もっと詳しく

How Imaginary Numbers Were Invented – “A general solution to the cubic equation was long considered impossible, until we gave up the requirement that math reflect reality.”[1]

also btw…

  • Galois Groups and the Symmetries of Polynomials – “No one knows why Galois found himself on a Paris dueling ground early in the morning of May 30, 1832, but the night before, legend has it that he stayed up late finishing his last manuscripts. There he wrote:”[2]
  • Go to the roots of these calculations! Group the operations. Classify them according to their complexities rather than their appearances! This, I believe, is the mission of future mathematicians. This is the road on which I am embarking in this work.

  • New Shape Opens ‘Wormhole’ Between Numbers and Geometry – “Coherent sheaves correspond to representations of p-adic groups, and étale sheaves to representations of Galois groups. In their new paper, Fargues and Scholze prove that there’s always a way to match a coherent sheaf with an étale sheaf, and as a result there’s always a way to match a representation of a p-adic group with a representation of a Galois group. In this way, they finally proved one direction of the local Langlands correspondence. But the other direction remains an open question.”

Galois Theory Explained Simply[3]
Galois-Free Guarantee! | The Insolubility of the Quintic
Group theory, abstraction, and the 196,883-dimensional monster[4,5]