Friday profile: Spinning towards a solution

“No-one grows up wanting to be a mathematician,” says mathematician Sophie Calabretto, perhaps a little ruefully.

Her own arrival in the field – specifically, applied maths, more specifically, fluid dynamics and dynamical systems – was “a huge accident”, according to the 29-year-old lecturer at Australia’s Macquarie University.

The original plan was astrophysics (“I was always a dork,” she concedes), but three-quarters of the way through her undergraduate studies at the University of Adelaide, a summer project changed her focus.

After graduating with a slightly lopsided double degree in arts and science (majors in physics, theoretical physics, applied maths, and French), Calabretto did an honours project on the mathematics of neurons firing in the brain.

It was while completing a PhD at the University of Auckland that she became interested in her current field: fluid mechanics. After a postdoc stint in Switzerland, she moved to Sydney to work at Macquarie.

Her research at present focuses on the mathematics of a deceptively simple situation: a solid sphere spinning in water.

“It’s a nice geometry to work with,” she says, meaning that the equations that describe the fluid flows are relatively tractable. Even so, the complexity of fluid motion quickly goes past what can be managed with a pencil and paper.

“When you get to a point where you can’t do anything more with the equations, you use computers to run simulations. And then eventually the simulation gets too big – it takes too much computer time – so you do an experiment.”

The key to the maths of fluid motion is a relationship between density, velocity and pressure called the Navier-Stokes equation. Solving the equation exactly is only possible in very specific circumstances, and once turbulence kicks in solutions become impossible. (Providing a better understanding of Navier-Stokes is one of the seven Clay Millennium Problems in mathematics: a million-dollar prize awaits whoever finds an answer.)

By studying the spinning sphere, Calabretto aims to understand the formation and collision of boundary layers, which are thin skins of fluid that are pulled along by a moving object. This has broad applications, but particularly in aircraft design: “If you understand how fluid moves across a sphere, you can, in some ways, understand how air moves over an aerofoil.”

Calabretto is also working on a subject she began studying during a postdoc position at science-tech university ETH Zurich in Switzerland: small-scale vortices in the Gulf of Mexico.

“The way that these eddies move interacts with major ocean currents,” she says. “We’re interested in that because ocean currents are tied to weather, and we’re interested in that because of the effects on climate change. It’s about taking the big picture and breaking it down into fundamental questions.”

While Calabretto likes to work on problems that connect to the real world, the maths itself is the important thing: “I’m an applied mathematician, but a very theoretical one.”

When we speak, Calabretto is back in Adelaide, preparing for a session on dynamical systems and fluid dynamics she is organising for the Women in Mathematics Special Interest Group (WIMSIG) 2017 conference at the University of South Australia.

“All the presenters at the conference are women,” says Calabretto, “and the idea was to get a 50:50 split of women and men in the audience. Not sure if we’ll quite get there.”

Helping people understand the changing face of mathematics, and clearing up misunderstandings about who mathematicians are and what they do all day, is important to Calabretto.

“When people think of mathematicians they think of slightly strange old men – which was probably quite accurate in the past!” she laughs.

There’s also a common perception that mathematicians must be geniuses with lightning-fast powers of calculation.

“People always ask me to split the bill at restaurant, but I’m awful at mental arithmetic! I use a calculator. People don’t understand what maths is at this level. It’s not about being some kind of genius. If anyone had done maths as long as I have, they’d be good at it too.”

Even within universities, ideas about who can be a mathematician sometimes make selling the idea of maths difficult: “When people talk about promoting STEM [a common acronym for the disciplines of science, technology, engineering and mathematics], they usually just mean STE.”

“It’s a pity,” says Calabretto, because understanding maths is one of the best ways to get ready for the future. “A background in maths and statistics is a good background for all the careers that don’t exist yet.”