Ouch. My back has been causing me excruciating pain all day. When someone has had severe back pains reguarly for the past 20 months, I think that’s a sign that something is very wrong. It hasn’t been this bad for a long time though.
I constant alternate between thinking I sort of understand algebra and thinking that I don’t understand any algebra at all. Why am I so incompetent? I should understand this stuff perfectly. I don’t think it’s particularly difficult. I just can’t visualize anything. What does it mean if there’s a homomorphism from one group to another visually? What does it mean if we take a quotient group? I can understand all these things if I have concrete examples to work with. I guess that’s why algebra is hard. I guess I’m not destined to become an algebraist. I also don’t really see anything amazing in algebra. We prove all these theorems that are basically obvious once one understands what they’re saying. I don’t see the same brilliance in algebra as I do in analysis. There’s no Cauchy Integral Theorem or Picard’s Theorem or anything like that in algebra. It’s hard for me to deal with that. I guess I’m just too stupid for algebra. Not understanding what’s going on in a math class feels very strange. It has never happened to me before, but now I feel confused each day in algebra. On the other hand, I feel on top of things in analysis and topology. Maybe it’s just an illusion, and I’ll sink in those classes too, but I doubt that will happen.