The Concept of a Riemann Surface

A Riemann surface is a multilayered surface used in complex function theory. It allows a multivalued complex function to be treated as a single-valued function of a complex variable.1

Hermann Weyl, a mathematician influential in linking pure mathematics and theoretical physics, created a new branch of mathematics by uniting function theory and geometry in his work The Concept of a Riemann Surface (1913). This approach opened up a modern, unified view of analysis, geometry, and topology. Bernhard Riemann, another mathematician, introduced the concept of a Riemann surface in the context of complex variables, defining it as a real surface spread over a plane that arises from equations involving two complex variables. He also showed how these surfaces could be classified by a number called the genus.23