Not only is she Australia’s most cited pure mathematician and in the top 200 worldwide, she’s received numerous awards and international tributes for her work in several countries including China, Belgium and Thailand.

The attraction of maths, she says, is more than numbers, it’s almost a way of life.

“It’s the way I view the world. Some people are artistic, but for me mathematics is a language,” she says.

“I understand the structure and I see many problems and I can’t stop doing it, I can’t stop problem solving.”

Prof Praeger is Professor of Mathematics at the University of WA and is one of three finalists in the Scientist of the Year award. The award, worth $100,000, will be announced on 4 December at the Premier’s Science Awards.

Over the past 30 years, Prof Praeger has developed a reputation as Australia’s most cited mathematician who’s written some 280 refereed papers, several books, and scores of other publications.

Last year, she became the first pure mathematician awarded a prestigious Australian Research Council Federation Fellow, designed to attract and retain ground-breaking researchers in Australia.

For her services to maths, she was also elected a Fellow of the Australian Academy of Sciences, as well as being appointed a Member of the Order of Australia (AM).

She’s so well-known internationally that earlier this year, colleagues around the world gave her an unusual birthday present - dedicating the entire Beijing and Kunming Second International Workshop on Group Theory and Algeraic Combinatorics mathematics conference to her.

“My passion is for mathematical objects called groups, which were designed to measure the symmetry of various systems,” she says.

Although a theoretical mathematician, she says such symmetries crop up all the time in real life, in such commonplace things as the patterns in weaving or wallpapers or the structure of crystals.

Prof Praeger’s work also involves the mathematics of computing and algorithms, with the success Google, for instance, relying on the type of algorithms used to make very fast calculations.

Over the years, she and colleagues have developed breakthrough algorithms that are still in use.

“My algorithm with Peter Neumann, the Neumann-Praeger algorithm, was the first one to allow a computer to compute very quickly with matrix groups to answer a certain question,” she explains.

“They’re kind of recognition functions. Someone feeds in a couple of matrices generated and wants to know ‘have I made a mistake or is this group one of the giants?’ And the system will call our algorithm and give an answer.”

Prof Praeger is also the national chair of the Australian Mathematics Olympiad Committee which runs maths programs for students vying for a spot in Australia's team competing in the annual International Mathematics Olympiad.

Also, while some might think there are few jobs in mathematics, she says there are countless opportunities.

“There’s a huge demand for mathematicians – it’s just that the title ‘mathematician’ doesn’t get put on the job advertisement,” she says.

“There are jobs in computing and the financial industry where you might be a statistician or data analyst and all those other names.

“But a mathematician is what they want.”