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Part of the book series: Classic Texts in the Sciences ((CTS))

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Abstract

Riemannian geometry today is a central and essential part of mathematics, with many connections to other fields. This is uncontroversial. The philosophical debates and controversies are largely decided. Although modern physics is still struggling with the fundamental problem of the unification of all forces, specifically on one hand the electromagnetic, weak and strong interactions, which are already unified in the so-called Standard Model, and gravity on the other hand, it is also undisputed that Riemannian geometry provides an essential formalism for this purpose.

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Notes

  1. 1.

    See, for example, the collection Raumtheorie, ed. Hans Freudenthal, Darmstadt, Wiss. Buchges., 1978, which, however, leads into research directions that are somewhat off the main courses of modern geometry, or the more mainstream treatment in Joseph A. Wolf, Spaces of constant curvature, New York, McGraw-Hill, 1967.

  2. 2.

    See p. 142 above.

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Jost, J. (2016). Modern Research. In: Jost, J. (eds) On the Hypotheses Which Lie at the Bases of Geometry. Classic Texts in the Sciences. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-26042-6_6

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