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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 from antiquity to the early
nineteenth century, published in three volumes from 1970 to 1972. 1
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. 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. Through an 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."
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