Cauchy theorem may refer to:
Cauchy's integral theorem in complex analysis, also Cauchy's integral formula Cauchy's mean value theorem in real analysis, an extended form of the mean value theorem Cauchy's theorem (group theory) Cauchy's theorem (geometry) on rigidity of convex polytopes The Cauchy–Kovalevskaya theorem concerning partial differential equations The Cauchy–Peano theorem in the study of ordinary differential equations Cauchy's limit theorem Cauchy's argument principle Poincaré separation theorem, also known as the Cauchy interlacing theorem