“Comprehending the Connection of Things”: Bernhard Riemann and Conceptual Thinking in Mathematics

Arkady Plotnitsky
Additional contact information
Arkady Plotnitsky: Purdue University, Literature, Theory, and Cultural Studies Program, Philosophy and Literature Program

Chapter Chapter 3 in Logos and Alogon, 2022, pp 99-135 from Springer

Abstract: Abstract The subject of this chapter is the conceptual nature of Bernhard Riemann’s thinking and its impact on mathematics, physics, and philosophy. Following a brief introduction in Sect. 3.1 and a general outline of the argument in Sect. 3.2, Sect. 3.3 considers Riemann’s concept of manifold [Mannigfaltigkeit], and Riemann’s understanding of space and geometry, grounded in this concept. Section 3.4 discusses the relationships between mathematics and physics in Riemann. Thus, Sect. 3.2 is more philosophical, Sect. 3.3 is more mathematical, and Sect. 3.4 is more physical. When, however, it comes to Riemann’s thinking, philosophy, mathematics, and physics are never separate from each other. Accordingly, the workings of all three in Riemann’s thought will be considered throughout this chapter.

Keywords: Concept; Continuity; Discreteness; Foundations of geometry; Hypothesis; Manifold; Reality; Space (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-13678-8_3

Ordering information: This item can be ordered from
http://www.springer.com/9783031136788

DOI: 10.1007/978-3-031-13678-8_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().