Letters from William Burnside to Robert Fricke: automorphic functions, and the emergence of the Burnside Problem

Abstract

Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of the Burnside Problem prior to its first publication. We present these letters as a whole to the public for the first time. We draw a picture of these two mathematicians and describe their activities leading to their correspondence. We thus gain an insight into their respective motivations, reactions, and attitudes, which may sharpen the current understanding of professional and social interactions of the mathematical community at the turn of the twentieth century.