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

In: Logos and Alogon

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  • Arkady Plotnitsky

    (Purdue University, Literature, Theory, and Cultural Studies Program, Philosophy and Literature Program)

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.

Suggested Citation

  • Arkady Plotnitsky, 2022. "“Comprehending the Connection of Things”: Bernhard Riemann and Conceptual Thinking in Mathematics," Springer Books, in: Logos and Alogon, chapter 0, pages 99-135, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-13678-8_3
    DOI: 10.1007/978-3-031-13678-8_3
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