Complex analysis
2 quotes
Biography
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that studies complex-valued functions of one or more complex variables. It is used in many branches of mathematics, including functional analysis, algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory.
"Le développement naturel de cette étude conduisit bientôt les géomètres à embrasser dans leurs recherches les valeurs imaginaires de la variable aussi bien que les valeurs réelles. La théorie de la série de Taylor, celle des fonctions elliptiques, la vaste doctrine de Cauchy firent éclater la fécondité de cette généralisation. Il apparut que, entre deux vérités du domaine réel, le chemin le plus facile et le plus court passe bien souvent par le domaine complexe."
"The result has caught the imagination of most mathematicians because it is so unexpected, connecting two seemingly unrelated areas in mathematics; namely, number theory, which is the study of the discrete, and complex analysis, which deals with continuous processes."