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