Geometria: la visione matematica dello spazio

(Geometry: The Mathematical Vision of Space)

Abstract

What does the word “space” mean for a mathematician? What did it mean in the past? This essay takes a brief historical tour and describes some important steps in the evolution of geometry, from Euclid to Gauss and up to the breakthrough of non-Euclidean geometry. Then it explains the fundamental ideas that underlie modern geometry using the privileged viewpoint of Bernhard Riemann, one of the most brilliant mathematical minds ever. Finally, it makes some reference to the challenges that contemporary geometry is facing.