Groups encode symmetry.
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Huang, Jackson, Lee, Poonen, Pries and Zhang construct an explicit degree-23 polynomial whose splitting field over the rationals has Galois group M₂₃. They also construct a regular M₂₃ extension of Q(t), completing the realization program for all 26 sporadic finite simple groups.
Read original source Original paper v2: theorems and human/AI attributionarxiv.org
Original report: 2026-08-09OpenAI claims Lie-group structure for any locally compact second-countable Hausdorff group with a faithful jointly continuous action on a connected finite-dimensional manifold under the stated topological conventions.
Read original source Pinned primary manuscript · family 304github.com
Original report: 2026-10-06OpenAI claims that a hyperbolic group with a two-sphere boundary has a proper cocompact action by isometries on hyperbolic three-space, allowing a finite kernel.
Read original source Pinned primary manuscript · family 246github.com
Original report: 2026-10-06Groups encode symmetry. Their boundaries, actions, equations, and algebraic finiteness conditions supply distinct mathematical problems.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
AI-assisted realization of the Mathieu group M₂₃ over the rationals
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