For many, many years a lot of mathematicians struggled to prove the Fifth Postulate of Euclid ("through a point outside of a line there exists a parallel to that line"). It was only in 1831 that Bolyai and Lobacevski realized (independently) that this statement cannot be proved based on the remaining axioms and that a geometry based on a negation of this postulate is equally possible. What they started to build was continued by many mathematicians, lead to the idea that our space might be curved, and was lately used by Einstein in his Relativity theory. In my talk, I shall try to explain the main moments of this story. The talk is mainly addressed to an audience with only high-school knowledge of mathematics.

Pizza will be served.

Tesselation of the hyperbolic plane (Escher)