A Character
Jun. 30th, 2015 04:34 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowIn Winter Quarter of my first year of grad school, I took a course in ring theory from Dr. Israel "Izzy" Herstein. This was the second part of the three-quarter sequence in abstract algebra; I'd passed out of the first quarter, on group theory, and regarded algebra as my mathematical forte. Dr. Herstein was (like most of the Chicago faculty) an outstanding mathematician; his book on noncommutative rings is still, I believe, a standard text.
He was an irascible and stubborn man; I caught the blast of his annoyance more than once, that quarter, for one or another silly assertion. He was an unapologetic smoker (and it eventually killed him); he blatantly ignored the "NO SMOKING" signs on the walls of every classroom. (He occasionally confused himself, putting a piece of chalk to his lips instead of a cigarette.) But he was a good teacher, all things considered.
The first midterm, that quarter, covered material I was more or less familiar with, and I am not boasting when I say that I aced it: 150/150. I am not boasting, because of what happened in the second midterm. This one covered one of his favorite areas, something called "character theory". I walked into the classroom the day of the second test, picked up a blue book and the test paper, and sat down. I looked at the first question. I made a few tentative pencil marks in the blue book. I looked at the second question, and the third, and... And I picked up the blue book and the pencil and walked out.
A few days later, Dr. Herstein called me in to ask what had happened; he was concerned I'd become overconfident. I told him that no, I simply didn't understand the material. Somehow he found this a better response.... I did well enough on the final to wind up with an A- in the class, but I still didn't understand character theory.
In my current research, I'm investigating "first-order pure CAT-invariant classes of polygons". A few days ago, I noticed something interesting happening with regard to pentagons, and saw that it could be tweaked to apply to quadrilaterals and hexagons as well. That it happened was clear; why it happened escaped me - until I sat down and started cranking symbols, and saw what was going on.
The explanation? Character theory. I know exactly what happens when the polygon has an odd number of sides (and character theory is the explanation); I know why it doesn't quite happen when the number of sides is even (and character theory explains it); I know what I need to investigate to clarify what does happen when the number of sides is even; and I have a vague suspicion what I will have to do when I move from pure classes to mixed classes (and character theory is lurking underneath).
Israel Herstein died in 1988, just a few years after I graduated from Chicago. One of his less satisfactory students today salutes him.
He was an irascible and stubborn man; I caught the blast of his annoyance more than once, that quarter, for one or another silly assertion. He was an unapologetic smoker (and it eventually killed him); he blatantly ignored the "NO SMOKING" signs on the walls of every classroom. (He occasionally confused himself, putting a piece of chalk to his lips instead of a cigarette.) But he was a good teacher, all things considered.
The first midterm, that quarter, covered material I was more or less familiar with, and I am not boasting when I say that I aced it: 150/150. I am not boasting, because of what happened in the second midterm. This one covered one of his favorite areas, something called "character theory". I walked into the classroom the day of the second test, picked up a blue book and the test paper, and sat down. I looked at the first question. I made a few tentative pencil marks in the blue book. I looked at the second question, and the third, and... And I picked up the blue book and the pencil and walked out.
A few days later, Dr. Herstein called me in to ask what had happened; he was concerned I'd become overconfident. I told him that no, I simply didn't understand the material. Somehow he found this a better response.... I did well enough on the final to wind up with an A- in the class, but I still didn't understand character theory.
In my current research, I'm investigating "first-order pure CAT-invariant classes of polygons". A few days ago, I noticed something interesting happening with regard to pentagons, and saw that it could be tweaked to apply to quadrilaterals and hexagons as well. That it happened was clear; why it happened escaped me - until I sat down and started cranking symbols, and saw what was going on.
The explanation? Character theory. I know exactly what happens when the polygon has an odd number of sides (and character theory is the explanation); I know why it doesn't quite happen when the number of sides is even (and character theory explains it); I know what I need to investigate to clarify what does happen when the number of sides is even; and I have a vague suspicion what I will have to do when I move from pure classes to mixed classes (and character theory is lurking underneath).
Israel Herstein died in 1988, just a few years after I graduated from Chicago. One of his less satisfactory students today salutes him.
