Approaching maths with curiosity: Meet Mathematician, Associate Professor Marcy Robertson

How did you get into mathematics?

It was a process of elimination. I wanted to be a painter, but it turns out I’m not very good at it. I wanted to be an astronaut, but I learned that I don't like jogging, so the Air Force was not a great option for me. I studied astrophysics, but I learned that I don't like lab work. Then, I studied mathematics!

Can you tell us about where you grew up?

As it turns out, Melbourne is the longest I've ever lived anywhere. I grew up all around the Southern United States. I'm originally from a small town in East Texas. I lived all over Texas and New Mexico, with extended periods in New Orleans, Oklahoma and six months in Ohio.  I moved to Chicago for university, where I stayed for nine years to do my undergrad and graduate studies.

After graduate school, I lived in Canada, in London, Ontario for three years. I lived a year in in France in Lille. I then moved to Los Angeles, before moving to Melbourne.

How has living in lots of different places had an impact on your career?

Travel is incredibly important to my research! Science, in general, is an international endeavor, but math is very, very international. In each place, I learned new techniques and met new people. I still collaborate broadly across Europe, the US and Canada. I actually consider this one of the perks of my job. I had always wanted to live abroad, and I found a job that allowed me to move around the world easily.

What would you say to someone who thinks they’re just not a ‘maths person’?

I didn't think maths was for me either and didn't intend to be a mathematician! Even if you don't like maths at school, university maths is very different and comes in a lot of flavours that you probably haven't seen before. Most people don’t really experience statistics, optimisation, combinatorics and many other topics until they get to university. I would say stick with it a little bit longer before you decide if you’re a ‘maths person’ or not.

Would you still say studying maths at university is harder than at school?

Yes, but in a good way! The challenge is part of the joy of it. Maths is solving puzzles and hard puzzles are more rewarding to solve. If you go to an escape room and you're done in five minutes, then you feel like you've wasted your money, right?

On the other hand, there is less pressure in higher-level math to find the correct answer. The answer is often not the point. The point is to think about how you set up a problem, how you can make the problem easier to solve, how you can extend a solution to a harder problem, and so forth.

Can you tell us about the research you do?

So, it is difficult to answer this question without a chalk board. What I actually do is try and develop structural connections between seemingly different areas of math.

My main area of research is algebraic topology. One way to think about what I do is that I try to understand the properties of spaces.

Topology is about trying to understand the shape of a space in a flexible way. We are not so worried about exact distances or angles. We care more about things like whether the space is connected, whether it has loops, whether it has holes, and whether one shape can be deformed into another.

I also do some work in category theory, which is an area of maths that develops tools and language for comparing different kinds of objects and understanding the relationships between them. It is a very abstract language, but it turns up in surprisingly concrete places, including computer science. For example, some of the ideas behind programming languages and the way different systems communicate with each other can be described using category theory.

How does AI relate to maths?

The short answer is that AI is maths. AI, a neural network, or an algorithm is not actually intelligent. When you ask one of these programs a question, it sifts through large amounts of data and then tries to provide you with an answer that fits the question, up to some probability. The better algorithms are those which can sift through data faster and better calculate an approximation of what the user wanted to hear. This is maths!

There is a bit of paranoia about AI, but I don't think it's even close to being able to do real mathematics. It is the case that mathematicians are playing with AI as a tool for mathematics, and this is kind of exciting. Tools are always changing, and mathematicians have a long history of using computers as tools. We used to use calculators, now we use AI, and you just evolve to go with it.

What do you want people to remember most about you and your work?

I'd like to be known for being a good teacher. I teach across the University of Melbourne’s mathematics curriculum. I have taught linear algebra, masters subjects in topology and am currently co-teaching our new second year subject in discrete maths.

I like making other people realise that mathematics is interesting and useful for them. I think literacy in mathematics could do a lot for society, and I would like to help more people approach mathematics with curiosity instead of fear.

This article was published on International Women in Mathematics Day, which celebrates the achievements in mathematics of women around the world. Held each year on May 12, the date honors Professor Maryam Mirzahkani, who in 2014 became the first woman to win the prestigious Fields Medal. Read more interviews featuring Women in Maths and Stats from the University of Melbourne’s School of Mathematics and Statistics.