Sometimes the solution to a mathematical problem seems so obvious that you don’t think you should even bother writing it down. I often make that mistake.

But every once in a while I think about something that seems obvious on the face of it, and I take the trouble to write it down. And then suddenly I realize I’d had it all wrong.

I discover that the thing that had seemed to consist of just one simple step actually consists of three different steps. And each of those steps can be unpacked to contain sub-problems that are all interesting in their own right.

Before I know it, I’m generalizing the problem. I’m connecting it to other problems I’ve seen, and getting a whole new set of insights.

That’s why I try, on my better days, not to take mathematical problems for granted. And also to remember to carry a pen.