Hilbert's theorem may refer to: Hilbert's theorem (differential geometry), stating there exists no complete regular surface of constant negative gaussian curvature immersed in Hilbert's Theorem 90, an important result on cyclic extensions of fields that leads to Kummer theory Hilbert's basis theorem, in commutative algebra, stating every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated Hilbert's finiteness theorem, in invariant theory, stating that the ring of invariants of a reductive group is finitely generated Hilbert's irreducibility theorem, in number theory, concerning irreducible polynomials Hilbert's Nullstellensatz, the basis of algebraic geometry, establishing a fundamental relationship between geometry and algebra Hilbert's syzygy theorem, a result of commutative algebra in connection with the syzygy problem of invariant theory
See also List of things named after David Hilbert