How math habits make you better at life

Matt Fahy on a rugby field writing on a clipboard.

With International Mathematics Day coming up on March 14, we talked to mathematics and statistics professor Matt Fahy—a student favorite—to find out what drives his interest in math and how the rest of us might learn to love it, too.  

Your Calculus III course came up twice in our crowd-sourced list of students’ favorite classes last year. Why do you think that is? 

Because everyone loves calculus! 

In general, my classes are pretty informal and relaxed, and I think that’s popular with students. Math classes—and math faculty—are often perceived as intimidating. I am intentional about making the environment in my classes welcoming, the type of environment in which students feel comfortable asking questions, making mistakes, needing extra explanation—all of the things learning usually requires.  

Calculus III is a really fun class—we get to explore the most fundamental concepts and tools of calculus in new contexts. So instead of just grinding out more difficult versions of a recent technique, we get to revisit core concepts that students, at this point, are comfortable with, but in higher dimensions, dealing with different types of mathematical objects, etc. I think students appreciate that mix of familiar ideas with new perspectives. 

I also am intentional about thinking about and explaining concepts from a non-expert perspective. Students don’t have the same mathematical background I do, so it’s generally ineffective for me to explain things the way I “see them.” Instead, I try pretty hard to imagine seeing a concept for the first time—the way students do—and build my explanation from that perspective. Maybe students appreciate that? 

Also, I tell bad jokes! 

What do you like about teaching math? 

Teaching at the university level is a great way to live dozens of potential life trajectories vicariously through my students! I have no idea what organic chemistry is about, but I love having a conversation about it with my students before a calculus class. Why would you choose a major in physics versus astronomy? I wouldn’t choose either, but it’s cool to hear two students discuss the pros and cons of each. And when I am fortunate enough to have students in multiple classes over the course of a couple semesters, I really enjoy hearing about their progress, new challenges, new things that are exciting them, etc. It’s really amazing to be able to help invest in students during this incredibly formative time in their lives. 

Why is math important? 

While I definitely think math itself is incredibly important, I think in a more general way the habits of mind math can instill in you are of more practical importance for most people. Math teaches you to be analytical and precise—skills that can be applied in a huge range of contexts.  

Even more so, I find that doing math (and maybe to a greater extent, teaching math) forces you to notice how necessarily scaffolded math is. You MUST understand the fundamental concepts and skills before moving onto something more advanced. That skill—deconstructing a complicated task or concept into a clear sequence of steps—is INCREDIBLY important in basically every job, most interpersonal relationships, etc. I think it’s valuable for students to be mindful of these “soft skills” that they’re learning while also learning specific math content. 

Matt Fahy coaching a group of rugby players gathered around him on a field.Are there any unexpected ways being good with math has benefited you in everyday situations? 

Not really that unexpected, but (building on the scaffolding comment above) I coached rugby here in Flagstaff for about 10 years and one of my strengths as a coach (I think, at least!) was taking a large-scale chaotic situation in a rugby game and breaking it down into digestible pieces, then building drills around developing the small-scale skills that comprise that large-scale situation. I wasn’t using formulas to compute the optimal trajectory of a pass, but the style of thinking I have developed by doing a lot of math translated into effective coaching. 

March 14 is not only International Mathematics Day but also Pi Day. Any thoughts on why pi (π) has captured the attention of so many?  

What I’ve been struck by recently is how ubiquitous pi is. Many people are familiar with its role in geometry—divide the circumference of any circle by its diameter and the answer will always be pi. (A fact my father explained to me once when we were preparing to dig into a pizza when I was roughly age 10.) 

But pi also arises in several not-obviously-geometric contexts. For example, the gamma function is a generalization of the factorial operation that shows up in probability contexts, such as models that can be used to describe—for example—how long you have to wait for your drink at Starbucks. If you evaluate the gamma function at 1/2, the answer is the square root of pi. Wild! This is just one example of pi showing up in an unexpected place.

What’s the best and the worst thing about being a math nerd? 

I’m not sure I really identify as a “math nerd,” but one drawback of having a reputation for being good at math is that no one in my family will play board games or card games with me. They immediately assume the game is complicated and that knowing some math will give me an insurmountable advantage. I just want to hang out and play some cards! 

The best thing about being good at math is that I always win at cards. 

NAU Communications