Mathematics of the 19th Century: Mathematical Logic Algebra Number Theory Probability Theory

This multi-authored effort, Mathematics of the nineteenth century (to be followed by Mathematics of the twentieth century), is a sequel to the History of mathematics from antiquity to the early nineteenth century, published in three 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 well. 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.