Mathematics is a misunderstood degree.
University Mathematics is very different from what’s gets taught beforehand during your school years. I yearn for the good old days where I could answer a simple ‘find x’ algebra problem without considering what ring we’re working in. Without quoting the relevant theorems and lemmas. Without any trace of a thought about whether my answer is ‘mathematically rigorous’ enough. Although hindsight has made this old style of mathematics seem invitingly, deliciously simple. I wouldn’t dream of trading what I’m learning now for those old, boring sums. Not a chance.
It took me a while to really wrap my head around what a Mathematics degree is. I remember during the early days of university, one of our lecturers said something that has stuck with me ever since. I didn’t quite understand what he was trying to say at the time, but it makes perfect sense now I’m coming towards the end of my degree. I can’t remember his exact words, but it went something like this:
“There are two types of Maths in the world, Maths that we know & Maths that no one knows. Throughout school you only get taught about the Maths that we know, but a degree in Mathematics prepares you for the Maths we don’t.”
What he was trying to get at is linked again to the idea that Mathematics is based on proofs, and therefore every theorem and result can be traced back to some chosen assumptions or axioms. At one point Pythagoras’ Theorem wasn’t known, and not considered formal Mathematics until Pythagoras proved it. Each and every new mathematical theorem has been proven logically and rigorously. What my lecturer was trying to express was that a degree in Mathematics provides the tools to seek out these new theorems or as he put it, ‘the Maths that no one knows’.
Except, even two years into my degree, this new exciting unknown Mathematics we were apparently being prepared for was seeming even more illusive. Sure, we had learnt the basic logical ideas of proofs, the language of pure mathematics. Sure, we’d spent two years studying and delving deeper into the field we’ve chosen to study, but it was all still just maths of the first category. ‘Maths that we know’. The horizon was nowhere to be seen.
However, halfway through a recent lecture, we were told that for the remaining time what we would be learning would be non-examinable. Instead of providing us with a particularly hard proof of a theorem in the course, our lecturer actually showed us some new Mathematics. Providing a brief overview and part of a proof for some work that had recently been published by members of our Universities mathematics department.
And I followed it. It’s the first time I’ve ever felt close to the frontier of my subject. Obviously the bulk of the published paper would be beyond the scope of what I’m currently learning, but I’d caught a whiff of this illusive kind of new mathematics, ‘the Maths no one knows’.