The View From Mathematics


I have a lot of respect for Professor Sylvia Serfaty. Not only is she a brilliant and esteemed mathematician, but she recently brought two of my favourite things together when she said this:

“You enjoy solving a problem if you have difficulty solving it. The fun is in the struggle with a problem that resists. It’s the same kind of pleasure as with hiking: You hike uphill and it’s tough and you sweat, and at the end of the day the reward is the beautiful view.”

There is a certain exhilaration you feel when – after carrying a heavy pack on your back for kilometres on end through mud, up hills, feeling that gross sweat trickle down your back, and running out of things to say to your hiking partners – you arrive at your destination. There you are in the middle of dense bushland, with not a roof, road or electricity wire in sight. Instead, stretched out around is unending greenery and the vastness of the sky above. You are in a patch of the world that very, very few people will ever get to see. And yes, you can be proud in knowing that you worked hard to get there.

And this natural beauty can be compared to maths?!

Just like hiking, there is much in the journey of problem solving that is hard work and will challenge you. Mathematicians – and I use that term broadly, to describe educators, academics, students and those who are in some way engaged in the field – take joy in getting to the destination. Problem solving is not like relying on your GPS to get somewhere, where each step you are told what to do next. “At the roundabout take the third exit. In five hundred metres, use the second from the left lane to turn left. You have arrived at your destination.” Nope. Why would we bother with mathematics if it was that mundanely easy? It’s hard and mathematicians knowingly struggle. Serfaty took nearly 18 years to solve one problem. She’s also not the first to show such extreme mathematical persistence (e.g. Andrew Wiles‘ momentous  journey with Fermat’s Last Theorem).

On solving a problem, mathematicians reach a point of (sometimes momentary) finality. There is perspective on the method used to get there- what was effective, what held them back, how they failed, but then learned from it. And, just like the hiker’s view, there is immense satisfaction that comes with overcoming your own personal limitations to arrive somewhere new.


(As inspired by Serfaty and Ben Orlin)

As a teacher, there’s no such thing as easing back into a new school term. From day 1 you are bombarded with everything from new timetables, class lists and topics to teach, to IT stuff-ups and the same old problematic behaviours. Coming out of the last five days, I feel like I’ve been smacked in the face.

I want to take a step out of all that though and focus on one young lady, whom I’ll call Tina, who in my opinion is one of the most patient people I’ve ever met. Tina is in a maths class that comprises about 75% boys. Many of these boys walk into class each day, ignoring any implicit (or explicit) distinction that exists between the classroom and the playground. For some of these boys, I am slowly applying Skinnerian operant conditioning techniques in order for them to independently get out a pen and begin their work each lesson.

In class, Tina sits alone, but positions herself between two of the more “studious” groups of her classmates. At first glance, Tina doesn’t appear to fit the mould of the model student: she has straightened bleached hair, wears heavy make-up and manicured nails. Yet she is respectful, hard working and somehow seems to always remain unfazed by whatever crap is going on around her.

Ideally in a lesson much of my time should be spent wandering around the room assisting students with small but meaningful questions about the maths they are working on. In reality, my time gets distributed very differently. I ask Student A to put away their phone for the n-th time; request that Student B stops drawing on Student C or ripping pages out of their peer’s book; write an out-of-class slip so that Student D can stop sniffling and go and find a tissue; legitimately assist Student E with a problem that then takes 10 minutes to explain given that they are three years behind the level that they should be at… And during all of this time Tina continues with her work. As she tells me, when I finally get around to assisting her about 2 minutes before the bell, “I’m not sure if this is right. I just guessed for some of the questions”. Looking down at her book I see neatly set out rows of equations, showing a fluent understanding of the required procedure. With only a minor error here or there, I can’t fault Tina’s work.

In amongst the many disruptions, I honestly don’t know how Tina’s drive and perseverance is maintained. I haven’t seen her once get angry or annoyed with her peers, and perhaps that day will come.

What I do know is that much of my own learning and development as a teacher is occurring so that I can better manage the behaviours in my classroom to not just help students like Tina, but push them to be more confident and to excel in their learning.