How I went from loathing math to loving it

Math is a fraught topic, but it doesn’t have to be.

Like many people, I’ve had a lot of negative experiences with math. In Grade 3, math class was centred around Mad Minutes—timed worksheets that I could never complete fast enough. The message was clear: if I couldn’t do math quickly, I wasn’t good at math. I shut down. Math class grew harder and more opaque with each passing year until I was sure I would never be able to catch up. Then in Grade 8, thankfully, I was given a second chance. 

That year, my math teacher preached radical ideas about how anyone could do math, even if they learned it very slowly. He offered us (practically) infinite chances to learn the material. At the same time, my stepdad started asking me thought-provoking math questions on the way home from school, and in doing so, he pulled back the curtain. He showed me that math could be so much more beautiful than what I’d seen in school. It could even be fun.

Today, I’m completing my final year of a Bachelor of Arts in mathematics at UBC. Once I was given a second chance at math, I couldn’t get enough—but I can’t shake the feeling that I was extremely lucky. How many other students would have flourished in math if they had gotten a second chance? I want to live in a world where positive experiences with math are the standard, not something you have to luck into. 

The good news is that we can start building that world simply by shifting how we think about and engage with math. For me, resilience against discouragement came only after I had had tangible experiences with beautiful, interesting math outside of school and, even more crucially, was empowered to explore the subject on my own terms. The three ideas below provide a starting place for how to foster these experiences—for ourselves and for anyone in our lives (especially if you’re a parent of school-aged children) who might be struggling with math or wondering about its relevance.

1. Math is an art

When I tell people I’m getting a Bachelor of Arts in math, they’re usually surprised. Isn’t math a science? Admittedly, UBC’s Bachelor of Science in math is the more popular program, and that’s because math and science are inextricably linked. But I think we’re doing math—and ourselves—a disservice when we conceptualize it as science alone. 

Math has proved an incredibly useful tool in humanity’s quest to understand the world. In some realms (e.g., physics, computer science, finance), math is right below the surface. In others (e.g., psychology, music), math is deeper down and less obvious, but it’s still there. However, math is also a practice you can appreciate and engage in purely for its own sake. This is what makes it, in my view, something closer to art. 

At its heart, mathematics is the exploration of imaginary worlds. The particular imaginary landscape you explore and the objects you’ll find there is up to you (or more often, up to your math teacher). For example, you could decide one day to think about the world of whole numbers, then find yourself wondering just how many prime numbers there are (a number is prime if it is only divisible by 1 and itself, so think 2, 3, 5, 7, 11, but not 4, 6, 8, 9, 10). You might ask, “What is the largest prime number?” or “How can I predict the next prime number?” In fact, there are an unlimited number of questions you could ask because even a world so simple it consists only of whole numbers is chock full of patterns, complexities, and surprises.

But why should we bother exploring imaginary worlds? Any lover of the fantasy genre will tell you there are numerous reasons, and many of them apply to math too: to marvel at the wonders we might find there, to challenge ourselves to think differently, to exercise our creativity and imagination. One of the most compelling reasons, one that has drawn in many a math lover, is the search for truth. 

Once a mathematical world is created—its objects conceived of, its rules established—something magical happens: a bunch of things automatically become true or false. It’s a mathematical thinker’s job to figure out the truths about their imaginary world. 

To use the example above, if we’re exploring the world of whole numbers and wondering how many prime numbers there are, it happens to be true that there are infinitely many. There is no largest prime—they just keep going forever. No one decided it would be this way. As soon as we conceived of whole numbers, it automatically became true. But it isn’t immediately obvious that primes are infinite—in fact, it might seem counterintuitive—so we have to go on a journey to find this truth, and that’s what math is really about.

If this version of math sounds unfamiliar, it’s probably because you didn’t encounter it in school. Often, math in school focuses on memorizing formulas and procedures, with little emphasis on exploration, imagination, or play. But that is not to say that one conception of math has nothing to offer the other. Instead, I firmly believe that engaging with math as exploration gives meaning to the math we encounter in school, which is often disembodied and hard to contextualize, and, in turn, the concepts taught in school turn out to be tools we can use in our explorations.

Importantly, we don’t find mathematical truths using the familiar protocols of science. We don’t conduct experiments or collect data. As mathematician-turned-grade-school-math-teacher Paul Lockhart says in his essay A Mathematician’s Lament, “The only way to get at the truth about our imaginations is to use our imaginations.” Once we suspect something is true about an imaginary world, we must go about the creative work of arguing that it is definitely true, and that is quite an interesting process.

2. Math is about the journey

One of the most pernicious ideas in math education is that math is about getting the right answer as quickly as possible. This was the message I got when I failed at Mad Minutes back in Grade 3. I think most people who dislike math will find a moment like this, or perhaps many such moments, in their own experiences with math.

In reality, mathematical thinkers must cultivate a diverse set of skills in order to solve interesting problems. By broadening our definition of “good at math” to include these skills, we can more readily recognize mathematical thinking—in others and ourselves—and seize the opportunity to validate it. 

When a mathematical thinker encounters an interesting problem, especially one they don’t know how to solve, they begin by investigating. They might carefully consider how this problem relates to others they’ve seen before, or they might start throwing strategies at the wall to see what sticks. They might break the problem up into cases, or try a simpler example, or look for counterexamples. They will make predictions. They will almost definitely ask a lot of questions.

This goes not just for students but for professional mathematicians too. In his book Mathematics for Human Flourishing, mathematician Francis Su writes, “The beginning of a research project is playful exploration: contemplating patterns, playing with ideas, exploring what’s true, and enjoying the surprises that arise along the way.” 

False starts and wrong answers are not to be feared. These are a natural part of the process at any level. The value is in reflecting on why a strategy didn’t work and using the insight to revise understanding of the problem. That is perhaps the most vital skill—and it’s one we might fail to develop at all if we’re taught that getting the wrong answer makes us bad at math. 

Encouraging the development of these mathematical skills can have impacts far beyond math. As Su puts it, the endurance cultivated by mathematical struggle “produces an unflappable character that benefits us in addressing life problems—calming us with the knowledge that it’s okay if we don’t solve a problem right away.” 

3. Math is a communal act

There’s a caveat often tacked onto the aforementioned pernicious idea: math is about getting the right answer as quickly as possible by yourself. Sometimes, we’re even taught that being good at math means doing it faster than anyone else. 

This model works for a small subset of people, but it leaves many more in the dust because, well, it’s hard to do math by yourself! No one knows this better than professional mathematicians, for whom collaboration is the norm. Applying many minds to a problem is often more productive than a single person toiling away, and there’s real joy in combining your creative powers with someone else’s. All of my most cherished UBC memories are of doing math with other people.

Luckily, collaborating on math problems is not reserved for university-level math. There is no rule against tackling an interesting problem (like the ones you can find on Play With Your Math) for enjoyment with friends or family in the same way you might do any other fun activity. In fact, it’s probably the best way to shift math from something others make you do to something you do with others. Even just keeping an eye out for interesting patterns in the world around you and mentioning them to the people in your life can help foster mathematical community.

Early in my transformation from math hater to math lover, I got a glimpse of just how communal math could be, and it cemented my belonging and agency in this new space. I hope my experience provides a blueprint for what mathematical investigation can look like, and how best to encourage it. 

It started with a noticing: I was 14 and my mom was 41. Our ages were the reverse of each other. I had barely begun to like math and I still had very few tools at my disposal, but I felt the urge to investigate further. What needed to be true for us to have this fun mirror-imagery in our ages? 

Eventually, I worked out that it happened because of our 27-year age difference, which is a multiple of 9. In fact, it seemed that if you took any two-digit number, reversed its digits, then subtracted one from the other, you’d get a multiple of 9, like how 41 – 14 = 27.

This is where my investigation would have stopped if I hadn’t brought it up to my stepdad. Just as he had the year before, he spent the drive home from school asking me questions that helped me figure out, step by step, how to prove this property was true for all two-digit numbers. (Notice that he did not outright tell me how to do it!) When we got home, I ran upstairs to write it down on paper. This was my first ever proof—a piece of mathematical writing that shows incontrovertibly that your discovery is true.

That could also have been the end, but he left me with another question: “How would you prove it for numbers with any number of digits?”

This question, way above my pay grade as it was, wouldn’t leave my mind. The only thing I could think to do was ask every person I knew for their ideas, and each person I spoke to offered a perspective I never would have considered on my own. With each insight, the solution came into slightly sharper focus. 

Eventually, I peddled my problem to a math teacher visiting from another school. He listened intently, then asked, “Does this happen just when the digits are reversed, or does it work for any rearrangement of the digits?” For example, I was claiming 4321 – 1234 must be a multiple of 9 since the digits are reversed, but what about 4321 – 3214 or 4321 – 2143? Would those also be multiples of 9? 

Looking back, he definitely knew the answer was yes. But by framing his observation as a genuine question, he encouraged my curiosity and ushered me further down the path of inquiry. This is how we can help the people around us take charge of their own mathematical explorations: by meeting them with curiosity and offering them new perspectives, but never robbing them of the magic of discovering something for themselves.

This is the world I want to live in—one where curious people are encouraged to become mathematical thinkers, where they are empowered to find truth and beauty in the mathematical worlds that interest them, to cultivate the persistence to problem-solve, and to build supportive mathematical communities. My hope is that by taking these ideas into consideration the next time you encounter math (or a math student), we can all take a step closer to that world. 

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If you want to explore these ideas more deeply and start applying them in your own life, here are some excellent starting places:

• Francis Su's book Mathematics for Human Flourishing is a compassionate exploration of how math can and should fit into human life. I recommend it to everyone, no matter where you are in your mathematical journey. 

• Math for English Majors by Ben Orlin gives explanations of mathematical concepts in relatable language you won’t find anywhere else. Orlin also runs the provocative and humorous blog Math With Bad Drawings.

• Self-described “mathemusician” Vi Hart’s video series Doodling in Math Class exemplifies breaking away from prescribed memorization to see where simply exploring can take you.

• If you’re wondering where these explorations of imaginary worlds ultimately lead, Numberphile explains intriguing concepts from higher mathematics in videos you don’t need a math degree to understand.

• 3Blue1Brown makes visual explanations of mathematical concepts that are often taught in unintuitive ways—I particularly recommend the series Essence of linear algebra and Essence of calculus to anyone who (justifiably) thought those subjects made no sense.

• Play With Your Math is an online repository of exactly the kinds of math questions that lead to deep exploration and further inquiry. Don’t be afraid to scroll through and pick a question that fits your taste—it’s all just for fun!