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Although a simple EE, I learned Galois Theory in college (coincidentally also in Edinburgh, although <other-university>). In 4th/final/senior year there were va

Although a simple EE, I learned Galois Theory in college (coincidentally also in Edinburgh, although <other-university>). In 4th/final/senior year there were various elective classes including Advanced Mathematics which I chose as a kind of masochistic challenge. The class was very small, and it turned out taught by a "real mathematician" who commuted from the Mathematics department every day. Even though I've had a great deal of mathematics education I think this was the only time the teacher was someone who did mathematics all-in (as in he created new mathematics, published papers etc.) as opposed to someone who had the job of teaching some field (sic) in mathematics. He taught Galois Theory using its application to coding theory for worked examples. That class was something of a turning point in my life to be honest. I'd never think of constructing a heptagon again, for example. Definitely avoided Duels, and Montparnasse. Ok joking aside, it caused the proverbial lightbulb to turn on in my brain, and helped tremendously in my career later when I ran into folks trying to seem smart because they understood ECC or ZKPs. It was like the extreme opposite of those people who say "I never used a single thing I learned in college".

JadeNB 2y ago
> Ok joking aside, it caused the proverbial lightbulb to turn on in my brain, and helped tremendously in my career later when I ran into folks trying to seem smart because they understood ECC or ZKPs. Presumably it helped to know that there was something beyond these folks' knowledge, but did it help in any more direct way?
- dboreham 2y ago
  The main benefit was to do with how I conceived mathematics as a subject: In the before times, it appeared to be an infinite linear journey with subjects already studied in the set of "understood" things, and everything else in the "hard" set of things. Proceeding on the journey, subjects are expected to become harder and harder until eventually you're defeated and have to stop trying to learn more mathematics. After that class, my conception of mathematics was of an extensively cross-linked tree of subjects where seemingly unrelated fields connect to each other, and where although the number of fields is large, it is not infinite, and with effort and time everything can be understood if required. To be fair, that was the stated objective of the guy teaching the class. On day 1, he said "my objective is to teach you enough that you can understand whatever mathematics you need to understand in the future" and darn it he pretty much succeeded. In summary, more of an attitude than specific knowledge of anything in particular.
whitten 2y ago
What was the name of your professor ?
- dboreham 2y ago
  Interesting question, and I don't remember. This was 40 years ago. I did find the final exam paper recently and marveled that at one time I was able to ace it. Notable in that there was a typo in one question that rendered it unsolvable. I was able to gain credit nevertheless by showing it to be unsolvable. I think that's the only case I remember where an exam had been printed with a major mistake.

JadeNB 2y ago

> Ok joking aside, it caused the proverbial lightbulb to turn on in my brain, and helped tremendously in my career later when I ran into folks trying to seem smart because they understood ECC or ZKPs. Presumably it helped to know that there was something beyond these folks' knowledge, but did it help in any more direct way?

dboreham 2y ago
The main benefit was to do with how I conceived mathematics as a subject: In the before times, it appeared to be an infinite linear journey with subjects already studied in the set of "understood" things, and everything else in the "hard" set of things. Proceeding on the journey, subjects are expected to become harder and harder until eventually you're defeated and have to stop trying to learn more mathematics. After that class, my conception of mathematics was of an extensively cross-linked tree of subjects where seemingly unrelated fields connect to each other, and where although the number of fields is large, it is not infinite, and with effort and time everything can be understood if required. To be fair, that was the stated objective of the guy teaching the class. On day 1, he said "my objective is to teach you enough that you can understand whatever mathematics you need to understand in the future" and darn it he pretty much succeeded. In summary, more of an attitude than specific knowledge of anything in particular.

whitten 2y ago

What was the name of your professor ?

dboreham 2y ago
Interesting question, and I don't remember. This was 40 years ago. I did find the final exam paper recently and marveled that at one time I was able to ace it. Notable in that there was a typo in one question that rendered it unsolvable. I was able to gain credit nevertheless by showing it to be unsolvable. I think that's the only case I remember where an exam had been printed with a major mistake.