The geometry of manifolds and the perception of space

2016/05/02 by Raymond O. Wells, Wells, Raymond O.
Physics and Astronomy · #FOS: Mathematics #History and Overview (math.HO) #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.1605.00890

openalex publication_date 2016/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This notion of manifold and the geometric ideas which could be formulated and utilized in such a setting (measuring a distance between points, curvature and other geometric concepts) was an essential ingredient in Einstein's gravitational theory of space-time from 1916 and has played important roles in numerous other theories of nature ever since.

Related

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• The problem of space in the light of relativity: the views of H. Weyl and E. Cartan
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• Geometry and Astronomy: Pre-Einstein Speculations of Non-Euclidean Space
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