Show threadƧƿѦςɛ♏ѦਹѤʞMay 2, 2025
@catselbow
Astonishing! I hadn't come across this before - absolutely fascinating!
#maths #mathematics #polynomial #polynomials #CatalanNumbers #combinatorics #Galois #GaloisTheory
https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true
N-gated Hacker NewsMar 15, 2025
🚨 Breaking news for math enthusiasts: a blog post on a *single* lemma from a 2023 textbook! 📚😴 Apparently, you need a PhD just to understand the introduction. But don’t worry, the Fundamental Theorem of Galois Theory itself isn’t explained here, because who needs the main course when you can have a crumb? 🥖🙄
https://susam.net/lemma-for-ftgt.html #mathnews #mathenthusiasts #GaloisTheory #academia #blogpost #2023textbook #HackerNews #ngated
Lemma for FTGT - Susam's Quick Notes

Hacker NewsMar 15, 2025

Lemma for the Fundamental Theorem of Galois Theory

https://susam.net/lemma-for-ftgt.html

#HackerNews #Lemma #GaloisTheory #FundamentalTheorem #Mathematics #Research

Lemma for FTGT - Susam's Quick Notes

Simon Koch Sep 12, 2023

I'm trying to wrap my head around the basics of #Galois theory.

If anyone versed in Galois theory or #Algebra could check my thinking I'd be very grateful.

Take the polynomial x⁴+x³+x²+x+1. It's root have the symmetry group C_4.
Am I correct when I say that this polynomial is solvable by radicals because you can find a tower of normal subgroups with prime order with regards to the previous group, that being:

C_4 → C_2 → {e}

with |C_4/C_2|=2 (prime)
and |C_2/{e}|=2 (prime).

#galoistheory

Show threadMarek GluzaJul 5, 2023

@deilann
Bouncing back on the subject, I took Artin's #GaloisTheory with me to #Benasque and I think on page 25 there is a complete discussion. As you said any #algebraicNumber, defined as a root of a real polynomial, can be seen as a root of a unique polynomial of lowest degree which is irreducible, i.e. not divisible by any other poly omial with coefficients in the base field.

The coefficient of the highest power needs to be 1, one should divide the contending polynomials by each other and evaluate at the shared root showing that, having the same degree, they have 0 polynomial ring division remainder so must be the same.

Marek GluzaJul 5, 2023

I'm reading Artin's #GaloisTheory and I'm wondering if the #math exposition of the #matrix #determinant relying on homogeneity properties is related to the #BrunnMinkowski #inequality

I will check my handwritten notes when I'll be in Poland end of July but I remember that homogeneity played a role there.

This rambling is related to my struggle to understand the #BrascampLieb and #rearrangementInequality. Any hints much appreciated 🥹😅🙈😊