Huang, Jackson, Lee, Poonen, Pries and Zhang construct an explicit degree-23 polynomial whose splitting field over the rationals has Galois group M₂₃.
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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: 2026-08-09Huang, 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.
The other 25 sporadic simple groups had been realized over the rationals, but M₂₃ remained the last unresolved sporadic case. Earlier M₂₃ constructions over other number fields did not settle the rational case.
If correct, completes a decades-long program in inverse Galois theory with an explicit construction and a regular realization, rather than a heuristic search result.
A sourced advance or substantial formalization with the exact target, hypotheses, baseline and AI role stated. Importance and verification are assessed separately.
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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