2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163628Hilbert's Theorem 90 is a classical result in the theory of cyclic extensions. The quadratic case of Hilbert 90, however, generalizes in noncyclic directions as well. Informed by a poem of Richard Wilbur, the article explores several generalizations, discerning connections among multiplicative groups of fields, values of binary quadratic forms, a bit of module theory over group rings, and even Galois cohomology.v2 (15 pages); followed Monthly style sheet and added additional expositionNumber TheoryRings and Algebras12F10; 12G05text