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> I was a bit upset, because I thought, “I can’t believe I could have enjoyed this when I was much younger!” Yea, wish I had known about Galois theory when I

> I was a bit upset, because I thought, “I can’t believe I could have enjoyed this when I was much younger!” Yea, wish I had known about Galois theory when I was younger got sucked into junk lit and computer games instead, now I have to wait until I retire or get some economic buffer from grinding to learn what I want.

wolverine876 3y ago
Sometimes I think a powerful factor in high-level accomplishment is appreciating something valuable sooner than others, which may depend on opportunity, luck, and the capability to appreciate (e.g.) high-level art or math as a teenager.
graycat 3y ago
Of course, Galois and his fatal pistol duel were a long time ago, soooo, there are many polished presentations of Galois theory. E.g., in the abstract algebra text by I. N. Herstein can learn the basics of Galois theory in a few hours of study. Apparently the idea of using abstract algebra, especially fields (each of the rational, reals, and complex numbers are fields but not finite), for applications, especially to error correcting codes and, eventually, cryptography, date from Hamming back at Bell Labs. In college and grad school, I got dragged into finite fields and related topics over and over. I was too patient and tolerant: I just don't like that math. I DO like linear algebra, especially for its connections with Hilbert space, differential equations, the math used in Maxwell's equations, differential geometry, optimization, relativity theory, Markov processes, and more but somehow I just don't like cryptography and error correcting codes. Back in college one of my profs just observed and remarked that I'm an analyst and not an algebraist! So, this situation may help others here at HN: Some people like math analysis while mostly others like math abstract algebra! Still, just for Galois theory, if want to learn it, then can do that in a few hours!
- haskellandchill 3y ago
  Heh, just an example. But at the level of my interest it's not a few hours, I like to learn math so that "you could have invented galois theory", and I want to go up to Grobner basis at least.
  - graycat 3y ago
    The I. N. Herstein text does Galois theory with fully precise proofs. Learn those and could see how to "invent" Galois theory yourself. As I recall Herstein does not cover Gröbner basis. By now don't really have to look for a book and, instead, can use the Internet -- yes, some Internet material does provide careful proofs.

wolverine876 3y ago

Sometimes I think a powerful factor in high-level accomplishment is appreciating something valuable sooner than others, which may depend on opportunity, luck, and the capability to appreciate (e.g.) high-level art or math as a teenager.

graycat 3y ago

Of course, Galois and his fatal pistol duel were a long time ago, soooo, there are many polished presentations of Galois theory. E.g., in the abstract algebra text by I. N. Herstein can learn the basics of Galois theory in a few hours of study. Apparently the idea of using abstract algebra, especially fields (each of the rational, reals, and complex numbers are fields but not finite), for applications, especially to error correcting codes and, eventually, cryptography, date from Hamming back at Bell Labs. In college and grad school, I got dragged into finite fields and related topics over and over. I was too patient and tolerant: I just don't like that math. I DO like linear algebra, especially for its connections with Hilbert space, differential equations, the math used in Maxwell's equations, differential geometry, optimization, relativity theory, Markov processes, and more but somehow I just don't like cryptography and error correcting codes. Back in college one of my profs just observed and remarked that I'm an analyst and not an algebraist! So, this situation may help others here at HN: Some people like math analysis while mostly others like math abstract algebra! Still, just for Galois theory, if want to learn it, then can do that in a few hours!

haskellandchill 3y ago
Heh, just an example. But at the level of my interest it's not a few hours, I like to learn math so that "you could have invented galois theory", and I want to go up to Grobner basis at least.
- graycat 3y ago
  The I. N. Herstein text does Galois theory with fully precise proofs. Learn those and could see how to "invent" Galois theory yourself. As I recall Herstein does not cover Gröbner basis. By now don't really have to look for a book and, instead, can use the Internet -- yes, some Internet material does provide careful proofs.