Letters from William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem

TL;DR

This paper presents newly discovered letters from William Burnside to Robert Fricke, providing historical context and insights into their mathematical collaboration and the early development of the Burnside Problem.

Contribution

It publicly shares previously unknown letters that contain early references to Burnside's Problem and explores the professional and social interactions of Burnside and Fricke.

Findings

Letters contain early instances of Burnside's Problem

Insights into mathematicians' motivations and reactions

Historical understanding of mathematical community dynamics

Abstract

Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's 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 20th century.