Meet Bendigo's answer to world Internet congestion and hospital queues

These days she is considered a world-renowned expert in her field and - according to the University of Melbourne's Dean of the Faculty of Science, Professor Moira O'Bryan, Professor Williams - "has made awe-inspiring contributions to mathematical theory and helped alleviate many real-world problems".

This includes Internet congestion, choked factory lines, customer service queues, crowded freeways and even gene regulation.

Now a Distinguished Professor at the University of California in San Diego, Professor Williams was back in Australia recently to receive an Honorary Doctorate in Science from the University of Melbourne.

As part of trip home, she took time out to wander through the Bendigo Senior Secondary College and reminisce about the old days.

In some of her old classrooms platforms have been removed due to OH&S while a fireplace has been preserved (even though its boarded up) along with heritage cupboards and boiler heaters, even though they no longer work.

"They're there for decoration," Professor Williams observes.

"I remember it being very cold some days, particularly in the mornings."

Walking around her old science and physics rooms that border the school's historic quadrangle, she notices even more changes.

"I remember a platform there and a pedestal in front where the teacher stood, and a door led through to where the chemicals were kept for experiments," Professor Williams said.

"In some ways it's very familiar, but it feels a lot bigger."

When she started at Bendigo High School (as it was known then) in 1967, there were probably about 700 students. In 2024, that number has more than doubled with about 1800 at the school.

Professor Williams graduated as dux in 1972 and went on to study mathematics at the University of Melbourne where she earned her Bachelor of Science (Honours) and Master of Science degrees.

In 1978, she travelled to the United States to complete her PhD in Mathematics at Stanford University.

"That was unusual at the time," Professor Williams said of her move to Stanford.

"People would often go to the United Kingdom to complete their PhDs but Stanford had experts in a field of mathematics I was interested in.

"When I left Australia I thought I would come back to an academic position but there was none here at the time. Fortunately I was offered a position as assistant professor of lecturing and research at the University of California in San Diego (UCSD)."

That was in 1983 but she deferred for a year to take up an offer of postdoctoral research at the Courant Institute of Mathematical Sciences in New York.

"A postdoctoral positions were rare back then so I was lucky to get one. It gives you more research experience," Professor Williams said.

She took up her position UCSD in 1984 and has been there ever since, now holding the title of Distinguished Professor of the Graduate Division, and of Mathematics Emerita.

"It's a great university," she said.

It's where she met her husband, Bill Helton, a fellow mathematician who lectures and pursues research at the university.

Professor Williams was drawn to mathematics at an early age.

"I really enjoyed maths, figuring things out from the basics and understanding it," she said.

"At university I found maths fundamental, and inspirational professors showed me the beauty of mathematics and it gave me a great career."

Although based in the United States for the past 45 years, Professor Williams has made regular trips back to Australia and to her old school in Bendigo.

She remembers her time at Bendigo fondly, recalling the early days of the computer age.

Along with fellow high school students, she joined the Bendigo Computer Club for 20 cents a year.

"That was the slogan: Your computer for 20 cents."

They had free programming classes on Saturday at the old Bendigo Institute of Technology and there were people from industry and teachers in the class.

"It was a mainframe computer which took up the whole room and they had the air-conditioning on and a student could submit one job a day on punch-cards," Professor Williams said.

She said the University of Melbourne's highest honour came as a surprise.

"I got an email in 2018 saying they would like to give me this honour, based on my research and as a professor mentoring and educating the next generation," Professor Williams said.

She said she tries to get to know each individual student, identify their strengths and weaknesses and help them improve.

"It's a wonderful process to be involved in, to see them end up with a PhD through their own independent research having learnt so much from when you saw them at the start," Professor Williams said.

While notice of the honorary doctorate came through in 2018, Professor Williams had to wait for a conferral ceremony which coincided with her availability to travel form the United States.

The COVID-19 pandemic delayed things even further until finally she she was conferred with the honorary doctorate on December 11, 2023 at the Royal Exhibition Building in Melbourne.

Professor Williams said she was "very honoured and humbled to be recognised in this way".

"It's a nice recognition of my research and it's especially significant for me that it was University of Melbourne where I learnt so much as an undergraduate," she said.