Development Of Mathematics In The 19th Century

Development of Mathematics in the 19th Century

Mr Hopkins' Men

A few years ago, in the Wren Library of Trinity College, Cambridge, I came across a remarkable but then little-known album of pencil and watercolour portraits. The artist of most (perhaps all) was Thomas Charles Wageman. Created during 1829–1852, these portraits are of pupils of the famous mat- matical tutor William Hopkins. Though I knew much about several of the subjects, the names of others were then unknown to me. I was prompted to discover more about them all, and gradually this interest evolved into the present book. The project has expanded naturally to describe the Cambridge educational milieu of the time, the work of William Hopkins, and the later achievements of his pupils and their contemporaries. As I have taught applied mathematics in a British university for forty years, during a time of rapid change, the struggles to implement and to resist reform in mid-nineteenth-century Cambridge struck a chord of recognition. So, too, did debates about academic standards of honours degrees. And my own experiences, as a graduate of a Scottish university who proceeded to C- bridge for postgraduate work, gave me a particular interest in those Scots and Irish students who did much the same more than a hundred years earlier. As a mathematician, I sometimes felt frustrated at having to suppress virtually all of the ? ne mathematics associated with this period: but to have included such technical material would have made this a very different book.

Mathematics of the 19th Century

This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend, first, to unravel the forces that shape mathe matical progress. We examine the interaction of mathematics with the social structure, technology, the natural sciences, and philosophy. Throughan anal ysis of mathematical history proper, we hope to delineate the relationships among the various mathematical disciplines and to evaluate mathematical achievements in the light of the current state and future prospects of the science. The difficulties confronting us considerably exceeded those encountered in preparing the three-volume edition.