This text leads us on a journey through five revolutions in geometry, via biographical stories, from the Greek concept of parallel lines to contemporary notions of hyperspace. It reveals simple questions that have been the hidden engines of major achievements in science and technology.

This text leads us on a journey through five revolutions in geometry, via biographical stories, from the Greek concept of parallel lines to contemporary notions of hyperspace. It reveals simple questions that have been the hidden engines of major achievements in science and technology.