A engineer, a physicist and a mathematician are on a train to Scotland. Past the border, they glimpse a lone black sheep standing in the grass. “How interesting,” says the engineer, “Scottish sheep are black.” The physicist retorts, “Not necessarily. Some Scottish sheep are black.” Puzzled, the mathematician declares “You’re both wrong. In Scotland, there is at least one field, containing at least one sheep, at least one side of which is black.”How funny those mathematicians are. How pedantic, how quirky; how disconnected with real life. Just give them a little pocket money and a pat on the head so they’ll leave us alone and play in their fractal sandbox. We don’t have time for them when we’ve got so much real science to do.
Don’t be that person. Don’t dismiss mathematics as false, or less worthy, just because its world is intangible. We need mathematics—and we need mathematicians.
The standard defence of mathematical research is that of serendipitous rebirth: existing abstract theories may one day find new life doing something ‘useful’. An oft-cited example is the number theory behind e-commerce encryption. Others in the long list of beneficiaries include programmable computers, subatomic particle physics and Einstein’s general relativity. Thankfully, this argument is getting hackneyed, at least to scientists.
I say “thankfully” because this means such eloquent communicators as Simon Singh, Marcus du Sautoy and Keith Devlin are succeeding. I’m not saying their work is done; indeed, while Joe Public can still declare “I was never any good at maths” as a badge of honour, their work must charge forward apace. But in a world where every grant application demands to know immediate ‘useful’ impacts, mathematics is done a disservice by having to mumble “We might create some stuff the scientists might find kinda handy.”In fact, the study of mathematics isn’t always about the end results—it’s about the journey of those who discover them. Armed only with chalk and their minds, mathematicians sally forth into the dark cave of mysteries, fashioning everything they need from whatever they find, permanently mapping the nooks and crannies for everybody who follows. They embody the purity and innocence of discovery.
Mathematicians also embody the bravery and joy of discovery. They are not afraid of the unknown. In fact, the more seemingly fundamental the question, the more tempting the problem becomes. If it is solved, they revel in adding another route to the mathematical map handed down over millennia; and even if not, they still revel in the unmarked paths trodden.
We need mathematics for the mathematicians behind it. Be motivated by their intellectual purity, and draw strength in their love of discovery for discovery’s sake. They understand that anything and everything is worth exploring—and in this way, they are examples to us all.