Baron Cauchy is oft celebrated as the developer extraordinaire of complex function theory.
The first influential theorem he proved was Cauchy's integral theorem, also known as the Cauchy-Goursat Theorem (CGT).
(Goursat, though lesser known than Augustin-Louis Cauchy, was also an extraordinary mathematician where mathematical analysis was concerned)
The CGT is an important statement about integrals for holomorphic functions in the complex plane. A holomorphic function is a complex valued function, that may have one or more complex variable arguments, which is broadly speaking "complex differentiable". The notion of complex differentiability in this context has a specific interpretation.
