As a child, Kate trained to be a ballet dancer. She was five when she started lessons which continued all through primary school and for most of her secondary school years. So, outside of school, ballet was her passion. Inside of school, Kate enjoyed maths and found it easy, but will never forget a day when it wasn’t. On the day the teacher taught long division, Kate missed school because of a ballet exam. In class the next day, the teacher put a problem on the board and Kate stared at it and had no idea how to go about solving it. Her confidence plummeted, even though logic told her that she couldn’t be good at maths one day, and then suddenly not good at it the next day. She just needed to be shown the procedure, but she was too afraid to ask for help. Kate had a reputation for being good at maths and didn’t want people to think she wasn’t. As a result, she sat there for far too long not knowing how to do long division. The longer she waited, the more she could feel it eroding her confidence. For days, she tried to do the homework and couldn’t. After a week, she finally asked for help and the teacher sat with her and showed her how to do long division.

And then she could do it.

She wondered why she sat on the problem for a week when she could have just asked the teacher. Kate realised that many of her friends felt like that in maths classes every day.

If kids don’t ask for help, it gets worse. No one is born knowing these things, although there are always those exceptionally gifted kids who somehow seem to understand things without being taught. Unfortunately, lots of kids seem to believe that if they aren’t a genius, and need to work a bit to understand maths, then they don’t have a ‘maths brain’. But that’s not true. Everyone is capable of understanding maths with the right help.

Kate was a kid that other kids would come to in the class and ask for help. She felt that in helping others, she always saw things in a new light, so it helped her as well. Her mum used to pay her five dollars a week to tutor her little brother in maths. Kate made worksheets for him every night after school and helped him solve the questions. Kate’s brother taught her that to be a good teacher, you have to have lots of ways of explaining things. Kate knew it from teaching ballet too. Some ballet students understood how to successfully do movements by imagining something else (like lifting the spine like a puppet on a string), while others needed more technical instructions such as which muscles to flex. Everyone thinks differently, and a good teacher has to understand how to explain things in many different ways.

Kate enjoyed maths right from the start even though she couldn’t imagine where she would ever use it. She liked the certainty of maths. In English, you could write an essay that you thought was great but the teacher may not give it the mark you thought it deserved. In maths, it’s easy to check the right answer by working it backwards and you know it’s correct.  Kate believes that once our interested has been sparked by something, we naturally want to get better at it. It’s easy to be motivated to get a ball in a hoop and kids know they have to practise, but if they don’t know how to solve a maths problem, they sometimes don’t apply the same persistence to the task unless their curiosity has been sparked and they really want to get better at it.

By the time Kate was in Year 11, she was dancing part time in a professional company. As much as she loved ballet, there came a time when she needed to make a choice between dancing and her studies. She did both well, but at 16, Kate decided that she wanted to pursue her academic studies. Even though she gave it up, none of the time she spent training as a dancer was wasted. Any child who puts their heart and soul into something they love – ballet, sport, music, maths – learns the importance of hard work. They learn about persistence. And most importantly, they learn that if they want to achieve something, they keep trying until they get it right. The time and commitment she put into ballet, could be put into another area with the same expectation of improvement.

As she got to the final years of secondary school, Kate continued with maths while many of her friends dropped it. She did all the maths she could. In Year 12, Kate had an inspiring maths teacher who tried to discourage her from studying maths.

‘Where will it take you?’ the teacher asked. ‘You want to become a maths teacher like me?’

Kate thought: What’s wrong with that? You inspire me. I could inspire others.

Kate did well at school and lots of people said she should do medicine because of her high grades, but her dad was a doctor and Kate realised it wasn’t her passion. Law or medicine shouldn’t be the natural progression following high grades in school. Kate loved maths but she didn’t know where it would take her as a career. Even so, she decided to keep learning more maths at university and see where it would lead her. She believed if she followed her passion, she couldn’t go wrong.

On the first day of university, Kate was sitting in a massive lecture theatre with about 600 other students. The lecturer was boring and lacked passion. No one was focusing. He was explaining concepts that were elegant and beautiful but he was mangling it.

Kate thought: I think I could explain this much better. I want his job!

Everyone was complaining about him, and the person next to her leaned over and said, ‘You wouldn’t believe how much he is getting paid – $157 per hour. Kate was getting $20 an hour tutoring maths and she decided on that day, she would become a maths lecturer. She just needed a PhD to get there.

Kate did a four-year undergraduate honours degree, then did a PhD in three years and ended up standing in front of her own large university classes. She loved teaching and communicating beautiful ideas. As a teacher, she knew a lot of people couldn’t see that maths is beautiful because they became bogged down in its procedural elements. But she knew once they started to understand the bigger picture, they could find the beauty.

Kate feels mathematics has given her an enormous opportunity to contribute to the world. All the pressing world problems need maths. Climate modelling is one example. Mathematicians can use data to predict extreme weather events. During Covid, mathematicians worked with epidemiologists in disease modelling to figure out the best preventative action. From tackling challenges like understanding the brain, improving traffic flow, and managing renewable energy, there is no limit to the ways mathematicians can improve the world.

Kate still does ballet and loves going to see the ballet, even though it didn’t end up being her career. Her best advice to students is to listen to yourself and figure out what energises you and drop what drains you. There are lots of kids out there who are excited about STEM and even if you can’t see where it will take you, it’s worth pursuing. The world needs more mathematicians.

Kate Smith-Miles is a Melbourne Laureate Professor of Applied Mathematics in the School of Mathematics and Statistics at the University of Melbourne, and Director of the ARC Industrial Transformation Training Centre for Optimisation Technologies, Integrated Methodologies and Applications (OPTIMA). She is also Associate Dean (Enterprise and Innovation) for the Faculty of Science at The University of Melbourne. Kate was elected Fellow of the Institute of Engineers Australia (FIEAust) in 2006, and Fellow of the Australian Mathematical Society (FAustMS) in 2008. Learn more about Kate on her website.

Professor Kate Smith-Miles works in a branch of mathematics called optimisation which is about making the best decisions from a huge number of choices.

When we used Google Maps, we are asking the computer: what’s the best way to get to a location? Your search asks the computer to solve that problem for you.

• Try solving the problem by hand rather than asking a computer.
• Look at your destination on a map and run through all the possible combinations of roads you could take to get there.
• Which choices are shorter?
• Which choices are likely to be faster, given traffic conditions?
• Which choices can you eliminate as clearly bad?
• Think about how you make decisions, and how a computer algorithm might consider the same things – but much faster – to efficiently crunch through all the sensible choices.