud of the Mathematics Building.

Your job originally was a temporary one, wasn’t it?

It was called a ‘special temporary lectureship’, and it was for two years. During the second year I applied for a tenured lectureship which had been advertised. During that year also, Chuck Miller arrived at the University of Melbourne and offered me a three-year lectureship. I really wanted to go to Melbourne: there was a very nice group of people I could have worked with there, whereas in Perth I was a little isolated. I found it difficult to encourage my colleagues to talk serious mathematics with me, leading to joint research or serious mathematical discussion. But John very much wanted to stay in Perth to be involved in applications of statistics. Terry Speed had been appointed to the Chair in Statistics not too long before we arrived in ’76, and he wished to start up a statistical consulting group. John was very interested in working in such a group so we decided that if I were offered the tenured job we would stay in Perth, and if not we would go to Melbourne. I was offered the tenured job and so we stayed in Perth.

I hope you’ve never regretted it.

No. It’s a very nice place to live, and with modern electronic communications it is not nearly as isolated as it seemed when we first went there. We did move house, though. In 1978 we moved from the college to a small unit, and our first child, James, was born in ’79. Then our second son, Timothy, came in 1982 and we moved again – the unit was just a bit small for us. We couldn’t close the door because of the cot. Our house now is lovely, and very nice for a family with teenage children who want their own space.

Your sons are now big. The elder one has finished his first year at university?

No, he is now finishing his third year, so he will have completed the requirements for a Bachelor of Science degree. He has two years to go to finish his double degree in engineering and science. The younger one is – right as we speak – sitting for one of his year 12 examinations. We hope he will want to go on to university.

John, our sons James and Tim and
me on the top of Cradle Mountain in
Tasmania on day 10 of our 12 day
hike on the Overland Track in
January 1999.

They sail with the local Sea Scouts, I believe, and also your family and I share a love of cycling, of the ordinary push-bike. In fact, there is a lovely picture of the four of you on two bicycles.

That’s right. We used to cycle to work, which worked very well with two adults: one child on the back of each bicycle. But when John left the university to work for a company called Siromath and was no longer on the campus, I had to transfer children between the childcare centre and kindergarten in the middle of the day and then take them home. I really didn’t want to have to drive a car the short distance to collect them, so we looked around for other ways to manage two children and one adult on one mechanical contraption. The solution turned out to be a tricycle. John constructed an aluminium frame at the back of it, fitting on two cut-down bicycle child seats for the two boys, and that’s the image that many of my colleagues at the University of Western Australia have of me and the children. They still think of them as toddlers, even though they’re 17 and 20 now.

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Applying group theory and combinatorics

One thing a mathematician learns very early is never to talk mathematics to people except when collaborating with a colleague on something mathematical. But now we must put in a little about the particular mathematics you have been working on – even if some of the technical terms are a bit difficult. Probably some of your most significant work has been in permutation groups.

Yes. The common thread through most of my work is group actions, both for their own sake and to understand the structure of other objects which have some symmetry.

That got you into combinatorics as well, which got you into a mathematical theory of weaving, did it not?

That’s correct. I was asked to referee a paper by Jan Hoskins for the proceedings of a combinatorics conference at which I had heard her talk about the mathematics of weaving. It led to my working with Anne Street and Jan on some problems of weaving. I became more interested in the way this very simple mathematical model applied to the weaving process, and the direct relationship between the mathematical model and the sorts of diagrams that weavers would draw up for themselves to enable them to create a pattern and then decide how to tie up the loom and weave that pattern. It’s very beautiful and it’s so easy that I began to be asked to talk about it to high school students and then mathematics teachers, and it became one of my hallmark lectures. Everyone was asking me to give ‘that’ lecture.

It is quite serious mathematics but still something that a general audience can understand. You have been interested also in group theoretical aspects of designs.

Yes. My interest in design theory, the theory of combinatorial designs, came about in two different ways. The first was indeed looking at the symmetry of designs, arising first from work of Peter Cameron. But I also became involved in designs used for experimental layouts for agricultural experiments that statisticians would analyse – to help statisticians to understand what symmetry groups were involved in the particular experimental designs which they were interested in. This became a collaborative work with Terry Speed, for whom it was first a teaching and then a research interest. He was trying to understand what types of designs statisticians might be interested in, to get a feeling for the class of designs that they needed to understand: he went away for a year in 1978–79, and every time he found a new design in the research literature somewhere he would send it back to me and say, ‘Analyse this one.’ The object was to analyse the variance of this design, and in the analysis we could point out and identify the various factors which were significant in trying to analyse data arising from using this layout, for example, comparing the yields of different varieties of wheat.

Did you at that stage collaborate with your husband John?

I spoke a lot with John, but our only joint paper is in group theory. It was John who passed on Terry’s question to me – John was attending an Honours course that Terry was giving in experimental design. He came to me and said, ‘Well, for this particular design I think the symmetry group is a direct product. But what about this other experimental design? What’s happening here? I don’t understand it.’ I was then led to explain to Terry what a wreath product was – I think even some group theorists don’t like working with them so much.

And John later created his own consulting firm, which goes from strength to strength.

Yes. He worked first for Siromath – a private company set up by CSIRO – but about 10 years ago he set up his own firm, Data Analysis Australia. It is a mathematical and statistical consulting company.

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Getting into the mathematics of computing

I believe you got also into the mathematics of computing. Why was that?

After my appointment to the Chair in 1983, I felt a responsibility to introduce computers into the teaching of mathematics and I knew that I would only have a really serious interest in doing this if I also had a research interest in computation. Then Gordon Royle, a PhD student, arrived and said he would like to do ‘any project whatsoever, as long as it requires the use of a computer’. Gordon was very interested in discrete mathematics so I contacted colleagues in Melbourne and Canberra to ask for some suitable area in which to work, and he ended up by being supervised jointly by me and Brendan McKay, of ANU, on a project involving vertex transitive graphs. That was a link between combinatorics and group theory, involving enumerations of some of these objects by developing algorithms and implementing them on a computer. So my first introduction was having a PhD student in the area.

I next thought I needed to learn about groups on the computer, so John Cannon very generously offered to visit Perth for two weeks and run some workshops to teach us about his then new system, CAYLEY, named after the 19th century mathematician. While he was there, he would mention various aspects of the system which didn’t run as well as they might – areas where there weren’t, to his mind, optimal procedures for doing various computations involving groups. I picked up on one of these and developed an algorithm, in very close consultation with John. I had no idea how a computer thought about a group in a particular instance, so he would tell me what the computer knew about the groups and what could be done easily and what would take longer to do. And I developed this interest, starting with this baby problem that John had given me.

Then he suggested that we might write a book together. I visited him in Sydney and we produced a possible schedule and obtained a contract to write a book. John gave me all of his lecture notes and, by working through the notes and converting them into several chapters of a book, I learned about algorithms for computing with groups on the computer. Unfortunately, that project didn’t eventuate in a book – it wasn’t a high enough priority for either of us, I guess – but it taught me a lot. I understood a lot of the algorithms which were used and which ones were more expensive than others, because I had to learn about them in such detail.

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‘Surely somebody can suggest an algorithm’

How did you get in touch with Joachim Neubüser, the mathematical computing expert at the Rheinisch-Westfälische Technische Universitat, in Aachen?

I met Joachim Neubüser at a computational group theory week at Oberwolfach in Germany in 1988. John Cannon encouraged the organisers to invite me, and I gave a talk about the algorithm which I had developed with John’s encouragement and then developed further with Charles Leedham-Green and Leonard Soicher in London during the year I was on study leave in England. One evening in Oberwolfach, when a group of us were talking after dinner, Joachim said, ‘There are so many wonderful algorithms which work very efficiently for computing with permutation groups, but many people want to compute with groups of matrices. We have no very good, general-purpose algorithms for computing with matrix groups. Why, we can’t even decide efficiently whether a collection of matrices would generate a really large group, a group containing all of the matrices with determinant one – a special linear group. Surely somebody can suggest an algorithm by which we could at least manage to recognise a special linear group.’

Because of my involvement with John Cannon, I had a picture immediately that the algorithm should look, in a way, like the randomised algorithms for recognising whether a group of permutations was the full alternating or symmetric group – the really big groups. They operated by making a random selection of permutations and understanding that some permutations were actually very common in the alternating and symmetric group and very rare in other permutation groups. I thought, ‘Maybe we can find some matrices which are very common (so we can find them easily) in these very large groups, but are actually very rare in any other matrix group.’ Your son Peter Neumann was also in that group speaking after dinner, and when I explained that this was the sort of algorithm we would need, Peter very quickly thought about what those special elements ought to be. Within a week we worked out what the algorithm ought to be like, but it took two years to completely work out the fundamental theory which was going to prove that, firstly, it would work, and, secondly, it would be implementable and work in practice. That was the first of the new range of general-purpose algorithms which have been developed for computations with matrix groups.

Alice Niemeyer, from Aachen, was a pupil of Neubüser. Was it through him that you met Alice in Canberra?

I first met Alice in Canberra after she had completed her Diplom with Neubüser in Aachen. She and her colleague Werner Nickel had come to ANU for one year and then decided to return to do their PhDs here. So they were working as students of Mike Newman when I visited Canberra for your 80th birthday celebrations in 1989.

This family photograph (from left, Cheryl,
James, John, Timothy) was taken on
the weekend before my DSc graduation
at the University of Western Australia
(April 1989).

They had been involved with the new group theory system, GAP, for their Diplom program projects. At a 'chocolate party' organised by the graduate students, they said, ‘Has somebody got any problem at all involving groups that we can try out, using this new GAP system?’ I said, ‘Of course I’ve got a problem.’ The problem involved groups acting transitively on the lines (or blocks) of designs, and I knew exactly what computations were needed to decide whether any of these designs existed or not. It was down to a computational problem.

I eventually persuaded Alice and Werner to take on the problem – that it would not take 100 years of CPU time, it would be feasible. Indeed, it was feasible, and we discovered and characterised this very beautiful class of designs. The result was that Alice and Werner expressed some interest in working with me after the completion of their doctorates. As it turned out, I got a research grant and Alice came to work with me in Perth as my postdoctoral fellow but Werner decided to return to Germany.

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A mathematics professor of a new flavour

Could we look some more at your career. From your special temporary lectureship you became a tenured lecturer. Then did you go straight from lecturer to professor?

No. I had been promoted to senior lecturer by the beginning of 1983. Larry Blakers retired at the end of ’82 and the university decided to advertise a Chair in any area of pure or applied mathematics. John Mahony was still Applied Maths Professor and Phil Silberstein was Pure Maths Professor, so the university weren’t really sure what other flavour of mathematics they wanted in the new professor and they made a very general advertisement. Terry Speed suggested that I apply for the Chair, although I hadn’t really thought seriously about applying for Chairs at that stage. Timothy was only a few months old, James was 3½, and I had only just been promoted to senior lecturer. But I thought about it very seriously over the time in Thailand and decided that I had something to offer. I put in my application at the end of February – a month or two after becoming a senior lecturer – and in the October I was interviewed and offered the Chair. So I was a senior lecturer for less than a year.

So you became the only female mathematics professor at that time – the first after Hanna. And also you got into administration, not only as head of your department for quite a while but then as a Dean.

I was asked whether I would be interested in becoming the inaugural Dean of Postgraduate Research Studies at UWA, and the idea took my fancy. I have a great commitment to postgraduate students and I wanted to assist them and the university to provide a very good research environment for the students, to make sure that there were appropriate workshops and procedures, policies, in place to support them during their candidacy. I really enjoyed my time there. I was very tired, because I was working as a half-time secondment in the position as Dean and was still half-time in the department, probably doing a 70 per cent job in both spheres. So my 2½ years as Dean was about as much as I could manage and stay alive.

Two 70 per cent jobs plus a family and all your other interests is quite a heavy load, yet your research did not suffer.

Well, I had two postdoctoral assistants during that period, and at the beginning of the time I still had five postgraduate students, so in some ways they helped form the agenda. They had their own time deadlines and I had to meet them.

Are you still a member of the Senate at the University of Western Australia?

Yes. I have been an elected staff representative on the University Senate for two or three years, with a year to go. It is very interesting.

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Participation and advice

You have followed Hanna in another way, by being elected a Fellow of this Academy. She was elected in about 1969, when she was 55 years old.

I was elected in 1996, when I was 47.

Since then you have been a member of Sectional Committee 1, and you have just been elected to the Council. You’ve held also many advisory positions. For example, you were a member of the Prime Minister’s committee, weren’t you?

Yes. It was set up as the Prime Minister’s Science Council. During the time that I was a member of it, it became the Prime Minister’s Science and Engineering Council, and it would have had two more names since then. I was invited to membership there towards the end of 1989 and was a member for about 2½ years. It was a wonderful experience of a very good, non-partisan way for science, engineering and technology in the country to provide advice to a range of senior Ministers in the government – an excellent initiative.

You are deeply involved also in the Australian Mathematics Trust, which brought you here yesterday for its board meeting. How long have you been with the Trust?

I’ve been a board member since the Trust was set up in 1992. I remember Peter O’Halloran asking me for some suggestions of women who might be on the board. I gave him names of other people, but he then invited me to be a member. I have enjoyed that involvement very much indeed, because I feel very sympathetic with the aims of the Australian Mathematics Trust and it was a great act of generosity and will by the various components, the subtrusts, in coming together to form the Trust. I greatly admired Peter O’Halloran’s vision, his energy, his total commitment to providing a mathematics challenge for young Australians. I really wanted to support that in whatever way I could. Probably the Trust activities have always been ahead of their time for setting the agenda. The Trust now, I believe, has very strong support from government for its altruism and the quality of the programs that it offers.

The Trust has gone from strength to strength, beginning with the Australian Mathematics Competition, incorporating the support of the Australian Mathematical Olympiad and moving on to enrichment activities for both students and teachers. I am a strong believer in the Trust, although I am only on the advisory committee.

‘Only’ on the advisory committee! You are an integral part of the Trust. There are the B.H. Neumann awards and the Bernhard Neumann medals. In 1977, the participants of the first International Combinatorics Conference that was held here were taken by bus to see the University of Canberra, and I remember Peter O’Halloran’s talking with you about his vision of a national competition which would involve all Australian children. I believe that the Australian Mathematics Competition began really from about that time.

When the firm that originally supported the Trust moved out, Westpac came in. The combination of the University of Canberra’s resources and Westpac’s completely different but complementary resources has been marvellous. I very much value my connections with the Trust, where now I represent the Canberra Mathematical Association. It’s very good that you are on that board, because it brings you here from time to time!

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A special relationship marked by an honorary doctorate

You developed a special relationship with a Thai university. Did that have anything to do with your stop off in Thailand on your way to Oxford in 1970?

The relationship developed with a relatively new university, the Prince of Songkla University, which had started off in Bangkok and had then been relocated further south. At first the only campus was in Haad Yai, in the neck of Thailand going down towards the Malay Peninsula, although now there are three campuses.

The mathematicians there had asked for some interest from the mathematicians at the University of Western Australia. There was already a relationship between the chemists, with joint research projects and students coming to Perth from Haad Yai to study. Terry Speed was the first mathematician to travel to Haad Yai, in the summer of ’81–’82, and he was asking the department if someone else would be interested to going there in the summer of ’82–’83. John and I were both very interested and we went there, travelling with three-year-old James and our seven-month-old baby, Timothy. This could only happen because my parents agreed to meet us in Singapore and travel with us, as a sort of a holiday, up the Malay Peninsula. My mother then stayed a full month with us at Haad Yai, but my Dad had to return to work in Brisbane.

We had a whole month working and talking with the mathematicians at Haad Yai and arranging for the next part of the relationship – what sort of mathematician they would like to meet with, what their problems were, who might be able to benefit from visiting the University of Western Australia. I didn’t return to Haad Yai but various members of staff from PSU visited Perth, where I made sure they formed the right links with mathematicians and were looked after properly.

Didn’t you also have research students from there?

Not actually research students, but while I was in Haad Yai the first time I had worked together with a staff member, Chaufah Nilrat, on a problem in combinatorics – we published a paper deriving from that – then we worked on another problem when she visited Perth for two months a couple of years later. It was rather difficult for them, because one of their priorities had to be to translate mathematics texts from English or other languages into Thai and so a lot of their time, apart from teaching, went into preparing resources for the next generation of students in Thailand.

My next association, in 1993, came as a great surprise. I received by fax a letter from the President of PSU saying that they wished to award me an Honorary Doctor of Science in Mathematics, and that this would be presented by the King of Thailand some time in September – the timing of it depended on his diary.

And so you got your DSc honoris causa in mathematics. But in the end the King couldn’t come.

Taken in September 1993 at the
graduation ceremony at Patani Campus
of the Prince of Songkla University in
southern Thailand. The three men to my
right also received honorary doctorates,
and the two men to my left received
excellence in teaching awards.

That’s right. He was represented by the Crown Princess, who is very popular, a wonderful person. The presentation took place at the campus in Pattani, on the coast. It was the one graduation ceremony for PSU for that year: in three hours she presented 1,200 degrees. It was so well organised, the most efficient ceremony I’ve been to. Beforehand we had to tiptoe on the outside of her red carpet, because we weren’t allowed to stand on it. It was great fun. The whole family came for the presentation, and it was wonderful to see all our old friends again.

So now you have got two doctorates of science, having already taken an earned DSc at the University of Western Australia in 1989. I was one of the examiners.

Which I wasn’t supposed to know about!

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One of many side interests

One of your many side interests has been music. When did that start?

My mother tells me that when I was two years old I used to ‘practise the piano’ on the kitchen table. My mother’s youngest brother, Uncle Darcy, played the organ at a central Brisbane Baptist Church that we went to whenever we visited my Grandma. I could see him up in the organ loft at the front of the church, and I think I always wanted to play the piano. So my mother put away the money that the government used to give mothers in those days – it was to buy us milk, I think – and when I was eight years old she was able to buy a piano and I could begin to learn to play it.

We were still living at Margate at the time, where Jean Skennerton (a very good teacher) had just begun teaching when her children were old enough. I had a private lesson and then Jean organised a community theory and band afternoon each week. It was good fun and I loved it.

You gained a good qualification. You must have been good on the piano.

I just managed to do the Associate of Music Australia, the AMusA, in piano performance. When I was quite young I thought about taking up music seriously, but at age 11 – because of a certain amount of disobedience – I had an accident in a pool and dislocated my finger and fractured it in a couple of places. It took two years of very serious physiotherapy for me to get it strong enough and straight enough to be able to play the piano again. So it was my ambition to play the piano but I certainly couldn’t have taken it up professionally.

But you got much joy out of it. Do you still play now, in your church?

Occasionally I play the organ or the piano at church, but not as much as I used to.

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Collaborations with a Who’s Who of colleagues

You have, over the years, collaborated with colleagues in many countries – Israel, the United States (a number of times) and England. Have you been to Italy?

Only briefly, and I haven’t really worked with many Italian mathematicians. I’ve been to Germany.

The last time I saw you in Germany was at the Mathematics Research Institute at Oberwolfach, where you were with Peter.

Yes. Peter, Jason Fulman – a former student of Persi Diaconis – and I were there for five weeks working in the RIP program, which I think really means ‘Research in Pairs’.

Peter invited me to come there from the International Congress of Mathematicians in Berlin last year. We had some chamber music, didn’t we?

Yes, in the music room next to the library.

Your collaborations have been with very many mathematicians in many fields.

It’s a bit hard to know why it happened that way. My first collaborative work, apart from my position as a student, happened while I was a research fellow at ANU. Just after I returned from America, Marcel Herzog arrived as a senior research fellow. Having just come back after six months in the army, he wasn’t really into serious mathematical work but wanted to get back into research work. He asked to see my papers, began to talk with me about permutation groups – the area of my doctoral work – which he wanted to learn about. So we worked together, at the beginning on a lot of problems which arose from my work. I learned a lot of things from Marcel.

Was it he who then attracted you to Israel?

Yes. In 1980, John and I and James – as a 20-month-old baby – visited for a month to work with Marcel and to meet his former students and colleagues. I have since returned to work with Avinoam Mann, in Jerusalem.

Your long list of publications shows that you have collaborated with a fantastic number of people, really a Who’s Who of algebra, combinatorics – everything! Clearly you have always been at least an equal partner, and often the senior partner.

The collaborations have been different in nature, yes.

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An Australian representative and ‘assertive’ lecturer

And also you have represented Australia in various overseas activities, haven’t you?

Yes. I represented Australia at the Pan-African Mathematics Conference in Morocco in 1995. I had just finished my term as President of the Australian Mathematical Society and I happened to be in Europe on study leave at the right time, so I attended that very interesting conference. I think it’s been my only contact with a lot of African mathematicians and African mathematics societies.

They have an intriguing set-up there, especially in regard to the history of African mathematics. Mathematics not only in South Africa but also in the rest of Africa is very interesting. It was probably the rest of Africa mainly represented in Morocco.

Yes. It was at that meeting – the first occasion on which South African mathematicians had been present – that the Pan-African Mathematics Congress decided to accept the South Africa Mathematical Society as members. There was a diverse delegation from South Africa involving both black and white: English-speaking, Afrikaans-speaking and the black mathematicians. It was very, very good.

Was Egypt represented? Two of my PhDs were Egyptians, who returned to Egypt.

I believe it was. My involvement, I suppose, has been more with the Middle East than with Africa. I have visited Israel and it turned out that my very first PhD student is an Israeli citizen. She is an Israeli Arab who had emigrated with her family to Perth and decided she wanted to do a PhD. After completing her PhD with me, she returned to Israel and is now a deputy vice-chancellor or deputy vice-president of Bir Zeit University in Ramallah, on the West Bank – a very fine woman.

You have also visited Iran, I believe.

Yes. At the International Congress of Maths Education in Adelaide in 1984 I met again Akbar Hassani, who had been two years behind me when I was a student in Oxford. As a result, he asked if he and his family could spend their sabbatical year in Perth. They came in the early 1990s, and after his return he repeatedly invited me to visit Iran. It was very difficult for me to do so because I was head of department, but eventually in late ’94 I found the time to visit Iran for a few weeks. And I gave numbers of lectures while I was there!

Ah yes, they do work one hard. But how did you get on with the dress in Iran?

I am standing outside the lecture room at the
Institute of Theoretical Physics and
Mathematics in Tehran with the female
Iranian graduate students who attended my
lectures there in November 1994.

Oh, I’m not very competent at wearing Islamic dress. I found it very difficult to keep my hair from showing from underneath the scarf. Eventually the few women mathematics research students who were attending my lectures explained to me how to make attractive headdresses – comparing the different types of headdress each of them was wearing, and each deciding that hers was the best. If I went there again I would try to get an authentic headdress, which looked very much easier to wear than my silk scarf. I took a little while to get used to what I should be wearing where, and to be able to wear such a lot of clothes comfortably while lecturing. The comment was made to me by both male and female mathematicians that I lectured in a very ‘assertive’ manner. I thought I was just trying to communicate.

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Research students and barricades

What other countries have you visited for some time?

I’ve had a lot to do with mathematicians in the Philippines. A very strong relationship between Australia and the Philippines was started by John Crossley from Monash University, who encouraged me to first of all accept two research students from the Philippines in 1986, Florita Capao-An and Luz Nochefranca. They came to work with me for six months, Luz originally to write up her thesis and Florita to begin her research program. I ended up suggesting a new research project for Luz after she pleaded with me to be allowed to sit in on the supervisions with Florita and to be given a project in that area. So I began working quite intensively with Luz, and she visited me on two occasions for over a year, each time as a postdoctoral researcher. On the other hand, Florita decided that she would like to work on crystallographic groups, with my support. She returned home, got married, had three children and still hasn’t finished her doctoral work. Those were my two first contacts, and after they returned to the Philippines John and I visited for a month in early 1987. The children stayed with one set of grandparents, were transferred by plane to John’s parents in Adelaide, and then flew home by themselves to be met by us just after we had arrived back.

Our visit to the Philippines was very exciting. While we were there, only one year after the People’s Revolution, we listened to stories from every mathematician about what they had done during the very tense period just before Cory Aquino came to power. We visited Mindanao, one of the southern islands, for a few days to visit a university in Davao, and on our return the flight was very late. Apparently every flight was very late because there had been an attempted coup and the rebels had almost taken over an air force base which was adjacent to the civilian airport in Manila. When we eventually managed to land, Luz and Florita were there to take us home because they were very concerned at our trying to get between the airport and the university by ourselves. It was very difficult to get back to the university because of barricades on every road the taxi tried to take. There were young men with red bands around their heads and we weren’t quite sure which side they were on, but we managed eventually to get back to the university. We were then told that we must be very careful and we should move offices to one particular side of the mathematics building, because the offices on another side were ‘within range of the military’s guns’ – which were trained on a television station which had been captured by the rebels.

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More visits to and by algebraists

I have met you at conferences in yet another country, South Korea.

Yes. I have been to three conferences there.

You were invited by Ann Chi Kim, weren’t you?

Yes. I met Ann Chi when he arrived in Canberra – in 1975, possibly – to work with you in mathematics. It was after Kyou Il’s death, I remember. At the end of 1977, John and I visited Ann Chi in Pusan. It was our first visit to South Korea and we were the first Western mathematicians to visit that university. It was a very nice time. Ann Chi met us in Seoul, and in the train on the way down to Pusan he told me that I would have to give a two-hour lecture. In some surprise, because I was used to lecturing for a little under an hour, I started preparing a two-hour lecture. But by the time we got there, I had only enough time to give a 30-minute lecture!

I briefly visited him in Pusan – after a conference in Singapore, perhaps – to encourage him to return to research. He had got too much into administration. But he has encouraged a lot of his young people to study wherever he thinks best for them, through his many contacts overseas.

Yes, and encourages them back again. He has been a wonderful influence on Korean mathematicians and mathematics.

Then didn’t you have connections also with Vietnam?

I have never been to Vietnam, but Ngo Duc Tan from the research institute in Hanoi visited me for two months and we worked together. I still have email contact with him. His son Ngo Dac Tuan was an extremely good mathematician who won a Gold Medal at the International Mathematics Olympiad a few years ago and was hoping to study at the University of Western Australia. He won a scholarship but because of a health problem we lost him. He ended up doing his degree in Paris, but he may still come to work with me next year to do his Honours project.

And it was in Perth where I met some of the Vietnamese colleagues.

That’s right. The President of the Mathematics Societies of Ho Chi Minh City and also of Hanoi were at an Australian Mathematical Society conference in Perth in ’92. One of those people, as well as being a mathematician, is a minister in the government. I met him again when he visited the University of Western Australia on other occasion.

You must have been to Singapore too.

Oh yes. I’ve been there a few times.

Well, there are few places you haven’t been to yet, and very few algebraists you haven’t worked with. Is there anything I haven’t covered?

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A wonderful tutorial after 16 years

One thing is my association with Russia. In 1974, when I was a research fellow in Canberra, you asked me to consider writing a letter to Professor Kaloujnine, in Kiev. He had written to you, saying he would like to hear from some young Australian mathematicians about their research work. I replied, telling him what I was doing and saying that I would very much like to hear back from some young Russian mathematicians. But I heard nothing. Then, 16 years later when I visited Russia for the first time, I was collected from the airport by Igor Faradjev and Mikhail Klin. Misha Klin said to me, ‘I read the letter you wrote to my professor.’ He had been a student in Kiev at the time, and it was impossible for them to reply. My information got to them but they weren’t allowed to write back.

Misha knew a lot of my work and the work of my colleagues, but because I am not a very good linguist I hadn’t read the Russian papers and so I didn’t know a lot of the work of the Russian school. I had one week in the system studies laboratory in the Academy of Science in Moscow, talking with a lot of the people there, and one particular day I was taken by Misha Klin to see the Kremlin and to an art display, and then to his home. We began mathematical work at 3 o’clock in the afternoon and worked without stopping for eight hours. Misha wanted to tell me about all of the relevant results by Russian mathematicians, of which some was in parallel with developments in the West and some was different, as you would expect. It was fascinating and exhausting, but a wonderful tutorial. I think we got back to my hotel in the centre of the city about midnight – I almost missed the last train back! That was a very interesting trip.

I had planned to go to Russia to work with Sasha Ivanov, A A Ivanov. He had read some of my work and had discovered a mistake in a paper I had written in 1984, and he had written a very substantial paper picking up on this mistake and doing the sort of work that I should have done, I guess. He was allowed, therefore, to send me his pre-print in English in about ’85 and I was able to correspond with him with very brief letters. In 1988, when I was in England, I received a phone call from him – from Eindhoven, in the Netherlands, where he was on his first visit outside of the USSR. He said he was there for only a number of weeks. I was giving a lecture in Cologne and then, two days later, a lecture in Essen, so I took the train from Cologne to Essen via Eindhoven – not a very direct route – for the opportunity of meeting Sasha for about half a day, and consequently I visited Moscow the following year.

Fantastic contacts, very impressive. Well, your care for students, your mathematical and other interests have brought you membership of the Order of Australia. That came this year, didn’t it?

This year, in the Queen’s Birthday Honours List. It was a great surprise.

It was less of a surprise to me, although I had hoped for something higher for you. But there is still time. Thank you very much for the opportunity to interview you. It has been a great pleasure. After all, you have long been essentially a daughter, in that I introduced you to research in 1968–69, and a great-granddaughter through being the pupil of my son Peter, who ‘mathematically’ is my grandson because he learned his mathematics research from Gilbert Baumslag, who took his PhD with me!

Thank you for agreeing to interview me, Bernhard. I really appreciate it.

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