Student Profile: Adam Humeniuk

Star math student is this year's Faculty of Science Gold Medal and Mathematics and Statistics Silver Medallion winner

Imagining a mathematician can conjure up the mental image of someone drawing calculations over the entire surface of a chalkboard, much like this article's cover photo. However, what a mathematician actually does is shrouded in mystery. Adam Humeniuk, who convocated June 8 with an honours degree in pure mathematics, wants to help change that.

The two-time graduate, and this year’s winner of both the Faculty of Science Gold Medal and Mathematics and Statistics Silver Medallion, has focused his scholastic efforts in pure mathematics, which Humeniuk says is to study math by way of math. “You take mathematical ideas and use them to study other mathematical ideas,” he explains, “and in the end, you learn more about both.

“The aim is to figure out how the ideas interplay, how they work, and how they work with each other. The way that you do that is to start figuring out as many basic facts as you can. What does it seem like should be true? And can you prove that it’s true?”

The concepts, he says, can be applied in areas like physics, a subject in which he earned an honours degree in 2015 before completing an after-degree in pure mathematics with a perfect GPA of 4.0.

“I had been looking at grad schools, and I was tentative about it. I came to the conclusion that I would regret it if I didn’t give math a shot,” he says. “I took everything that we have to offer here in pure math, and some graduate level courses too. It’s something that I wouldn’t have had the opportunity to do if I’d done a combined degree.”

Research opportunity connects math and meteorology

Humeniuk’s research alongside assistant professor Kristine Bauer, for which he earned a PURE Award in 2016, focuses on the emerging field of topological data analysis (TDA). “Topology involves the study of shapes,” he explains. “TDA is really exciting because it’s applied pure math. Topology is pure math, but the idea is to apply it to data analysis problems — real world data.

“Topology is about shape in a way that’s kind of flexible. It’s about shapes that are insensitive to being deformed or squished. That’s why we wanted to try it on something like a cloud; they’re all different, but they have commonalities even though their shapes are not exactly the same. The reason why we used topology is that it is insensitive to small changes in the shape. The goal was to focus not on those small changes, but the overall shape,” he says.

The two initially set out to build an algorithm to classify cloud shapes, based on freely available data, to improve meteorology. The focus of the project ended up shifting, however, to how their algorithm would actually work.

“Adam found a way to randomly generate complex shapes which approximate high-dimensional data sets. He measured how frequently the resulting shapes had torsion, a kind of twisting behaviour,” Bauer explains. 

“The goal of the research was to rectify a difference of viewpoints between the pure mathematical literature on so-called homology theory and the application of this theory to data analysis.”

Humeniuk will return to campus after graduation to work as an undergraduate researcher with Bauer, where they will write up their findings.

Opportunity to help others understand mathematics inspires career path

Communicating about mathematics is something Humeniuk plans to focus on as he continues his career. “When I started my math after-degree, I discovered that there’s a lot that I’d never seen before. Mathematics as a discipline is huge — there’s much more to it than people outside of math are taught about,” he says.

I feel like there is often a lot of groundwork that people miss in their foundational years about what you actually do in math. For example, people have an idea of what a physicist does. They do experiments, they do equations and they try to understand the universe; but when you ask ‘What does a mathematician do?’ they don’t really know.”

After working as a teaching assistant for a first-year honours math course in 2016, Humeniuk got his first taste of life as an educator. “It was a really good experience, and challenging,” he says. “I really enjoyed it, and I want to teach more.

"What I’ve come to learn is that my values and what I’m interested in thinking about are more along the lines of what people in math do. I’ve been increasingly interested in teaching, and communicating mathematics. The more math and physics I take, I wonder how I would teach this myself.”

This desire to connect with others interested in mathematics is reflective of Humeniuk’s experience in the Faculty of Science, where he found like-minded peers, and engaging instructors.

“Math is a very open department. There are a lot of open doors and people who will just talk to you and offer you advice on math and even life,” he says. “It was a very friendly experience and a good environment.”

Next up for the Calgary native will be a Master of Mathematics degree at the University of Waterloo. His current long-term plan is to do a PhD.