Collection: Cauchy's Integral Theorem

In 1821 the French mathematician Augustin-Louis Cauchy published a series of lectures titled “Cours d’analyse,” a rigorous text that quickly became the manifesto of analysis in its time. Cauchy’s most significant contribution to mathematics was his work in complex analysis, to which the later half of his Cours d’analyse is dedicated.

The Cauchy integral theorem is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if two different paths connect the same two points, and a function is holomorphic everywhere in between the two paths, then the two path integrals of the function will be the same.