Ups and Downs

I proved another theorem last night. This time, it was a theorem of the type W and I have been wishing for. Unfortunately, it's not a very broad theorem; it only applies, as far as I know, to about half-a-dozen cases. Still, if it isn't a breakthrough, it's at least a hole in the dike, and I've been fiddling with it in hopes of pushing it further. Things look mildly promising.

The downside was that I got the key insight just after going to bed. I got up again and made a note to myself, so that I wouldn't forget; then I spent most of the night examining the shape of the argument, and making sure the pieces fit together right. Thus, once again, I spent today in less than optimum condition. Fortunately, I was giving tests in both of my classes, so neither prep nor lecture was required. I did sketch what I'd discovered to W and L (T wasn't in today), but I'm not sure how much sense I made.

I'm tempted to think that proving theorems is bad for my health.