Several theorems are named after Augustin-Louis Cauchy. Cauchy theorem may mean:

• 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