### Introduction

Despite his short life, Robert Murphy (1806-1843) was a mathematician and physicist who “had a true genius for mathematical invention,” according to Augustus De Morgan (1806-1871) [Venn 2009]. Murphy’s mathematical research can be categorized into three areas: Algebraic Equations, Integral Equations, and Operator Calculus [Allaire 2002]. The majority of the scholarship on Murphy is centered around his contributions to physics; however, historians such as Petrova [1978] and Bradley and Allaire [2002] have explored Murphy’s linear operator theory. The purpose of this paper is to provide a unified exposition in which we synthesize and expand on existing accounts of Murphy’s life and mathematical contributions. Additionally, we give an overview of his mathematical papers and accomplishments in hopes of inspiring historians to examine and analyze his original works.

The authors have also provided a detailed bibliography, which lists where all but one of Murphy’s books and papers are available for download, either Google Books or the Journal STORage database (JSTOR). Murphy’s first paper,

*Refutation of a Pamphlet Written by the Rev. John Mackey Entitled “A Method of Making a Cube a Double of a Cube, Founded on the Principles of Elementary Geometry,” wherein His Principles Are Proved Erroneous and the Required Solution Not Yet Obtained* [1824],

has not been available in the United States. As a result, the authors have provided a transcription of this paper with commentary as an appendix available here.