Complex analysis
Complex analysis is the area of mathematical analysis that looks at functions on the complex numbers. It has a wide range of uses, including algebraic geometry and analytic number theory, and areas of physics, such as string theory and quantum mechanics. Augustin-Louis Cauchy is normally credited with founding complex analysis, building on the work of Gauss and Euler. Other mathematicians that made significant advances in this field include Riemann, Weierstrass, Kiyoshi Oka and Lars Ahlfors.