Introduction

Abstract

Today the definition of geometry as the science of space is generally accepted by both epistemologists and mathematicians. The history of modern geometry is entirely built around the mathematical notion of space, and different approaches to this science, from Gauss ’ studies of intrinsic curvature to the Erlangen Program, from the discovery of General Relativity to the most recent developments in topology (take, for instance, Thurston ’s geometrization conjecture and its proof) rely on a general understanding of mathematical space that remains constant through different perspectives and offers a common ground for regarding all these developments as parts of a single enterprise. Modern geometry is simply inconceivable without the notion of space.