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The Inverse Galois Problem

Reviewing hundreds of pages for publication. AI will likely release first. But at least we will understand it. In the interim, here are some representations from a highly technical and not very fun area of math. Sidenote, the problem was conceived of by a 20-year-old, the night before his death by duel. Drama.

The modern version of the problem is framed by Hilbert and Noether. Emmy Noether, too, was overlooked in her time. Liouville published Galois fourteen years after his death. Since, Galois’s work has been ripe for misunderstanding. But Noether got it, and her symmetry saved Einstein’s relativity.

The inverse Galois problem: the realization landscape, M23 spotlight, moduli tower, braid orbit and realization pipeline Four branch points on the Riemann sphere, the five-branch viewpoint, and the special ten-state cell From the ordered Nielsen class to the reduced Hurwitz space, the five-branch refinement and the comparison-map chain Every finite group realized as a Galois group over Q: the unified construction, case study M23 and sample polynomials

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Posts here will cover mathematics, law, economics, and whatever runs between them: papers as they publish, progress as it happens, and occasional notes on everything else.