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.


About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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10 Responses to

  1. ywalme says:

    Have you or have you not gotten to the Feit-Thompson theorem yet? It has to do with simple groups and isomorphism to Z/pZ. Someone used it to solve one of our more simple homework problems, causing the teacher to make a motion as though smashing a fly with the largest imaginable hammer. It really is quite an impressive beast.

    • Simon says:

      No, we haven’t done that. We haven’t even mentioned Z/pZ except for a few times when we had examples with Z/2Z. I love theorems that smash flys with large hammers. I’m no good at using weak theorems to prove other weak theorems. I much prefer super-theorems.

    • aknoln says:

      huh cool I just looked it up in Dummit&Foote:
      Theorem. (Feit-Thompson) If G is a simple group of odd order, then G is isomorphic to Z_p for some prime p.
      This proof takes 255 pages of hard mathematics. 2
      2 Solvability of groups of odd order, Pacific Journal of Mathematics, 13 (1963), pp. 775-1029

  2. rippledance says:

    *patpat* for your back.

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