17 June 2021

Emeritus Professor Cheryl Praeger AC FAA has explored new territory and leapt career barriers, not just in the pure mathematical realms in which she is internationally recognised, but as a trailblazer for changing how maths is taught in schools and universities in Australia.

The recipient of the Australian Academy of Science's 2021 Inaugural Ruby Payne-Scott Medal and Lecture, Professor Praeger leads a team of pure mathematicians at the Mathematics of Symmetry and Computation Research Cluster at The University of Western Australia (UWA). Her research in pure mathematics has been recognised particularly in the field of group theory, including permutation groups and combinatorics, which is a branch of mathematics which studies symmetry.

Now a role model herself, Professor Praeger says that in the 1980s, when she was facing the challenges of juggling children while pursuing her career in mathematics, there were few examples that she could follow, and little support for a woman in her position.

‘I felt that I didn’t have any role models. I was only the second woman Professor of Mathematics in Australia – the first was Professor Hanna Neumann in Canberra – but although I had met her when I was an undergraduate student, sadly Hanna died before I became Professor. I did know that she had au pairs to help with managing her career and five children.’

‘I wanted to have children and was also passionate about being at the cutting edge of mathematics research. When I had my first child, I felt like I didn’t want to take a break – and after a couple of years I was so tired I felt like I would never again be truly creative.’

The solution was that Professor Praeger asked her colleagues what research projects they were doing that she could fit into. One colleague suggested she review a research paper from a Canadian group on the mathematics of weaving. Professor Praeger applied group theory to problems involving the specific design sequence of ‘overs and unders’ that make up woven twills, taking into account issues such as whether or not a piece of woven fabric will curl up at the edges, or have long `float’ threads affecting its appearance or durability.

‘They were having trouble getting their algorithms to work. I realised how beautiful the mathematics was and I wanted to contribute,’ says Professor Praeger.

The solutions Professor Praeger helped to work out have had important industrial applications, and continue to be a popular lecture topic.

‘My career has been all back to front, because after a little more than two years as a full-time researcher I began teaching, and after I was appointed Professor I had a huge administrative and service load. It was to be more than 20 years before I returned to full-time research on an ARC Federation Fellowship. Meanwhile the 1980s was a busy time, upskilling students. I was supported by several ARGS grants [from the Australian Research Grants Scheme – a precursor of the ARC] and was trying to change the way we trained students in mathematics.’

In 1989, Professor Praeger gave a lecture at The University of Adelaide, which caused ripples throughout the mathematics community, in which she advocated a different way of teaching mathematics that was more inclusive for all students, boys and girls.

‘I gave a lecture on gender and mathematics in Adelaide – which asked the question, “Why don’t girls do mathematics?” I wanted to explore how the teaching experience at university could be improved for girls as well as boys – given the findings of research on the differences in learning between boys and girls at the school level. Boys were more likely to follow the problem regardless of the context, while girls learn best when they can see some purpose for learning, some realistic application of the theory.’

Because of her work on the government’s Curriculum Development Council (CDC), Professor Praeger was intensely interested in curriculum development for primary and high school mathematics. This was especially true during her tenure as the first woman president of the Australian Mathematical Society (AMS), all on top of a huge increase in workload that came with her Professorship.

‘I was on so many committees – and I rarely had any proper study leave. For example, in my first year on the CDC I was still breastfeeding my second son and I had to fly to different states eight times per year attending 3-4 day CDC meetings. What I learned resulted in my role as ‘translator’ between research mathematicians, and mathematics educators in government and schools.’

All these efforts led to structural changes in the way maths was taught in schools across Australia, and new efforts were made to encourage mathematics as a subject that girls could excel in as well as boys.

At the same time, a game-changing breakthrough in group theory occurred, the classification of the finite simple groups, and Professor Praeger’s team were at the cutting edge of fundamental change in the way to solve many problems in symmetry. This research later received a huge boost with the award of her ARC Federation Fellowship in 2007, the first awarded in pure mathematics.

‘Mathematically we were doing something really new. There were these old stubborn problems that could be solved by using the simple group classification, so we developed new methodology allowing us to exploit the classification to solve them.’

Following intensive work during a 6 week stay in the UK and Germany, Professor Praeger and her colleagues were able to classify all the essential ways of splitting a simple group into two parts. This elucidated the internal structure of the alternating simple groups, an old and hard mathematical problem, resulting in international recognition and acclaim.

Nearly forty years after her first ARGS grants were awarded, Professor Praeger is currently Chief Investigator on two different Discovery Project grants, and still pursuing mysteries in the deep mathematics of symmetry, and its applications in fields such as error correction in computing.

Looking back on her career, Professor Prager acknowledges that she has opened the way for many people to follow, and made many breakthroughs, but there are still many unanswered questions.

‘I love solving problems – both in mathematics and with people – and there are still plenty of problems. After I was AustMS president, it was almost 20 years before there was another woman in the role. It was like the community thought “well, we’ve done it once…”. A single woman role model doesn’t change the culture, although the culture is now changing. There are now more leadership programs for women – there was a fantastic program at The University of Western Australia – but I’d come along too early for that.’

Professor Praeger says that there are still plenty of unsolved problems in the mathematics of symmetry that she cares about deeply as well.

‘We don’t really understand why these big sporadic groups exist – and why are there only 26 of them!’

Images (top to bottom):

Professor Praeger in 1997. 

Professor Praeger, with colleagues Philip Schultz, Bill Longstaff in 1980.

Professor Praeger with her children, around the time of her Professorial appointment in 1983.

A graduation photo from 1998 with Professor Praeger’s two honours students for that year: Michael Giudici, (right) who is now head of pure mathematics at UWA; and Akshay Venkatesh (left) who is now at Princeton University, and is the only Western Australian to win a Fields Medal – sometimes considered the ‘Nobel Prize of Mathematics’).