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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 ${\displaystyle \mathbb {R} ^{3}}$
• 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

• Disambiguation pages