In this chapter we present Richard Dedekind’s conception of continuity and his various approaches to continuous domains in a historical context. In addition to his seminal work on foundations of irrational numbers (Stetigkeit und irrationale Zahlen, 1872), we also include a discussion of more mathematical texts (both published and unpublished) in which Dedekind also treats other continuous domains, such as Riemann surfaces, spaces, and multiply extended continuous domains. Dedekind’s reflections on these matters illustrate the wide range and general coherence of his thoughts. In particular, while Dedekind’s approach to mathematics can be characterized as being axiomatic, mapping-based, structuralist, and increasingly abstract, we argue that there is also a more general outlook underlying his methodology, which can be described as being, broadly understood, arithmetical.
The Evolution of Mathematics in Ancient China: From the newly discovered 數 Shu and 算數書 Suan Shu Shu Bamboo Texts to the Nine Chapters on the Art of Mathematics
