I’m a teacher, and one of the most frustrating questions I ever get asked is some variant of, “But when am I ever going to use this?”. And that, right there, is a problem. Do they ever say to the history teacher, “But when I’ve got a job I won’t need to know about the complex web of events that preceded the Second World War”? Do they ever say to the geography teacher, “But when I’m doing my shopping I won’t need to know about an oxbow lake”? (I do like a good oxbow lake, by the way. The one pictured is in Sarawak, Malaysia). And do they ever say to the English teacher, “But I don’t need to have read Great Expectations in order to write a good CV”? Probably not, but they sure as heck say to the maths teacher, “But when will I ever use a quadratic equation once I leave school?”
The problem stems from a number of roots. Firstly, maths does have some inherent use in day-to-day life. We all perform mental arithmetic with our money, we see statistics when we read the papers, we reflect when brushing our teeth and rotate when laying the table (at least I do, when I can’t be bothered to walk round to the other side), and based on this it’s tempting to split the maths curriculum into two groups: the “useful” maths and the “pointless” maths. Percentages, calculations, some aspects of geometry, basic statistics and fractions (only when cake or pizza are involved) fall into the first group. Algebra of any sort: off you trot to the second.
Secondly, this kind of thinking is actively encouraged in a lot of schools. We’ve bought into the idea that we must give students “real-life” examples in order to justify the content (because, of course, school itself is not real life). Students are used to worksheets or textbooks that hide the maths under manufactured situations that they’re supposed to be able to relate to, all because we’re told a page of practice questions with no context is boring or ineffective. The problem is that these situations are often so convoluted or obviously manufactured that the students either can’t relate to them or they completely see through them, and are left with a bitter what’s-the-point-in-this aftertaste.
Then we have the problem of mathematical illiteracy, and the fact that people are generally comfortable with boasting about how they can’t do maths. So it’s become ok for our young people to switch off, to not see the point, to argue about its usefulness, because “I never got maths, and it hasn’t harmed me”, again playing to the assumption that we only do maths because we can apply it on a daily basis.
Somewhere along the way, we shortchanged ourselves.
Much mathematics has arisen from quite concrete problems (think Archimedes’ Eureka! moment), yet much more from abstract thinking. Irrespective of the motivation, humankind has developed a way of explaining and understanding the physical and natural world over the course of thousands of years, one that can be applied with equal success to the stars and to atoms and to airplanes. We have discovered (or created, but that’s a topic for another day) a language that describes science, that builds our modern communities, that models chaotic natural systems, that draws us to the infinite while keeping us firmly grounded in the finite, and that is unending in its content and capacity. What is even more exciting is that mathematics satisfies a curiosity in the human mind, a curiosity that leads us to find out about things just because they are there and just because we can. Some of the purest mathematics doesn’t have an obvious application right now, but that lack of application doesn’t make it pointless, not in the slightest. There will be applications one day and, judging by historical precedent, they will amaze us, but until then knowledge itself is the purpose, and that’s just wonderful.
We don’t do mathematics so that we can go shopping, just as we don’t do mathematics so that we can build a skyscraper, and certainly not so that we can pass an exam and get a job. When any education is given this purpose, it is devalued. We do mathematics because we can, and we teach it to our children because it is the language of the whole world and we want them to join in the conversation.
Something isn’t pointless just because we can’t see the point and I refuse to let my students disengage from mathematics before they glimpse its inherent beauty. For some, that time might not come until they understand its applications. That’s why this blog is here – all that mathematical knowledge, accrued over millennia, has built the world we know, and I’d like to try and show you how.