I could probably have framed this post as an “Ask Uncle Colin”, but it feels somehow different, so I’m going to do it as a Monday post. My blog, my rules.
On Twitter, @sharanjit asked:
I had a point in my education where maths went from being easy to suddenly being hard (University). Did you have that? When? Did you keep going? How?
I got it in my second year Algebra and Analysis exam, where I had an “… I think I can spell some of those words?” moment with the first few questions. I got through that exam by finding a few things I could do and going all out on exam technique.
In terms of how I got past the confidence knock, I had an academically poor year in France the following year, and came back with an attitude of “I’m much better than I’ve shown recently” and gave myself a colossal kick in the pants.
I figured out the things that interested me and specialised in those for my final year — I had been coasting a bit up until then and I knuckled down and knocked everything out of the park first semester back.
My big take-away was that maths isn’t a line, it’s a tree. Maybe if you’re Gauss, you can climb every branch. Picking the branches that looked interesting was the key for me.2
A follow-up question from @StephenPWooton:
What were your exam techniques which saw you through?
It was more than 20 years ago, so I’m not sure of the exact details, but I remember reading through the questions and saying “these ones look more familiar topics than the others, I’ll start with those”
Once I had a couple of questions under my belt, it jogged my memory on a few definitions/proofs I could write down after a fashion and pick up odd marks here and there.
Probably more than anything, I realised that panicking wasn’t going to help me and I needed to calm down, breathe properly and find something I could do.
Years later, I found a quote that said “set aside your fears and make a small, imperfect start”, which pretty much encapsulates what I did.