Lars Ahlfors, a Finnish mathematician then a visiting researcher at Harvard, publishes in 1935 a paper on covering surfaces related to the Riemann surfaces of inverse entire and meromorphic functions. The work opens what Constantin Carathéodory described as an entirely new chapter of analysis — a "metric topology" — and lays the groundwork for Ahlfors's later developments in quasiconformal mappings. The official 1936 Fields Medal citation, one of the first two ever awarded, explicitly recognized this result as Ahlfors's central contribution.