The discussion centers on the essay "The Geometry of Manifolds" by Raymond O. Wells Jr., which explores the evolution of geometric concepts in the 19th century leading to the abstract notion of manifolds introduced by Hermann Weyl in 1913. This concept is pivotal in understanding Einstein's gravitational theory of space-time formulated in 1916 and has influenced various scientific theories. The paper is accessible via arXiv, providing insights into measuring distances, curvature, and other geometric principles relevant to modern physics.
PREREQUISITESMathematicians, physicists, and students interested in advanced geometry, particularly those exploring the foundations of modern theories in physics and the mathematical underpinnings of space-time concepts.
Author: Raymond O. Wells Jr
The geometry of manifolds and the perception of space
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.
fresh_42 said:I have found this paper on the internet and think it might be interesting for some on this forum because there are frequently questions similar to the ones the paper tries to answer.
http://arxiv.org/abs/1605.00890
http://arxiv.org/pdf/1605.00890v1.pdf
jedishrfu said: