The sciences and the arts, but forget what you’ve heard about right-brain/left-brain division – there is something almost tangibly beautiful about an equation. So simple, so perfectly balanced, so free of unnecessary detail, and the product of such discipline and rigour – is this calculus, or a minimalist painting by Mark Rothko?
“I just really like realizing that I know how to solve the problem,” said Alex MacLean, an Elmira District Secondary School student whose mathematical skills led to him being invited to the prestigious Lloyd Auckland Invitational Mathematics Workshop.
Drawn to mathematical problem-solving, MacLean likes “seeing how much work went into it, and the feeling at the end of getting it right, and just the challenge of trying to understand it.
“For example,” he continued, “at the workshop, there were a lot of questions that were a lot harder than what I’d ever experience before, and seeing how other people solved the problems and methods of getting the correct answers were just really exciting for me.”
MacLean, a Grade 11 student, was one of only 60 students from across Canada invited to participate in the Waterloo event (and one of only two from the Waterloo Region), based on strong results from the Fermat Mathematics Competition (he tied for 121st out of around 12,000 who participated). At the workshop, held from June 2 to 8, MacLean said the event was a major learning experience.
“Every day we had different lectures, and one of them each day was about different problem-solving techniques,” he said. “So for example, number theory and geometry – getting taught by the people who create those contest questions, how they go about solving those problems, helps me to understand how to go about solving problems differently in regular math classes.”
Math has always been one of his favourite subjects, MacLean said. “In Grade 8, I received the math award from my public school. There were only 30 of us graduating, so it wasn’t that many, but during that time I realized how much I enjoyed problem-solving.”
What separates a great mathematician from those of us who still have to count on our fingers when figure out a bill?
“It’s someone who can make connections,” said Christine Ruza, a math teacher at EDSS. “They are able to take two separate things, see something that they saw months or years back, and make a connection. That’s the biggest difference.”
MacLean hesitates at the suggestion he may have a natural aptitude for the discipline. “I might have one. It might also be that I’ve enjoyed it, so I’ve put more effort into it over my life, so it then becomes easier to me because I’ve worked on it.”
And as for the great art/science divide, MacLean added, “I’ve also played piano since I’ve been about four or five, and I’ve heard that musical ability helps develop the mathematical side of your brain. I’m wondering if that doesn’t have some impact on just being able to comprehend things a little bit quicker.”
As EDSS prepares to close its doors for another year, MacLean plans to continue in Grade 12 with two standard university-stream math courses and calculus, plus all three science courses. When asked about future plans, he said he planned to focus more on the sciences.
“If you’re going into math, either you’re going into a pure math program or something more abstract, where you really have to be brilliant.”
As for advice for aspiring mathematicians, MacLean is direct. “Just do all the work you can. Get all the experience. One guy I met at the workshop just does math for an hour every day, so when he looks at a problem, he’s already seen it before, which makes it much simpler.
“If you enjoy it, just practice.”