This dissertation project explores the role of mathematics in its larger social context. It seeks to demonstrate the importance of the previously unexamined role of mathematics in Irish History by analyzing the relationship between mathematics, education, and social change in nineteenth century Ireland through an investigation of Trinity College, Dublin. Trinity's role in Irish society was to maintain the privileges of the Protestant elite in a predominantly Catholic country, and during the period in which those privileges were most forcefully challenged, mathematics came to play a central role in the college's curriculum. By tracing debates about the curriculum as well as debates about the religious or social implications of new scientific theories, the project will demonstrate how mathematics and mathematical science were seen as important tools in the struggle to accomplish specific social and political goals.