# 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)