The analytical society: mathematics at Cambridge University in the early nineteenth century
Keywords: history
Cambridge University
mathematical sciences

The thesis is a study of the Analytical Society (1812-1813) of Cambridge University. Its purpose is to present a detailed history of the Society, of which little has previously been known, in order to obtain an insight into the reasons for the transition in Cambridge mathematics in the early nineteenth century. A large part of the content of the thesis is based on research in extensive manuscript sources, especially various Charles Babbage and John Herschel collections. Two chapters in the thesis are devoted to the background to the Analytical Society. The curriculum of the University of Cambridge and the prominent position of mathematics there are examined. And the widespread lament about the decline of the mathematical sciences in England (1790-1815) is discussed and shown to have two connected features: a debate over analytical and synthetical mathematics, and a new view, for England, about the relationship" of mathematics and society. The lament along with, the Cambridge curriculum helped to provoke both the founding of the Analytical Society and the later changes in Cambridge mathematics. The Analytical Society is dealt with in a long chapter. It was a short-lived association of a small but remarkable group of students at Cambridge University. The Society was a manifestation of a larger movement towards Continental analytical methods in British mathematics. The Analytical Society did not attempt to reform Cambridge mathematical studies as is often assumed. However, the Society is an important illustration of the ways in which various features of Continental mathematics were being imported into England. Two other chapters are given over to an examination of the influence (mostly indirect) of the Analytical Society. It promoted and encouraged the mathematical work and vision of some of its members, in particular, the mathematical concerns of Charles Babbage, John Herschel and Edward Bromhead from 1814 to 1822. Also, several of its former members initiated an informal movement that led to a reform of Cambridge mathematical studies (1813-1820s). This transition to analytics took place through the structure of the studies of Cambridge. Thus not only did some members, of the Analytical Society do creative mathematics after the Society's dissolution, but many former members were also involved in changing Cambridge mathematics. All of these activities including the formation of the Analytical Society were expressions of the members' image of mathematics. The main theme of the thesis is the importance, for understanding early nineteenth-century Cambridge mathematics, of an intellectual and social framework which was composed of three key elements: ideas concerning the nature of mathematics (analytics versus synthetics) ideas about the purpose of a university (a liberal education), and a set of expectations concerning mathematics and science best described as professionalism. The thesis contends that the presence of this particular framework in/-early nineteenth-century England explains the activities of the Analytical Society and the revival of Cambridge mathematics. This thesis thus provides a valuable insight into the state and nature of mathematics at Cambridge in the early nineteenth century.