The Life of a Mathematician

Two more days before I'm supposed to get a root canal, and my tooth has decided to start hurting again. My plans of catching up with differential equations yesterday evening were derailed by the need to use strong medication and then wait for it to start working. I can't even chew with the teeth on the other side without bothering it. I'll have to call the dentist later and see if this is to be expected, but I imagine so. He said we ought to do the root canal after a week, but that there wouldn't be problems if we did it within two weeks. Then they couldn't manage to schedule it sooner than three weeks later.


I like working in the extended reals. I was introduced to the concept a few years ago, but it still feels like doing something exciting and forbidden. I've told undergraduates that the derivative allows us to sort of get around not being able to divide by zero; it's like saying, "We can't divide by zero, but if we could, this is what the answer would be." However, the extended reals allow for it much more directly. You can call infinity a number, and you can divide by zero, and various other impossible things. You just have to put a few restrictions in to avoid paradoxes. I remember wondering in high school why division by zero had to be "undefined". If it's undefined, why can't we just define it? The answer was that if we defined it in the obvious way, we got problematic results. Turns out you can just forbid any action that would lead to those results.