It starts with a deceptively simple question: “maths graduates… why do you like maths?” Equally this question could apply to any university graduates. Why did you do your degree? Are you glad you chose that discipline?
It can be hard to understand an aspect like this about yourself. As Paul Erdös, the famous mathematician covered in The Man Who Loved Only Numbers, said: “Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful? If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.”
The reasons could have changed over time. Why I liked maths before I did my degree is very different to what I loved about the field after 3 years of study. At high school mathematics was a very easy subject which required little effort, at least for me, to get an A at A-level. At that stage mathematics is just teaching you tools. Learn to differentiate and integrate by applying five or so simple, straight forward rules to good level of accuracy and you’re looking at a decent mark already. Maths classes were therefore a relaxing affair, a list of problems and you could even have a little chat whilst you were going through the problem set!
Mathematics at university isn’t just a different breed; it’s a completely different species. Where all maths up to the stage had been about the how, university is about the why and the proving why. Theoretical maths, at least at Warwick was about proving things to one extent or another. You either learned to love that about the subject, for most of us it wasn’t what we expected, or you grew to despise your degree – that happened to plenty of students too.
There’s a lot to enjoy about the subject though. The use of proof elevates mathematics to an almost unrivalled position in terms of rigour. There’s a lot of comfort in dealing with definites. Assignments and exam papers aren’t subject to personal prejudices. From my experience you can get marked down in essays in other subjects simply for making a point that is disagreed with by the marker. That’s never the case with maths. But beyond that, trying to find definitive truths is hugely exciting. It’s reassuring to work in a field where your life’s work can stand the test of time. Referring back to previous posts it might also explain why maths fails to generate much news coverage. It’s not just that the advancing methodology is difficult for journalists and readers to understand. Afterall, there are plenty of maths graduates who could explain at least what is being proved and might find this very interesting. There are also equally maths graduates who could move towards the field of journalism and cover these stories. No, the problem is that mathematics isn’t a field in debate. There aren’t controversies, reversals in understanding or figure head vs figure head debates. This is no more apparent in the little coverage that maths does get which always centres on the stranger figures of the field with the focus generally being “look at the freak. Point at the freak!”.
I also love the impracticality of mathematics. Creative mathematics for the simple joy of discovery. This has been recognised throughout the centuries. John Adams on the subject:
“I must study politics and war that my sons may have liberty to study mathematics and philosophy.” – President John Adams (1st!)
Just doing things for fun’s sake knowing that they probably will never have any practical relevance at all is great fun. Doing a degree where you actively learn things without any practical life relevance may not sound smart for a career choice, but that’s why degrees are good and one of the things they always used to be about. Sadly this might get lost in these super “pay £27k for university” scheme. What a travesty that would be.
Fundamentally I couldn’t imagine doing anything different. I tried a lot of other subjects at Warwick, thanks to the flexibility of the programme structure: from physics to computer science, japanese to operational research. None of them offered the same buzz as mathematics despite the difficulties that it sometimes offered. Despite writing this article I don’t feel like I truly understand the joy of mathematics. Like all art perhaps it just is beautiful.