What Is Geometry?

Jost-Hinrich Eschenburg
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Jost-Hinrich Eschenburg: Universität Augsburg, Institut für Mathematik

Chapter 1 in Geometry - Intuition and Concepts, 2022, pp 1-5 from Springer

Abstract: Abstract This introductory chapter has rather a philosophical, or more precisely a metamathematical character: It does not do mathematics, but talks about mathematics. We try to work out what “geometry” actually is, given the many “geometries” that will be talked about in our book, how we gain geometric knowledge and what its scope of application is. It is also about the second part of our title, Intuition and Concepts. Where do they each have their place and what is their relation to each other? In particular, we will talk about the importance of axiomatics, which has been the starting point of all mathematical reasoning since the beginning of the twentieth century, and we will give reasons why we no longer see any need for a separate axiomatic foundation for geometry today.

Date: 2022
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DOI: 10.1007/978-3-658-38640-5_1

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