I'm proving quadratic reciprocity in my Number Theory class. I have only taught Number Theory once before, so my notes have some mistakes. But I have two sections this semester, and the second section benefits from me having figured out most of those mistakes while presenting to the first section. My presentation in the second section today is perfect.

My students don't have facial expressions. The math student council sometimes has events, and it seems that one of these events is a disinterest contest. Math lectures are generally pretty entertaining, and it is difficult to show disinterest, but these students are competitive. I wonder if sleeping is a win, or a disqualification.

I complete the proof. Flawless. It is group theoretical proof by Rousseau that I found mentioned on MathStackExchange, but I had to remove the group theory from it, replacing it with some reflections of some symmetric pictures. Perfect.

There is a corollary, but I pause. I don't want to step on the applause. But what is this? There is no applause? I check my watch. It doesn't explain the lack of applause. Hard crowd! One student's mask of disinterest is broken when she looks up in curiosity at the pause. But then I realise:

"QED!" I announce, with a bow.

There is a smattering of polite claps, and a smile or two from the front row.

I blow on my chalk. Time for that corollary.