The difficultly with proofs at first is that you’re required to show things that feel *obvious*. A good proof should provide an explanation for something which isn’t clear. Unfortunately, when you start proving divisibility rules, there’s a limit to how much insight you get from the proof.

This is something I worry about a lot when learning. It’s why I try to teach and write about the topics I’m learning in order to push away that cliff.

24 Jan 2020

I understand the need for basic research, but I sometimes wonder how many different toy theories and models we really need.

22 Jan 2020

The eternal struggle: teacher finds new problems, and students react by combing every centimetre of the web for the solutions.

20 Jan 2020

As one of my professors used to say, “When you’re solving a problem, it doesn’t matter if your proof is messy, convoluted, or entirely unnecessary. If you’re using logic correctly, then it’s fine.”

17 Jan 2020

When a single sentence begins to have its own subplots and narrative structure, you’re probably going overboard.

15 Jan 2020

Maybe we need to throw in a bit more hyperbole at the top. You know, *really* dig deep and go for it here.

On second thought, maybe we just end up switching our idea of a “nice” answer.

08 Jan 2020

I think every student has found themselves sitting at a desk with a textbook, eyes glazed over. Unfortunately, putting your eyeballs in front of a textbook is not quite enough.

06 Jan 2020