Mathematics of the 19th Century

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This multi-authored work is a continuation of the History of Mathematics from antiquity to the early nineteenth century, which was published in three volumes from 1970 to 1972. The discussion of twentieth-century mathematics concludes in the 1930s. Our objectives mirror those stated in the preface to the earlier edition, viewing the development of mathematics not just as a refinement of concepts and techniques for understanding spatial forms and quantitative relationships, but also as a social process. Established mathematical structures can evolve autonomously, yet their development is ultimately influenced by practical activities and societal needs. We aim to explore the forces shaping mathematical progress, focusing on the interplay between mathematics and social structures, technology, natural sciences, and philosophy. Through an analysis of mathematical history, we seek to clarify the interconnections among various mathematical disciplines and assess achievements in light of the current state and future of the field. The challenges we face in this endeavor are significantly greater than those encountered in the preparation of the previous three-volume edition.