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Professor Cheryl Praeger was interviewed in 1999 for the Australian Academy of Science's '100 Years of Australian Science' project funded by the National Council for the Centenary of Federation. This project is part of the Interviews with Australian scientists program. By viewing the interviews in this series, or reading the transcripts and extracts, your students can begin to appreciate Australia's contribution to the growth of scientific knowledge.
The following summary of Praeger's career sets the context for the extract chosen for these teachers notes. The extract deals with her interest in how a simple mathematical model applies to the weaving process and the use of combinatorial designs for agricultural experiments. Use the focus questions that accompany the extract to promote discussion among your students.
Cheryl Praeger was born in Toowoomba, Queensland in 1948. She was educated at Nambour State High School and at Brisbane Girls Grammar School. 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. Praeger was interested in the area of design theory, including the direct relationship between a simple mathematical model and diagrams that weavers use to create a pattern on a loom. Her interest in design theory also included experimental designs used for layouts for agricultural experiments. Her research interests also include computation – developing algorithms and implementing them on a computer.
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).
Praeger is a member of the Australian Mathematical Society (president between 1992 and 1994), a member of the board of the Australian Mathematics Trust, and deputy chair of the Australian Mathematical Olympiad Committee. She is a foundation Fellow of the Institute for Combinatorics and its Applications, a member of the Combinatorial Mathematics Society of Australasia as well as the American Mathematical Society, and the London Mathematical Society.
Praeger was awarded an honorary DSc by the Prince of Songkla University in 1993 and was elected a Fellow of the Australian Academy of Science in 1996. In 1999 she was appointed a Member of the Order of Australia for service to mathematics, particularly in the areas of research and education and through professional organisations.
Interviewer: 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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