The big argument: Is maths discovered or created?

And who’s responsible for my minus sign errors?


Discovered, argues Ellen Jolley

For something to have been invented, it has to have not been there before someone made it—and maths has certainly been here long before we ever noticed it. Before arithmetic was ‘invented’, if someone picked one apple from a tree and then another, did they end up with a completely unpredictable number of apples? And before parabolas were ‘invented’, if someone launched a projectile at an upwards angle, did everyone take cover because who knows where it might end up? Clearly not—the universe has been doing maths much longer than us without even trying, and we are just slowly catching up.

We can take credit for inventing column multiplication, or counting on your fingers, but not laws of arithmetic themselves. They were there long before us and they will be there long after us—a fact I am very grateful for because I struggle to imagine what kind of chaos we’d be living in without them. Next time you find yourself frustrated at trying to split a bill here in the ordered universe we know and love, spare a thought for our poor ancestors who had to do it before the laws of arithmetic applied.

To accuse maths of being invented and not discovered is to reduce its explanatory power to merely a figment of our imagination—and I don’t think we’re clever enough for that.

Created, argues Sophie Maclean

I’m not about to tell you that Isaac Newton invented gravity. Obviously he didn’t. The laws that govern the world have been around since the beginning of time (though I’m not foolish enough to get into a debate about whether or not time would exist without people there to observe it). What Isaac Newton did discover, however, was why this is true.

Mathematics isn’t simply a set of rules to follow. To describe it as such is to do it a disservice. Mathematics is the language with which we describe how the world works. The universe is a beautiful symphony, and mathematics is the dance through which we interpret its song. The world is a tapestry on which mathematicians create their art.

When Andrew Wiles proved Fermat’s last theorem, did he simply discover what was already there? No, he created new maths beyond what had ever been before. When Maryna Viazovska proved the sphere packing problem in eight dimensions, did she just stumble across a pre-existing solution? Of course not.

So for all the mathematicians out there, this is your call to arms. You are explorers, yes, but you are also inventors. You are creators. Your work is your own and you deserve to be proud of that. Maths is created and that is what makes it so incredible.

Ellen is a PhD student at UCL studying fluid mechanics. She specialises in the flow around droplets and ice particles.

Sophie Maclean is a recent maths graduate from the University of Cambridge and very much misses her degree. She has no free time—she is a Chalkdust editor.

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